Hand No. 6
Hand No. 7
Its interesting to see Polaris fold the turn with king-high in Hand No. 3 but call all the way down with queen-high in Hand No. 4. The queen-high must be helped by the ace on the flop, while the queen on the flop hurts the king-high. As expected, Polaris plays these hands entirely like bluff-catchers, only betting ace-high on the river in Hand No. 1 and betting a flush on the river in Hand No. 2. (Note that in hand No. 2 Polaris has a flush draw in addition to its ace-high.)
Weak Draws
Hand No. 1
Hand No. 2
Hand No. 3
Hand No. 4
Hand No. 5
Hand No. 6
Hand No. 7
Hand No. 8
Hand No. 9
Hand No. 10
Hand No. 11
Hand No. 12
Hand No. 13
Hand No. 14
Hand No. 4 stands out the most here as this double-gutshot with two overcards is in fact a very strong draw. I’ll examine a feature of Polaris’s postflop game in the next chapter, but for now, let’s just say that I’m surprised Polaris didn’t bet the flop with the intention of reraising.
These hands all fold the turn without improvement, but the fold in Hand No. 6 with an open-ended straight draw is unusual, and Polaris could have also semibluff-raised the turn in Hand Nos. 7 and 8. (Hand No. 8 is also a good spot to bluff-raise the river.) Polaris correctly bet the turn and river as a bluff in Hand No. 5, and it’s interesting to see it checking back a very weak draw on the flop with the intention to bluff later on.
Looking at these hands as a group, Polaris does seem to play the turn and river quite passively after checking the flop. It also does check the flop occasionally with strong made hands and strong draws, so it should have enough strength in its range to play the turn a little more aggressively — raising with the top pair plus a flush draw, and semibluffing with the draws it’s otherwise folding. However, it could well be that Polaris has good reasons for making these plays such as perhaps waiting for a safe river card to raise with its top pair.
Multiway
You should often refuse your right to bet as the preflop raiser in non-heads-up pots too. Many of the same arguments are at work, but the case for checking is frequently even stronger against more than one player.
The asymmetry of the ranges is of course a factor. The stronger your range, the less need there is to ever check. If you raise from under-the-gun six-handed and get called by the two blinds, your range could be strong enough to always bet.
It’s when the ranges are more equal that checking behind becomes a useful weapon. Heads-up, we decided to check some hands that would run into difficulty against a check-raise. Multiway, there will now be at least one more player to check-raise your bets and place you into trouble. Furthermore, there is now the possibility that your bet will get raised more than once by the time it gets back to you — extremely bad news for weak draws.
The principal reason to continuation bet the flop with many hands is to pick up the pot cheaply. In multiway pots, this requires the parlay of each opponent folding. Due to the generous pot size, they will both be getting great odds not to fold, and against strong opposition, your flop bet may be more likely to get check-raised than it is to pick up the pot.
Additionally, checking behind allows you to save bets when the turn action indicates your hand is no good. Say on the flop you check behind a weak ace-high and the turn action goes bet-call or bet-raise. In both situations, your hand is likely no good and you’ve found out without committing any more money. If you had bet the flop, a check-raise, either once or twice, would have been the likely result. Against two check-raises, you could safely fold at a cost of a small bet. But against one check-raise, you might have been tempted by the good pot odds to call and see the turn, costing you two more small bets than checking (assuming you fold to a bet on a later street).
My recommended hands for checking behind multiway are similar to the hands I check heads-up: a combination of weak showdownable hands and weak draws. With the showdownable hands, my strategy is to often call down against one opponent, but safely fold against two. With the weak draws, I can freely see the turn compared to either paying multiple bets or being forced to fold on the flop.
In this chapter, I will attempt to cover some points of play that appear in the “middle” of a hand, not at the beginning or the end, and in many ways, the middle part of a hand is the most difficult.
Out of all the rounds, the opening round contains the smallest possible universe of situations and is also the round we play most often. My recommended approach to the first two cards cuts the complexity further: By neglecting certain strategic options, we can make the game easier for us to play while making it tougher for opponents to read us.
The end round is also relatively simple. It’s the only part of the hand where we don’t have to play with one eye toward what could happen later on. Looking at a model of the last betting round can help us play earlier streets too: it can show us which hands to bet (and in approximately what proportion between bluffs and value bets), and also the range of hands that should check. When playing the middle streets, you should mentally picture your range as a line (like in the U[0,1] model), then subdivide that line into action regions and place your current hand in the correct region.
With all of these lessons learned from the other streets, playing the middle game should become much easier. So let’s move on to some important middle game concepts.
Bluffing
On the river, you should bluff with your worst hands (if nobody has bet) or with the best of your worst hands (if there has been a bet). In the former case, you bluff with the worst hands since these hands have the lowest chance of winning when both players check to see a showdown. In the latter case, since there has already been a bet, you will have to fold some hands. Therefore, fold your worst holdings and bluff raise with the hands that are just barely too weak to call.
For the player last to act, the same logic of bluffing holds on the earlier streets. If nobody has bet, he should bluff his worst hands since they gain the most from forcing a fold and have the lowest chance of improvement with a free card. If somebody has bet, he should fold his worst hands and bluff-raise with the best hands that are too weak to call.
On the earlier streets, it’s more complicated when first to act. When nobody has bet the probability of you carrying certain hands to the next round should depend on your opponent’s tendencies.
Suppose your opponent will always check if you do. Therefore, checking will guarantee seeing the next card. In this case, bluff with your worst hands and check with the slightly better ones (since they gain more from the free card than the worst hands).
But what if your opponent will always bet? Now if you check a weak hand, it will be necessary to fold; your only chance of seeing the next card with these hands is if you bet and get called. In this case, check and fold your worst hands and bet the slightly better bad hands as a semibluff (since they have a better chance of improving on the next card).
If you are playing in an exploitive way, then your choice of bluffing hands out of position would depend on your opponent: how often does he check relative to betting? Against someone who usually bets, it’s best to bluff hands with a couple of outs as opposed to those with no outs.
Unexploitable (GTO) ways of playing, it seems, are more complicated here. Which hands to bluff depends on my opponent’s optimal betting strategy after a check, but this in turn depends on my checking strategy, which depends on numerous factors: the board, the size of the pot, the asymmetry of the hand ranges, etc …
Planning Ahead
I often see players making routine continuation bets on the turn without planning ahead. These spots occur much more frequently on the turn than the river since on the river there is less betting for protection and less raising, and there are much better pot odds on the flop. A player might raise preflop, bet the flop, and automatically bet the turn with a fair hand, then get raised and suddenly be face a tough decision. Here’s an example:
Game: $2-$4 limit hold ’em — 5 players with blinds of $1 and $2.
Preflop: Hero is the small blind with the A♣9♣.
Action: The first player folds. The cutoff raises and the button folds. Hero 3-bets, the big blind folds, and the cutoff calls. There is now $14 in the pot.
Flop: 5♦4♦3♠
Action: Hero bets and the cutoff calls. There is now $18 in the pot.
Turn: Q♥
Action: Hero bets. The cutoff raises.
Hero was strongly inclined to fold even thought he had ace-high and probably seven outs or more. The trouble with bet-folding a hand with this much strength is that it unbalances your range and makes bluff-raising the turn incredibly attractive to your opponent (since so many of your hands are bet-folding). Free showdown raising the turn — raising the turn and checking the river — is a highly used play at the lower limits, and bet-folding a hand like this makes the play profitable for your opponent.
If bet-fold here is preferred to bet-call, then I would instead recommend checking this hand and often calling all the way to showdown. Note that there is little reason to bet this hand: better hands probably won’t fold — it isn’t a bluff — and worse hands probably won’t call — it isn’t a value bet. Since this is limit hold’em, we can’t bet enough to force any but the weakest draws to fold, and even though continuation betting is a routine play, in this situation it doesn’t accomplish anything, so why not check?
When checking, it’s important to do so with a wide range of hands. (See “Balancing Your Checking Range” starting on page 100 in the “End Play” chapter.). Some hands should check-fold, more hands should check-call (due to the pot size), and others should check-raise. Of course, the question of whether to check or to always bet depends on the asymmetry of the ranges, and when your average hand is much stronger than your opponent’s you can get away with always betting. But this will typically not be the case heads-up; and the hands below show how Polaris balanced its out of position turn checking in the July 2008 match against Matt “Hoss_TBF” Hawrilenko:
Check-Call
Hand No. 1
Preflop: Polaris is the big blind with the Q♣9♣.
Action: Matt raises. Polaris 3-bets and Matt calls.
Flop: J♣6♣5♠
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 5♦
Action: Polaris checks. Matt bets and Polaris calls. There is now 6 big bets in the pot.
River: 6♥
Action: Polaris checks. Matt bets and Polaris calls.
Final Pot: 8 big bets. Polaris shows the Q♣ 9♣ (two pair, sixes and fives — queen kicker). Matt shows the A♦T♥ (two pair, sixes and fives — ace kicker). And Matt wins the 8 big bets.
Many people would bet the turn with the queen-high flush draw. However, not many better hands (or hands that will draw out) will fold to a bet, making it a poor bluff, and Polaris decides it has enough high card value to call down on a two pair board.
Check-calling the turn with some showdownable draws is a good balancing play: First, it allows you to credibly hit flush- and straight-draw rivers after calling the turn. Second, betting these hands isn’t an efficient bluff (since few better hands will fold).
Hand No. 2
Preflop: Polaris is the big blind with the A♣ T♦.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6
small bets in the pot.
Flop: 8♣7♠4♣
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 8♦
Action: Polaris checks. Matt bets and Polaris calls. There is now 6 big bets in the pot.
River: 7♣
Action: Polaris checks. Matt bets and Polaris calls.
Final Pot: 8 big bets. Polaris shows the A♣T♦ (two pair, eights and sevens — ace kicker). Matt shows the T♥4♥ (two pair, eights and sevens — ten kicker). And Polaris wins the 8 big bets.
This is a standard bluff-catcher.
Hand No. 3
Preflop: Polaris is the big blind with the Q♥J♠.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6
small bets in the pot.
Flop: A♠T♦7♥
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 8♦
Action: Polaris checks. Matt bets and Polaris calls. There is now 6 big bets in the pot.
River: T♣
Action: Polaris checks. Matt bets and Polaris folds.
This hand is similar to Hand No. 1, and check-calling on the turn with these sorts of hands prevents your range from being overly composed of low pairs and ace-highs (like in Hand No. 2). Polaris will still be betting the turn with strong draws that lack high card value.
Check-Raise
Hand No. 1
Preflop: Polaris is the big blind with the Q♥J♥.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6
small bets in the pot.
Flop: Q♠9♥7♣
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 8♥
Action: Polaris checks. Matt bets. Polaris raises and Matt calls.
There is now 8 big bets in the pot.
River: 3♥
Action: Polaris bets and Matt calls.
Final Pot: 10 big bets. Polaris shows the Q♥J♥ (flush, queen high). Matt shows the T♥8♦ (one pair, eights). And Polaris wins the 10 big bets.
The board is extremely coordinated on the turn which makes finding hands to check-raise difficult: They need to be strong, and ideally they should hold enough of the key draws so that there isn’t much danger from giving a free card. This hand fits the bill perfectly — top pair, a flush draw, and a gutshot.
Hand No. 2
Preflop: Polaris is the big blind with the K♦J♣.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6
small bets in the pot.
Flop: Q♥9♠3♦
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 5♥
Action: Polaris checks. Matt bets. Polaris raises and Matt calls.
There is now 8 big bets in the pot.
River: J♥
Action: Polaris bets and Matt calls.
Final Pot: 10 big bets. Polaris shows the K♦J♣ (one pair, jacks).
Matt shows the 9♥7♦ (one pair, nines). And Polaris wins the 10 big bets.
It’s important to check-raise some semi-bluffs for balance, and this hand has a total of ten outs that it can value bet on the river. Also notice that while unlikely, the king high may be the best hand.
Hand No. 3
Preflop: Polaris is the big blind with the J♦T♦.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6 small bets in the pot.
Flop: 8♣7♠6♠
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 9♠
Action: Polaris checks. Matt bets. Polaris raises and Matt calls.
There is now 8 big bets in the pot.
River: 2♦
Action: Polaris bets and Matt calls.
Final Pot: 10 big bets. Polaris shows the J♦T♦ straight, jack high). Matt shows the T♥5♦(straight, ten high). And Polaris wins 10 big bets.
You should frequently check the turn on a four-straight board like this. Therefore, it’s important to balance these checks with the right amount of check-raises.
Check-Fold
Hand No. 1
Preflop: Polaris is the big blind with the K♥7♥.
Middle Game Concepts 161
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6 small bets in the pot.
Flop: Q♣T♦4♦
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 2♣
Action: Polaris checks. Matt bets and Polaris folds.
King-high isn’t a bluff or a value bet on the turn, and is too weak to check-call. Therefore, check-fold is the correct strategy.
Hand No. 2
Preflop: Polaris is the big blind with the 7♦4♥.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6
small bets in the pot.
Flop: Q♠6♠2♦
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 9♠
Action: Polaris checks. Matt bets and Polaris folds.
Polaris gives up with its preflop bluff on the turn. This is an unusual hand to reraise preflop, and I have a strong suspicion that Polaris did it because one of its exploitive (i.e. non-GTO) “personalities” was in the driver’s seat in this hand. (See “Man Versus Machine” starting on page 221 for more on this.) If Matt had checked the turn, then Polaris would probably bluff on a blank river.
Hand No. 3
Preflop: Polaris is the big blind with the K♣T♦.
Action: Matt raises. Polaris 3-bets and Matt calls. There is now 6
small bets in the pot.
Flop: J♦7♥6♥
Action: Polaris bets and Matt calls. There is now 4 big bets in the pot.
Turn: 4♠
Action: Polaris checks. Matt bets and Polaris folds.
Similar to Hand No. 1. King high is too strong to bluff, but too weak to check-call. So folding is the best strategy.
When both your betting and checking ranges are balanced, it becomes difficult to exploit you (most commonly by raising the turn or by betting after a check). One potential imbalance would be to not check-fold enough: If your checks signify you are always calling or raising, your opponent can exploit this by taking free cards. Another imbalance would be to not check-raise enough: Here your opponent can exploit you by making thin value bets.
In order to check-raise with the right frequency, you should start planning for the turn after betting the flop. For instance, with a hand like the
with a flop of the
I would be planning to check-raise any turn that isn’t an ace, a seven, a six, or a deuce. Of course, you must also balance your check-raises, doing so with a mixture of value hands, strong draws, and weak draws (that can fold to a reraise).
Here is another hand that illustrates the importance of planning ahead:
Game: $30-$60 limit hold ’em — 6 players with blinds of $15 and $30.
Preflop: Hero is the cutoff with the 8♣ 8♦.
Action: The first two players fold. Hero raises, the next two players fold, and the big blind calls. There is now $135 in the pot.
Flop: Q♥J♥4♦
Action: The big blind checks. Hero bets. The big blind raises.
Many opponents will check-raise often in the big blind here, so you really need to anticipate it by planning ahead. Most players
would react to the check-raise by calling on the flop. This is fine, but what you really need to do is to be planning ahead with respect to the turn and river.
Say the turn is the A♥. Many hands are already beating you and the card improves a number of other hands in your opponent’s range, so folding is fine. But instead, say the turn is the 3♣, now what? If your answer is still to fold, then why did you bet the flop? Betting the flop and then folding on a blank turn means that you’ve turned your pair of eights into a bluff, but unfortunately it’s a bluff that won’t get any better hands to fold (although it will get hands with one overcard to fold).
The gist of this is that your flop action should be contingent on how you are intending to play the later streets. If you are happy to call down on safe cards, then by all means bet the flop. But if you are intending on folding at some stage no matter what, then betting the flop turns your hand into a bluff, in which case checking can make a lot more sense.
Checking to the Raiser
Checking to the previous aggressor is such a common move that betting into the player with the initiative is known as “donk betting” — the implication being that only a bad player would make these bets. But whether they are bad or not depends on the in position player’s strategy. If the second player always bets, either incorrectly or as a part of an optimal strategy, then the first player should always check.71 72
Many preflop raisers will always bet the flop, in which case checking and then raising is almost always the best, and simplest, way to play. If your opponent always bets a street, then this should impact your strategy for the previous street. For instance, if a player always bets the flop, then your best strategy preflop is to call-or-fold; delaying until the flop or later to show aggression.
More rarely, this concept can also apply to later streets. If your opponent will almost always bet the turn, then you are better off waiting until then to check-raise. If your opponent is playing optimally, then this should only occur if his range is much stronger than yours — he doesn’t hold enough bluffs relative to value bets on the turn. But in either case, if your opponent always bets the turn, waiting until that round to raise your value hands gives your weaker calling hands more protection (by hiding information for another street). It’s relatively rare that your opponent will have a range strong enough to correctly always bet the turn. Most commonly, these automatic bets will occur if you called the flop multiway (refusing to raise to knock a third player out of the pot indicates your hand is likely weak), or if your opponent is so bad that he always bets when checked to. Here’s an example:
Game: $25-$50 limit hold ’em — 5 players with blinds of $12.50
and $25.
Preflop: Hero is the small blind with the T♥6♥.
Action: The under-the-gun player calls, the next two players fold, Hero calls, and the blig blind checks. There is now $75 in the pot.
Flop: A♣T♦6♣
Action: Hero checks. The big blind bets, the under-the-gun player folds, and Hero calls. There is now $125 in the pot.
Hero’s flop check-call is an a weak looking play, so it’s likely that the big blind will continuation bet the turn. This play would have been even better if the big blind had raised preflop (giving him an even stronger range).
Hero certainly should have check-raised this flop if the under-the-gun player bet or if that player had called the big blind’s bet. It’s also important to check some strong hands in this spot, making it harder for the other players to steal the pot on the flop.
Turn: 8♠
Action: Hero checks. The big blind bets. Hero raises and the big blind calls. There is now $325 in the pot.
River: 9♣
Action: Hero bets and the big blind calls.
Final Pot: $425. Hero shows the T♥6♥ (two pair, tens and sixes). The big blind shows the A♠4♠(one pair, aces). And Hero wins the $525.
Returning to our topic, in heads-up situations where the second player, who was the preflop aggressor, sometimes checks the flop, betting out on the flop can be a viable strategy. This will most likely happen in a heads-up match or when the raiser has opened from late position in a ring game. For this reason, betting the flop is a strategy many poker robots, such as Polaris, occasionally use. However, this isn’t an option included in my strategy, and since most humans continuation bet the flop more than is optimal, I prefer the simplicity of always checking. It’s my opinion that you won’t lose much by always checking to the raiser heads-up on the flop as this is what most poker robots do the great majority of the time.
If my opponent bets into me on the flop, then my strategy in-position is to usually call-or-fold and then raise the turn with my best hands. However, against very aggressive players who will read my flop raise as a free card play, it may be best to raise the flop expecting them to 3-bet, lead the turn, and then to raise the turn with my best hands.
Here are the hands Polaris bet out on the flop after calling a preflop raise in the match against Matt Hawrilenko:
Hand No. 1
Hand No. 2
Hand No. 3
Hand No. 4
Hand No. 5
Hand No. 6
As you can see, there were only six occasions, a very small number, where Polaris decided to bet out on the flop, so clearly you are not losing much of a theoretical edge by never utilizing this option. However, the hands that Polaris did bet are very interesting. Except for the first hand, these are all very low flops two ten-high flops and most of them containing at least two wheel (A-to-5) cards. This must be because these flops hit the big blind’s hand range relatively hard since the big blind is playing more than 90 percent of the starting hands. Therefore, it will be dealt a lot of holdings that connect with these flops (especially since the big blind’s calling range is weighted towards low cards). If the button player is aware of this and is playing optimally, then he will want to check these flops more often than any other kind which means that the best way for the big blind to harvest its equity would be to sometimes bet.
Polaris bet the flop with middle pair three times (Hands Nos. 3, 4, and 6), a gutshot twice (Hands Nos. 1 and 2), and overcards with a backdoor flush draw in the other hand (Hand No. 5). This displays a good balanced between value bets and semibluffs. Importantly, Polaris will not want to unduly weaken its checking range on these flops, so it probably will often check-raise top pair and often check-call bottom pair (but playing some of these the opposite way for balance, and perhaps sometimes betting these hands as well).
In addition, Polaris used a similar unusual play in two other hands: 3-betting in the big blind and then checking the flop. The logic for this rare play seems similar:
Hand No. 1
Hand No. 2
These are both very low flops and they will improve the button’s wider range of hands more often than the big blinds 3-bet range (although the big blind does sometimes 3-bet with hands such as small suited connectors for balance, and holds some strong premium hands). Therefore, it makes sense for the big blind to check some hands on these flops to get a better balance between value bets and bluffs with its betting range. It remains to be seen what other hands Polaris would check on flops like these for balance — we need a larger sample. But this play is exceedingly rare, and so you shouldn’t lose much theoretical edge by always betting the flop after reraising preflop.
Due to the larger bet size on the turn and river, betting into the raiser is more common on these streets as it’s more likely that the in-position player will now check. Highly coordinated boards are good candidates to bet on because strong starting hands retain their value less well on them.
An example would be a three-way pot where the player in position has a marked overpair and there is a low four-straight on board. That’s because the overpair is relatively weak on this kind of board, and so betting with the straight has merit.
I will also bet out heads-up on the turn if the flop is a three-straight or a three-flush. In this case, mediocre made hands, such as middle pair, benefit from seeing a safe card come off on the turn which improves their equity against draws.
Finally, when using a betting out strategy, you have to be aware of how this will impact your checking hands. That is, it’s important to retain enough value with your checks so that your decision of whether to bet or check does not reveal too much information.
Here are the four occasions where Polaris bet into the raiser on one of the big betting rounds in the match:
Hand No. 1
Preflop: Polaris is the big blind with the 8♠4♥.
Action: Matt raises and Polaris calls. There is now 4 small bets in the pot.
Flop: 8♣6♣2♥
Action: Polaris checks. Matt bets. Polaris raises. Matt 3-bets and Polaris calls. There is now 5 big bets in the pot.
Turn: 2♦
Action: Polaris bets and Matt calls. There is now 7 big bets in the pot.
This is an interesting hand. As you will see later, neither of these players frequently reraises the flop when in position. (Matt is in the small blind and reraised the flop.)
Polaris often raises the flop in position with a combination of weak draws (like gutshots) and strong draws (such as straight and flush draw combinations). Polaris is mainly a GTO robot, and due to the symmetry of poker, whichever play it makes in a certain position is its estimation of a best-response strategy, and is what it assumes its opponent would make in the same situation.
Notice that this turn card is good for Polaris’s pair and bad for all drawing hands. Given that Polaris thinks Matt’s range will contain a lot of draws, the 2♦ vaults Polaris’s hand into the lead and makes betting out the best play (to prevent Matt checking behind and getting a free card).
River: A♦
Action: Polaris bets and Matt calls.
Final Pot: 9 big bets. Polaris shows the 8♠4♥ (two pair, eights and deuces). Matt shows the T♦8♦ (two pair, eights and deuces). And the pot is split.
Hand No. 2
Preflop: Polaris is the big blind with the T♦5♠.
Action: Matt raises and Polaris calls. There is now 4 small bets in the pot.
Flop: T♥8♣7♠
Action: Polaris checks. Matt bets and Polaris calls. There is now 3 big bets in the pot.
Turn: K♥
Action: Polaris checks. Matt bets and Polaris calls. There is now 5 big bets in the pot.
River: K♠
Action: Polaris bets, Matt raises and Polaris calls.
This river card weakens Matt’s range making it less likely he holds a king. Polaris is fairly unlikely to hold a king (since it didn’t check-raise the turn), and so the best way for it to harvest its equity is to bet the river.73
Final Pot: 9 big bets. Polaris shows the T♦5♠ (two pair, kings and tens). Matt shows the J♣J♠ (two pair, kings and jacks). And Matt wins the 9 big bets.
Hand No. 3
Preflop: Polaris is the big blind with the T♥2♥.
Action: Matt raises and Polaris calls. There is now 4 small bets in the pot.
Flop: T♠9♦8♣
Action: Polaris checks. Matt bets and Polaris calls. There is now 3 big bets in the pot.
Turn: 4♦
Action: Polaris checks. Matt bets and Polaris calls. There is now 5 big bets in the pot.
River: 2♠
Action: Polaris bets. Matt raises and Polaris calls.
Polaris makes two unusual plays on the flop and turn; most players who check-call the flop would check-raise the turn on a blank card like the 4♦, and they won’t make these sorts of balancing plays. But I can see the reasoning in preventing people from exploiting your check-calls (it also might be that this hand was played by one of Polaris’s exploitive personalities).
The river is a blank that also improves Polaris’s hand. Presumably, Polaris believes it can’t extract a lot of value on this card by check-raising (because Matt would check behind too often) and bets out instead.
Final Pot: 9 big bets. Polaris shows the T♥2♥ (two pair, tens and deuces). Matt shows the 9♠8♥ (two pair, nines and eights). And Polaris wins the 9 big bets.
Hand No. 4
Preflop: Polaris is the big blind with the 8 ♣2♥.
Action: Matt raises and Polaris calls.74 There is now 4 small bets in the pot.
Flop: J♠9♣8♠
Action: Polaris checks. Matt bets and Polaris calls. There is now 3 big bets in the pot.
Turn: 9♥
Action: Polaris checks. Matt bets and Polaris calls. There is now 5 big bets in the pot.
River: 8♥
Action: Polaris bets. Matt raises and Polaris calls.
Final Pot: 9.0 big bets. Polaris shows the 8♣2♥ (full house, eights full of nines). Matt shows the T♥6♣ (two pair, nines and eights). And Polaris wins the 9 big bets.
This river card significantly alters the hand rankings, propelling Polaris’s hand upwards. Since the 8♥weakens Matt’s range, it’s unlikely Polaris can get much value from check-raising, so the best way to extract value is by betting out (unless it’s more profitable to induce a bluff). Notice Matt’s river bluff-raise.
These four hands are all similar. The board cards make the button’s range relatively weak compared to the big blind’s (despite the button having been betting which would ordinarily make the button’s range stronger). This particular range asymmetry makes it difficult for the big blind to extract value by check-raising (which is the best way to get value out of an in-position player with a strong range), and so Polaris resorts to betting out. Four straight and four flush boards would also fit the profile as being good boards to bet into the raiser.
Checking Back the Turn
You will check the turn in position for the same reasons as checking the flop. However, since the bet size is now doubled, you will do so with some hands that differ in absolute hand strength. Hands that had enough outs to call a flop check-raise, such as a gutshot with no extra outs, could bet the flop. But with the larger bet size on the turn, this hand would now be unable to call a check-raise, and so should often check.
The other main class of checking hands, those with some showdown value, will also differ in strength. You might have bet middle pair no-kicker on the flop (because it could call a check-raise). But with the larger bet size on the turn, it would usually be a mistake for middle pair to call a check-raise and then a river bet (partly because your opponent should have a stronger range of hands to check-raise the turn with than on the flop), so your best strategy is to almost always, as just stated, check. The principle behind checking back is the same on both the turn and the flop, but the larger bet size changes the size and location of the relevant action regions.
Information Hiding, Again
In “Checking Back the Flop” starting on page 116, it was mentioned that my strategy heads-up against a flop check-raise is usually not to reraise straight away; with my strong hands I will call the check-raise and wait for the turn to raise. This is another example of information hiding at work: playing many different hands in a consistent way.
Consider a strategy where we call with our weak made hands and draws, and immediately reraise with our strongest made hands and draws. Obviously, such a strategy would reveal a lot of information about our hand via our reaction to the check-raise, and our opponent will know when to back off and when to keep applying pressure.
The strategy of just calling the flop and waiting until the turn to raise is much better. When your opponent check-raises the flop, you will be receiving odds of at least 7-to-1, meaning that you can call the raise with some weak draws. You are also calling with all of your strong hands and have up until this point successfully concealed the strength of your hand — your calling range consists of a broad spectrum of hands ranging from the very strong to the very weak.
One result of this is that your opponent will have to bet the turn in order to find out more about your hand. But if he always follows up his flop check-raise with a turn bet, then this is great news for your strong hands which can now happily get a raise in on the larger betting round (and also raising some semi-bluffs for balance). On the other hand, if he checks some hands then this is also good: You can still value bet and bluff appropriately, while taking free cards with hands that want to get to showdown cheaply.
This strategy might seem naively simple, but it’s actually highly effective. The great pot odds on the flop allow you to call the check-raise with all but your worst hands, and by waiting until the turn to raise, your opponent should become fearful about following up with a turn bet.
Acting last is the vital key to making this strategy work. In fact, always waiting until the turn to raise out of position can be a terrible strategy. Suppose you are playing heads-up limit hold’em and decide to use a strategy of never check-raising the flop, instead, you will call a flop bet with many hands and wait until the turn to check-raise with your best hands. Once your opponent catches on, he can exploit this by polarizing his turn betting range between strong and weak hands. His best hands will welcome a turn check-raise, and his worst hands are of course betting as bluffs. But when your opponent has a mediocre hand, he can inexpensively get to showdown by betting the flop, checking the turn, and calling a river bet. (This, of course, assumes your opponent’s range isn’t so strong that he wants to always bet the turn. In heads-up limit hold ’em, it’s unlikely that either player will have a range much stronger than the other.) The reason this strategy doesn’t work out of position is that after you check it’s your opponent’s decision whether the bets will go in on that round. However, when in position, the reason why waiting until the turn works so well is that even if your opponent checks, you can still get a bet in with the stronger hands in your range — the decision is yours to make.
The importance of position is almost always mentioned in poker books,75 but I think this example illustrates it most vividly. Just varying our position from first to last to act can move a candidate strategy of usually waiting to show aggression from being very poor to very strong.
It took me a long time to appreciate the power of always waiting until the turn to raise in position. Mostly, this is because I was aware of how bad the strategy fared out of position and couldn’t appreciate how the two seemingly similar situations are like night and day.
In order to validate the strategy, I had to see it in use by some of the game’s top players.76 Matt Hawrilenko only raised the flop in position on seven occasions in his match against Polaris. Here are the hands:
The first five hands are all on extremely low flops — all are ten-high or lower. On these flops, a lot of turn cards can significantly alter the hand rankings, either by being an overcard or a low card that completes a number of draws. For this reason, a lot of the holdings that he chose to raise on the flop would not be strong enough to raise after many turn cards. (This is also true in Hand No. 6). But it’s still important to delay some raises until the turn on the low flops. For example, he waited for the turn with the flop.
on an
The sixth hand is a three-straight flop where any one of 16 cards (although two are in his hand) can create a four-straight on the turn. Additionally, four aces can also come, making this a dynamic flop. The seventh hand is rather different as an ace-king high flop.
Polaris’s strategy in these situations is also worth noting. Polaris raised the flop in position even less, only four times the whole match! This is interesting because Polaris had many opportunities to do so since Matt frequently either reraised preflop or check-raised the flop. Instead, the robot almost always played call-or-fold on the flop; forcing Matt to either continuation bet the turn or give up. Here are the four flop raising hands:
Hand No. 1
Preflop: Polaris is on the button with the Q♠T♠.
Action: Polaris raises. Matt 3-bets and Polaris calls. There is now 6 small bets in the pot.
Flop: K♠9 ♣8♥
Action: Matt bets. Polaris raises. Matt 3-bets and Polaris calls. There is now 6 big bets in the pot.
Turn: 2♠
Action: Matt bets and Polaris calls. There is now 8 big bets in the pot.
River: A♦
Action: Matt bets and Polaris folds.
Hand No. 2
Preflop: Polaris is on the button with the T♦ 8♠.
Action: Polaris calls. Matt raises and Polaris calls. There is now 4 small bets in the pot.
Flop: A♦9♥4♣
Action: Matt bets. Polaris raises and Matt calls. There is now 4 big bets in the pot.
Turn: 5♥
Action: Matt checks. Polaris bets and Matt calls. There is now 6 big bets in the pot.
River: J♦
Action: Both players check.
Final Pot: 6 big bets. Matt shows the T♥9♦ (one pair, nines).
Polaris shows the T♦8♠ (ace-jack-high). And Matt wins the 6 big bets.
Hand No. 3
Preflop: Polaris is on the button with the Q♣3♦.
Action: Polaris raises and Matt calls. There is now 4 small bets in the pot.
Flop: K♣8♣7♣
Action: Matt checks. Polaris bets. Matt raises. Polaris 3-bets and Matt calls. There is now 5 big bets in the pot.
Turn: 9♣
Action: Matt checks. Polaris bets and Matt folds.
Hand No 4
Preflop: Polaris is on the button the with Q♥T♥.
Action: Polaris raises. Matt 3-bets and Polaris calls. There is now 6 small bets in the pot.
Flop: 9♥8♦5♥
Action: Matt bets. Polaris raises and Matt calls. There is now 5
big bets in the pot.
Turn: J♠
Action: Matt checks. Polaris bets and Matt folds.
Each of these raises from Polaris is with a draw of varying strength, from the very strong two overcards plus flush draw plus gutshot straight draw in the hand above, to the rather weak gutshot straight draw in Hand No. 2. This is an interesting strategy. It appears that Polaris is raising the strong draws on the flop for value like it would a strong made hand. (For instance, the strong combination draw in the last hand is a favorite against all one pair hands on the flop.) Polaris is then also raising some weaker draws as semi-bluffs. (It would be interesting to see what other hands Polaris raises on the flop in a larger sample.) This strategy allows Polaris to extract value with its strong draws and gives it bluffing equity with the weaker ones. But it would work less well on the turn since by then the strong draws would have either improved to a made hand or have been significantly weakened by missing. The key takeaway from this spot in the match is that here are two strong heads-up limit players who have independently arrived at a strategy that almost always waits to raise in position until at least the turn. (It could well be that Polaris reraises the flop with other types of hands too, for instance, strong made hands could make good candidates for fast playing, but these hands were absent from this small sample.)
The strategy of waiting until the turn to raise in position works best of all when the ranges are narrow. Specifically, if you are contesting a pot between two early position raisers, you generally want to wait until the turn to raise since a flop raise against a strong range reveals relatively more information. When the ranges are wider, you can afford to mix things up, delaying to the turn sometimes, at other times raising on the flop. This happens most commonly when you are defending the big blind heads-up against the small blind.
Information
in Multiway Pots
Information is also important is multiway pots: both collecting it and concealing it. In general, concealing information multiway is more difficult than heads-up, and if you are able to collect and process it accurately, your potential rewards can be increased.
As I mentioned in “Rules for Preflop Limit Hold ’em” starting on page 32, it can be worth revealing information about your hand when you are exploiting a poor opponent. For example, if someone calls first-in preflop, it makes sense to reveal some information about your hand in the small blind — calling with some hands and raising with others. Similar situations also arise on the midde streets, but it can also be right to reveal information about your hand even if nobody has yet made a mistake.
Consider the following situation: the cutoff raises, you reraise on the button, the big blind calls, and the cutoff calls. On the flop, the big blind checks and the cutoff bets out. Your choice of action must now inevitably reveal a degree of information. A number of your made hands will need to raise in order to reduce the big blind’s pot odds — allowing a third player to cheaply outdraw a vulnerable made hand is simply not an option. However, you cannot play a strict raise-or-fold strategy here because by doing so you will either be raising too many hands or folding too many hands.
So in this spot, good strategy will include the use of all three of your options: raising, calling, and folding. But in general, your action should correlate with your average hand strength.
This result is a boon for the cutoff: By betting out into the preflop reraiser, he can gain a degree of information about the button’s hand at relatively little cost. If the cutoff’s bet doesn’t get raised, instead being called in either one or two places, then this provides him with a green light that he can often win the pot with a bet on the turn.
The cutoff can also gain information by check-raising the flop. Say the button bets and the big blind calls, if the cutoff now check-raises, he puts the button in a similar situation — forcing the button to reraise better hands for protection (hopefully folding the big blind out). But with his weaker hands, the button will either call or fold. In addition, notice that the big blind has also revealed information by failing to raise the button’s initial bet on the flop.
If the big blind is tight and passive, then check-raising is the best way for the cutoff to acquire useful information on the flop. Despite the extra cost of check-raising, the cutoff can first see if the big blind calls, producing a “protected pot.”77 (The presence of the caller will generally make the button’s reaction more truthful.)
If the big blind is aggressive, then the cutoff is usually better off betting into the button. If the cutoff checks, the big blind will frequently check-raise the button’s continuation bets forcing the cutoff to fold more hands. (Note that the big blind could be raising with a broad range of semi-bluffs, so the cutoff can’t fold a marginal hand “safely.” Hence he would get more truthful information by betting out himself.)
Clearly, if its easier to collect reliable information in multiway pots, then we must also go to greater lengths in attempting to conceal it. And there are two main ways to do this: slowplaying and semibluffing.
Semibluffing in multiway pots is a well known concept. By playing aggressively, you can force some of the players involved to fold. Even if some people still call, this can still be a profitable move since you can increase the likelihood that hitting secondary outs, such as overcards in addition to a gutshot, will be enough to win.78
Slowplaying in multiway pots is a less well known concept, at least in limit poker, although it’s still important. Suppose you are in a three-way pot against two expert players and elect to just call a bet from one of them when you could raise and force the other player to face two bets cold. They both know that raising would be a very attractive play for you, even with a good draw or marginal made hand since knocking out the third player would improve your equity. Therefore, they can deduce that your holding is probably a weak draw, and if they can confront you with calling two raises cold, it’s likely your hand will be discarded. So for balance, occasionally slowplay a strong hand against two or more players to give some protection to your weak draws.
Here’s a hand from another high stakes regular in the hijack position.
Game: $30-$60 limit hold ’em — 6 players with blinds of $20 and $30.
Hijack’s hand: K♥K♣
Action: The first player folds. The hijack raises. The cutoff 3-bets, the next two players fold, and the big blind calls. The hijack caps and his two opponents call. There is now $380 in the pot.
The hijack raises with the K♥ K♣ , the cutoff reraises, a poor player calls in the big blind, and the hijack caps.
Flop: T♣6♠4♦
Action: The big blind bets and the hijack calls. The cutoff raises. The big blind 3-bets and both his opponents call. There is now $650 in the pot.
The poor player bets and the hijack calls with an overpair — refusing an opportunity to raise and confront the cutoff with two bets cold. The cutoff raises, the poor player reraises, and the hijack calls.
Turn: 5♠
Action: The big blind bets. The hijack raises and both his opponents call. There is now $1,010 in the pot.
The poor player bets and the hijack now raises with the overpair.
River: T♠
Action: The big blind bets and both his opponents call.
Final Pot: $1,190. The big blind shows the 6♣6♥ (fullhouse, sixes full of tens). The hijack shows the K♥K♣ (two pair, kings and tens). The cutoff shows the J♣J♦ (two pair, jacks and tens) And the big blind wins the $1,190.
The standard way to play the kings is to raise the flop after the poor player bets. There’s nothing wrong with usually doing this. However, because the player with the kings capped preflop, his range should be polarized towards good pocket pairs and good high cards, and with the low flop, that many straight draws won’t be created. Thus when the poor player bets out, the majority of the hands the cutoff will merely call with are overcard combinations such as the
If the cutoff holds an overpair, or a hand like the
he will usually be ahead of the hijack’s calling range and should raise the flop for value. This is why occasionally calling with a strong hand is such a good move for the hijack. It will balance his play and hopefully lead to many extra bets as the two other players attempt to force him off a “weak draw.” As it happens, the hijack was unfortunate that the big blind woke up with a monster hand this time.
Opportunities to balance your strategy by slowplaying multiway will frequently occur if you use a strategy of calling out of the big blind versus a raise and a reraise as suggested in “Rules for Preflop Limit Hold ’em” starting on page 32. Often, you’ll be facing a flop bet with a third player yet to act; in this situation, it’s best to both call some hands with outs and raise other hands for protection — indicating the need to occasionally slowplay a hand for balance’s sake.
As it happened, the big blind won the hand with a full house. But don’t let this result distract you from the key lesson from this hand: the hijack’s multiway slowplay on the flop. The big blind made at least two mistakes, missing out on a turn reraise and refusing a good chance to check-raise the river.
Exploiting Imbalances
Analysis of end play shows that against good players every value bet should be balanced with a correspondingly correct ratio of bluffs. Whenever people violate this principle by failing to correlate their bluffs and value bets correctly, we have an opportunity to exploit them.
This concept often arises on paired boards: Many players will always slowplay three of a kind which tilts their flop raising (and betting) range very strongly towards bluffs.
Of course, this also applies to habitual slowplayers whenever they show aggression on an early street. Since they often delay raising their strong hands, an early raise is likely to be a weak hand. The converse situation is where a habitual fastplayer bets out on an inconspicuous river card after playing the early streets passively: He has very few value hands, so is likely on a busted draw.
Another imbalance would be a player who always bets when a card hits him out of position. Betting can be a good move in certain situations, but always doing it can completely unbalance your play (assuming some hands still check). The best exploitation of this would be value betting aggressively after a check, even when the board is dangerous.
Waiting
Until the River to Raise
Waiting until the turn to raise when in position is usually good strategy. However, if we always raised our strong hands on the turn, then if we call the turn and an irrelevant river card comes, our opponents will be able to value bet us in safety.
Therefore, it’s good to balance our turn calls with an occasional stronger hand.
On the other hand, we don’t want to do this just for the sake of “balance.” I don’t agree with the idea of losing EV on an individual hand just to make our overall strategy better. Ideally, we would find some hands that actually play better by raising the river instead of the turn.
In general, the river tends to be played more passively than the turn. Many hands that would have bet mainly to prevent giving a free card will now check, and there are no more semi-bluffs, only pure bluffs. For this reason, bets and raises on the river tend to get more credit for being a real hand than on any other street. If you raise the river, many strong hands that might have reraised on an earlier street will now just call.
A hand strong enough to comfortably put only one raise into the pot will be a hand that often does better waiting for the river. For example, take top pair. This hand is strong and wants to raise, but is not so strong that it welcomes a reraise. If it does get reraised, pot odds will usually indicate an uncomfortable call down is required. But if you wait to raise top pair on the river, then it’s less likely that a better hand, such as two small pair, will feel strong enough to reraise.
When your river raise gets reraised, the right play will depend on the specific situation. If an unimaginative player instantly reraises, many hands that were fairly strong can now be safely folded. Against a strong player, look at the range of hands you are raising on the river and ensure that you are calling with enough of them so as to not make reraise bluffing a profitable play for your opponent.
Highly coordinated boards, such as two pair, four straights, or four flushes, are good situations to delay until the river to raise. If your hand is the large full house on a two pair board, it’s unlikely you will be able to get more than one raise in for value. If that’s the case, delaying your strong hands until the river will provide your bluff-catcher hands with additional cover as your opponent will only find out the true strength of your hand at that time, plus, waiting until the river will give your opponent more opportunity to bluff his weaker hands.
Here’s an example from the Matt Hawrilenko vs. Polaris match:
Preflop: Matt is on the button with the 9♣2♣.
Action: Matt raises and Polaris calls. There is now 4 small bets in the pot.
Flop: 5♥4♣3♦
Action: Polaris checks. Matt bets. Polaris raises and Matt calls.
There is now 4 big bets in the pot.
Turn: A♠
Action: Polaris bets and Matt calls.
Matt would no doubt raise this turn unimproved. The four-straight makes the board incredibly static, only a deuce will significantly alter the hand-rankings while a six or a seven will create a higher gutshot straight. This factor makes delaying until the river even more favorable. Note that when delaying until the river, you should also delay with your bluff-raises.
River: K♣
Action: Polaris bets. Matt raises. Polaris 3-bets and Matt calls.
Final Pot: 12 big bets. Polaris shows the 9♥2♦ (straight, five high). Matt shows the 9♣2♣(straight, five high). And the pot is split.
Note how loosely Polaris is defending from the big blind.
Here’s another hand where waiting until the river results in a bet saved:
Game: $50-$100 limit hold ’em — 2 players with blinds of $25
and $50.
Preflop: Hero is on the button with the Q♥9♣.
Action: Hero raises and the big blind calls. There is now $200 in the pot.
Flop: Q♦7♦6♥
Action: The big blind checks. Hero bets. The big blind raises and Hero calls. There is now $400 in the pot.
Turn: 5♣
Action: The big blind bets and Hero calls. There is now $600 in the pot.
Top pair would be strong enough to raise this turn, but if 3-bet, Hero would have to make a crying call. The extra gutshot straight draw also reduces the danger of allowing a draw to progress cheaply. In addition, the fact that Hero holds a queen makes it less likely the big blind is check-raising the flop with top pair, tilting his range towards stronger hands (which will reraise on the turn) or draws (where you gain from inducing bluffs by calling).
River: ♥
Action: The big blind bets. Hero raises and the big blind calls.
Final Pot: $1,000. Hero shows the Q♥9♣ (a pair of queens). The big blind shows the Q♠7♠ (two pair, queens and sevens). And the big blind wins the $1,000.
As it happens, the big blind had the stronger hand which would have most likely reraised on the turn, but was too scared to do so on the river. So by waiting to the river to raise, Hero probably saved $100.
“You really shouldn’t examine a hand street by street, just as you shouldn’t evaluate a strategy hand by hand. They are both pieces of a larger picture, a whole bunch of moving parts that must move together and say very little apart, but everything in how they interact.”
— Matt Hawrilenko79
I have tried to capture the essence of the above quote in the structure of this book. Many poker books cover the parts of a hand sequentially — preflop, flop, turn, and river. Instead, I have covered decision points in a hand by order of their importance in the formation of a cohesive overall strategy. Hopefully, this has made intuitive sense to you.
Now that each part of the hand has been covered, it’s time to see how all these pieces can be put together with some sample hands. In this chapter, I will be emphasising the importance of thinking about your entire range in a situation, not just the particular hand you were dealt. Doing so can improve your results and lead to easier decisions.
One quick comment. These hands are by no means representative of what you might get in a single session. Instead, I’ve tried to include hands that highlight unusual plays or situations to illustrate certain important points.
Hand No. 1: Assessing a River Range
(The Hero in this hand posted it online for advice on his river play.)
Game: $40-$80 limit hold ’em — 6 players with blinds of $20
and $40.
Preflop: Hero is the big blind with the 8♣8♥.
Action: The first player folds. The cutoff raises, the button calls, the small blind folds, and Hero calls. There is now $260 in the pot.
A pair of eights is too low to reraise out of the big blind three-way.
Flop: T♥8♦7♥
Action: Hero checks. The cutoff bets and the button calls. Hero raises. The cutoff 3-bets and the button folds. Hero caps and the cutoff calls. There is now $620 in the pot.
Turn: Q♦
Action: Hero bets. The cutoff raises. Hero 3-bets and the cutoff calls. There is now $1,100 in the pot.
The three eights are behind only J9, 96 (very unlikely), QQ, and TT. This is an easy reraise.
River: 6♠
In his original post, Hero was torn between check-call, check-raise, bet-call, and bet-fold. Analysis of this hand proceeds much easier when you consider the implications that each actionwould have on Hero’s strategy. The cutoff could credibly be holding a nine — he raised from late position, and the flop/turn raises could be semi-bluffs with an open-ended straight draw — so I think this hand isn’t strong enough to check-raise for value.
However, a set of eights is very high up in Hero’s range: only straights (which must include a nine, Hero can’t hold five-four) and higher sets are stronger. If Hero was to check a hand this strong, it would have negative implications for his strategy: he would be value betting seldomly which means he should also bluff fewer hands and loses value against the cutoff’s worse calling hands.
With check-call and check-raise both eliminated, only bet-call and bet-fold are left. Bet-fold can be eliminated for similar reasons as check-call was: folding a hand this strong would allow the cutoff an extremely profitable exploitive response of bluff-raising.
Therefore, the only play left is bet-call, and this is what Hero should do. Yes, he loses the maximum against a straight, but this is the only play for this particular hand that leaves Hero’s strategy balanced and allows him to extract the correct amount of value against his opponent’s worse hands.
Hand No. 2: Villain’s Range Misses the Scare Card (I played this hand online.)
Game: $30-$60 limit hold ’em — 10 players with blinds of $15and $30.
Preflop: Hero is the big blind with the A♥K♦.
Action: The first five players fold. The hijack raises, the next three players fold, and Hero calls. There is now $135 in the pot.
I never reraise in this spot. (See “Rules for Preflop Limit Hold ’em” starting on page 32.)
Flop: A♣T♦5♣
Action: Hero checks. The hijack bets. Hero raises. The hijack 3-bets. Hero caps and the hijack calls. There is now $375 in the pot.
The hijack’s range is weighted towards made hands, flush draws, and occasional weaker bluffs, My hand ranks strongly against his made hands.
Turn: 3♣
Action: Hero bets and the hijack calls. There is now $495 in the pot.
The turn completes the flush draw but the hijack doesn’t raise my bet — making a flopped flush draw unlikely since most players would raise flushes for protection and value. This means he could have been holding a weak bluff on the flop which he’s now calling after picking up a backdoor flush draw, but this is a small part of his range. It’s much more likely that he has a made hand. Considering his flop reraise, this would usually be a weaker ace than mine.
River: 2♣
Action: Hero bets.
If my read on the hijack having a weaker ace is correct, then this four-flush on board doesn’t hit his range very hard. If he holds an ace, then one of his holecards cannot be a club. This leaves him with a
probability of holding a club which is low enough to make this a value bet in limit hold ’em — his play on the earlier streets is the key to this river play.
Hand No. 3: Infamous Online Hand
(This is a well known hand between two high stakes players.)
Game: $500-$1,000 limit hold ’em — 2 players with blinds of $250 and $500.
Action: TexasLimitKing raises and eastsideslim calls. There is now $2,000 in the pot.
Flop: Q♣6♥2♦
Action: eastsideslim checks. TexasLimitKing bets. eastsideslim raises and TexasLimitKing calls. There is now $4,000 in the pot.
Turn: Q♠
Action: eastsideslim bets and TexasLimitKing calls. There is now $6,000 in the pot.
River: 6♦
Action: eastsideslim bets and TexasLimitKing calls.
Final Pot: $8,000. eastsideslim shows the 3♠3♦ (two pair, queens and sixes). TexasLimitKing shows the 4♦4♣ (two pair, queens and sixes). And TexasLimitKing wins the $8,000 pot (with his four kicker).
This hand was all standard until the river play lead to an eruption of infamy. The second pair on the river counterfeited each players’ small pocket pair, and when TexasLimitKing calls on the river, the only two cards he can beat in the entire deck are one of the pair of treys combinations his opponent is holding.
So is this the greatest call in poker history? No, I would call it the luckiest misclick of all time. Some people thought that TexasLimitKing could see his opponent’s holecards, but if this was the case, he should bluff-raise instead of calling. When your opponent has bet into you on the river and your hand is very weak, you should either fold or bluff-raise. (See “End Play” starting on page 93 for more discussion.) It makes utterly no sense to call with a hand this weak, even if eastsideslim was always bluffing and never value betting.
We can model this decision as an exploitive situation with the U[0,1] model. (See “Incorporating Exploitive Poker” starting on page 114 in the “End Play” chapter.) Suppose eastsideslim is bluffing the river too often. In this case, we have two proper exploitive responses: turning marginal folds into calls, and bluff-raising more. The more your opponent bluffs, the further down your range of hands you can go. However, no matter how often your opponent is bluffing, there is absolutely no way it can ever be right for you to continue with this process of loosening your calling standards until you reach the second nut-low. Therefore, this call must be a misclick.
The fact that misclicks do occur has implications for proper river bluff-raising strategy. In the absence of any specific reads or tells, you should bluff-raise with the best hands you are unable to call with (since these hands have the best chance of beating a misclick call).
Hand No. 4: River Balance Problem
(The Hero in this hand posted it online for advice on his river play.)
Game: $5-$10 limit hold ’em — 5 players with blinds of $2 and $5.
Preflop: Hero is the small blind with the A♣9♥.
Action: The first two players fold. The button raises. Hero 3-bets and the big blind folds. The button caps and Hero calls. There is now $45 in the pot.
Flop: 9♦7♣4♦
Action: Hero checks. The button bets. Hero raises and the button calls. There is now $65 in the pot.
Turn: J♣
Action: Hero bets and the button calls. There is now $85 in the pot.
River: A♥
Hero can either try to check-raise this river or bet with the intention of 3-betting. What should he do? Three bets are obviously better than two, but you also need to consider how it hits each players’ range. The offsuit ace is a bad card for Hero’s range: flush draws have missed and flopped pairs are now relegated to at best third pair. The card hits the button’s range much, much harder since he capped preflop but elected to only call the flop and turn bets.
The relative strength of the ranges means Hero will need to be checking this river with a high frequency since few of his hands will be strong enough to bet. In order to balance these check-calls and check-folds, he will need to check-raise with a number of strong hands, and this is one of them.
Hand No. 5: Hand Reading
(I played this hand online.)
Game: $25-$50 limit hold ’em — 6 Players with blinds of $12.50 and $25.
Preflop: Hero is the hijack with the A♥A♦.
Action: The first player raises. Hero 3-bets. The cutoff 4-bets, the next three players fold, and the remaining two players call. There is now $337.50 in the pot.
The cutoff cold-caps and has preflop stats of 33/13 (VPIP/PFR). The large difference between the two numbers indicates he frequently calls on the opening round, likely either by cold-calling or calling first-in. The fact that he chose to cap instead of calling the reraise indicates he probably has a premium hand, and not a hand like king-queen suited (which a more aggressive player could cold-cap).
Flop: A♠8♦2♣
Action: The first player checks, Hero checks, and the cutoff checks.
The cutoff checks the ace-high flop, thus almost certainly removing hands such as AK and AQs (if he caps that) from his range which is now strongly tilted towards premium pocket pairs such as KK, QQ, and JJ.
Turn: T♥
Action: The first player checks, Hero checks, and the cutoff checks.
It’s likely the cutoff would bet any of these pocket pairs on the turn if the action was checked to him, making this a good spot to go for a check-raise. But what went wrong? I’m not really sure. I felt comfortable putting the cutoff on an extremely tight preflop capping range, and most players would surely bet the turn after being checked to twice. My most likely explanation is that this player’s preflop cap was a misclick; maybe he had a hand like king-jack suited that he meant to call with but pressed raise instead.
Hand No. 6: Waiting Until the River to Raise (I played this hand online.)
Game: $30-$60 limit hold ’em — 3 players with blinds of $15 and $30.
Preflop: Hero is on the button with the Q♥J♠.
Action: Hero raises and both blinds call. There is now $180 in the pot.
Flop: J♥J♣8♠
Action: The first two players check. Hero bets. The small blind raises, the big blind folds, and Hero calls. There is now $400 in the pot.
On a flop like this, I will only call or fold after being raised typically with the intention of raising my current hand on the turn. (See “Middle Game Concepts” starting on page 152.)
Turn: 8♦
Action: The small blind bets and Hero calls. There is now $520 in the pot.
The turn pairs the board again and causes me to alter my plan. The board is now completely static: There are no feasible hands that could outdraw me — large pocket pairs are not in his range and an eight only has one out to hit four of a kind.
Additionally, it will only be possible to get one raise in against worse hands since a small full house will not reraise. Therefore, these two conditions make this a great spot to wait until the river to raise, allowing my opponent more opportunity to bluff (or pair the river) and balancing my calling down hands.
River: 9♥
Action: The small blind bets. Hero raises and the small blind calls.
Final Pot: $760. The small blind shows the 8♣ 6♥ (full house, eights full of jacks). Hero shows the Q♥J♠ (full house, jacks full of eights). And Hero wins the $760 pot.
Hand No. 7: High Stakes Flop Check
(I observed this hand online.)
Game: $200-$400 limit hold ’em — 6 players with blinds of $100and $200.
Player A’s hand: A♠3♣
Player B’s hand: 5♥4♥
Action: The first two players fold. Player A raises, the next two players fold, and Player B calls from the big blind. There is now $900 in the pot.
Flop: 8♠8♣2♣
Action: Both players check.
Player A checks back the flop after raising first-in from the cutoff. I would guess his preflop range looks something like this:
Table I: Potential Cutoff
First-In Raising Range (Top 43.3%)
You can see that any of those hands that don’t contain a pocket pair, an eight, a deuce, or a club have missed the flop. If Player A always bets the flop, then a lot of these hands would be playing themselves into trouble after a check-raise. The fact that he has a wide range and the flop misses a lot of his hands make this a good situation to check a portion of his range.
I would expect Player A to check hands like king-high, queen-high, and low ace-highs (betting the best ace-highs for value). He should bet his best hands for value and his worst hands as bluffs.
If Player A was raising from a much earlier position, then he would have a tighter range and at some point he would be able to always bet this flop.
Turn: 6♠
Action: Player B bets and Player A calls. There is now $1,700 in the pot.
Player B picks up a double-gutshot and bets.
River: 2♦
Action: Player B bets and Player A calls.
Final Pot: $2,500. Player B shows the 5♥4♥ (two pair, eights and deuces — six high). Player A shows the A♠3♣ (two pair, eights and deuces — ace-high). And Player A wins the $2,500 pot.
The river pairs the board again, giving Player B two pair six-high — the worst possible hand. Player B correctly bets his hand as a bluff, and Player A calls with his ace-high (which is a strong hand on this board and is high up in the range of hands he checks the flop with).
It might seem like Player A “obviously” has a hand like ace-high and is going to call, but Player B’s bet is a vital part of a well balanced strategy on the river. That’s because he will be betting a number of hands for value, especially since his opponent’s range is fairly weak after checking the flop and calling the turn, and to balance these value bets, Player B must also bluff his worst hands (or else Player A could exploit him by folding bluff-catchers).
Hand No. 8: River Bluff-Raise
(The Hero in this hand posted it online for advice on his river play.)
Game: $20-$40 limit hold ’em — 2 players with blinds of $10 and $20.
Preflop: Hero is on the button with the 9♠4♠.
Action: Hero raises. The big blind 3-bets and Hero calls. There is now $120 in the pot.
Flop: J♥9♥5♥
Action: The big blind bets and Hero calls. There is now $160 in the pot.
Turn: K♠
Action: The big blind bets and Hero calls. There is now $240 in the pot.
This is a standard call in heads-up limit hold ’em.
River: Q♥
Action: The big blind bets. Hero raises and the big blind calls.
Final Pot: $400. The big blind shows the A♣5♣ (a pair of fives).
Hero shows the 9♠4♠ (a pair of nines). And Hero wins the $400 pot.
The river card is incredibly bad for Hero’s hand: He’s now behind any heart, ten, king, queen, or jack. Therefore, Hero can’t call, but his hand has some value, and so it makes a good candidate for an undominated river bluff-raise. (See “End Play”starting on page 93 for more discussion.)
This sort of play is much more common in no-limit where hands with even a fair amount of strength will not be enough to call a big bet. Therefore, they can be used as bluff-raises.80 However, some no-limit players incorrectly calibrate their bluff-raises when playing limit; turning hands that had enough equity to call into bluffs.
This bluff-raise is an important balancing play, but it can also be a good exploitive move. Many opponents will check a number of the hands they were value betting on a coordinated river like this, but will still bet their bluffs, leading to a too high bluffing frequency. The correct exploitive response would be to make more call downs and more bluff-raises.
In this hand, the big blind called and Hero won the showdown! This is incredibly bad play since it makes no sense to value bet a hand which is at least as bad as a pair of fives on this board and then call a raise. When your opponents are capable of making such bad plays, it’s important to bluff-raise in an undominated fashion (using your best folding hands to bluff-raise).
Hand No. 9: River Check-Raise Bluff
(I played this hand online.)
Game: $250-$500 limit hold ’em — 2 Players with blinds of $125 and $250.
Preflop: Hero is the big blind with the Q♣T♦.
Action: The small blind raises. Hero 3-bets and the small blind calls. There is now $1,500 in the pot.
Flop: J♠7♦3♦
Action: Hero bets and the small blind calls. There is now $2,000 in the pot.
Turn: 7♥
Action: Hero bets and the small blind calls. There is now $3,000 in the pot.
River: 4♣
Action: Hero checks. The small blind bets. Hero raises and the small blind folds.
I checked the river as my hand does not fall into either my bluffing region (too strong) or my value betting region (too weak).
My opponent then bet, which is quite unusual since he would probably raise either a jack or a seven by at least the turn, and the river is an innocuous card which doesn’t complete any obvious draws.
Notice that my hand is too weak to call his bet: There are many better ace-high and king-high hands in my range which can call — I would still bet a hand like ace-king for value. However, this is a great spot to go for a check-raise for both exploitive and GTO reasons. The Q♣ T♦ fits into my optimal bluff-raising region, and I have a strong suspicion that my opponent is bluffing, but my hand is too weak to call (and was too strong to bluff initially).
Hand No. 10: Bluffing on All Streets
(I played this hand online.)
Game: $50-$100 limit hold ’em — 2 players with blinds of $25 and $50.
Preflop: Hero is on the button with the 7♥6♠.
Action: Hero raises and the big blind calls. There is now $200 in the pot.
Flop: A♥J♠8♠
Action: The big blind checks. Hero bets and the big blind calls. There is now $300 in the pot.
Turn: 2♦
Action: The big blind checks. Hero bets and the big blind calls. There is now $500 in the pot.
River: 3♦
Action: The big blind checks. Hero bets.
This hand might look like suicidal bluffing, but it’s actually an important part of a balanced strategy. Working backwards through the hand, my holding is only seven-high on the river. This hand is right at the bottom of my distribution, so I should bluff. On the turn, my seven-high has only six outs to fourth pair: a very poor draw. And even though I am acting last and can guarantee seeing the next card with a check, my strategy should be to bet this hand as a bluff. (I lose little equity if check-raised and have to fold). Also, the reasons for betting the flop are similar (andsince the board is good for my range, it makes sense to bet a lot of hands on the flop).
Hand No. 11: Asymmetric River Ranges
(I played this hand online.)
Game: $30-$60 limit hold ’em — 8 players with blinds of $15 and $30.
Preflop: Hero is the big blind with the T♠T♣.
Action: The first three players fold. The hijack raises, the next three players fold, and Hero calls. There is now $135 in the pot.
Flop: A♥ J♠J♣
Action: Hero checks. The hijack bets and Hero calls. There is now $195 in the pot.
Turn: 9♥
Action: Both players check.
River: Q♦
Action: Hero bets and the hijack calls.
Final Pot: $325. The hijack shows the K♦Q♥ (two pair, queens and jacks). Hero shows the T♠T♣ (two pair, jacks and tens). And the hijack wins the $325 pot.
The hijack’s turn check removes a number of strong hands from his range — perhaps he could hold kings or queens and be playing them in a way ahead/way behind manner. The Q♦ on the river is not the best card for my hand; nevertheless, I bet. The trouble with checking this river is that it would make the hijack’s decisions far too easy. He could make easy value bets with hands like king-queen and check behind with hands like king-high. So betting the river makes his life difficult: He needs to decide how many bluff-catchers to call with. Also, the only combinations he can possibly raise with are queens and king-ten, so when making these thin value bets, you seldom lose more than by check-calling and your opponent is now put to a tough decision with a lot of his range.
Hand No. 12: Detecting an Imbalance (1)
(I played this hand online.)
Game: $100-$200 limit hold ’em — 2 Players with blinds of $50 and $100.
Preflop: Hero is the big blind with the K♣J♠.
Action: The button calls. Hero raises and the button calls. There is now $400 in the pot.
Flop: 3♠3♣2♥
Action: Hero bets. The button raises and Hero calls. There is now $800 in the pot.
The button’s raise is very unusual. Trip treys would likely wait until the turn to raise, and pocket pairs or ace-high are unlikely given his preflop call. He could hold a deuce, but given the paucity of strong hands in his range, a bluff is likely.
Turn: 3♦
Action: Hero checks. The button bets and Hero calls. There is now $1,200 in the pot.
River: 5♦
Action: Hero checks. The button bets and Hero calls.
The turn and river are kind to my hand, and it is good enough to showdown.
Final Pot: $1,600. Hero shows the K♣J♠ (three of a kind, treys
— king-high). The button shows the 9♥6♠ (three of a kind, treys
— nine-high). And Hero wins the $1,600 pot.
This hand was made a lot easier for me because my opponent did not correlate his bluff with his value hands. Strong players make your life harder as they play their bluffs and value hands in a similar way, and in the right proportion.
Hand No. 13: Draw With Showdown Value
(I played this hand online.)
Game: $50-$100 limit hold ’em — 2 players with blinds of $25 and $50.
Preflop: Hero is on the button with the A♥K♥.
Action: Hero raises and the big blind calls. There is now $200 in the pot.
Flop: Q♥2♣2♠
Action: The big blind checks. Hero bets. The big blind raises and Hero calls. There is now $400 in the pot.
On a dry board like this, I will never reraise his check-raise on the flop; My strategy is to either call or fold. Furthermore, because my range is wide, I will frequently check this flop, but ace-king is good enough to bet for value.
Turn: 5♥
Action: The big blind bets and Hero calls. There is now $600 in the pot.
I pick up a flush draw. A lot of people might semibluff-raise, but there are some good reasons to call. First, no better hand is likely to fold, while trip deuces are reraising. Second, having some flush draws in your calling range adds balance to your strategy since it allows you to represent a flush on the river after calling the turn. This makes it more difficult for your opponent to make thin river value bets and allows you to bluff-raise with more credibility. I would play some king-high flush draws the same way, but would semibluff raise with smaller flush draws.
Hand No. 14: Turn/River Compound Play
(I played this hand online.)
Game: $50-$100 limit hold ’em — 2 players with blinds of $25
and $50.
Preflop: Hero is on the button with the 5♣4♣.
Action: Hero raises. The big blind 3-bets and Hero calls. There is now $300 in the pot.
I never cap here, but suited connectors are hands that many people would use to balance their capping range.
Flop: K♦8♠7♣
Action: The big blind bets and Hero calls. There is now $400 in the pot.
I’m playing call-or-fold on this flop. That’s because it’s my strategy to often wait until the turn to raise in position. (See“Information Hiding, Again” starting on page 176 in “Middle Game Concepts” for more discussion.)
Turn: Q♦
Action: The big blind bets and Hero calls. There is now $600 in the pot.
I call the turn without sufficient outs for my draw. My reason for this play is to set up a bluff-raise on many river cards. I can raise for value on a six, and bluff-raise on an ace, queen, eight, seven, or a diamond. My hand is probably sufficiently strong to catch a bluff on a five or a four.
River: 7♦
Action: The big blind bets and Hero raises.
If the big blind checks the river, my play is to bet because my hand is right at the bottom of my range. As it happens, he bets on one of my scare cards and I bluff-raise.
Hand No. 15: Turn Free Showdown Raise
(This hand is from Nick Grudzien and Geoff Herzog - Winning In Tough Hold ’em Games, pp.181-184. The stakes were not given.) Game: Limit hold ’em — 6 players.
Preflop: Hero is the hijack with the 6♣6♥.
Action: The first player folds. Hero raises, the next three players fold, and the big blind calls. There is now 4.5 small bets in the pot.
Flop: J♦T♦2♥
Action: The big blind checks. Hero bets. The big blind raises and Hero calls. There is now 4.25 big bets in the pot.
Turn: 3♣
Action: The big blind bets. Hero raises.
Grudzien and Herzog recommend raising this turn with the intention of checking the river or folding to a reraise. The trouble is that this fails to extract the most value from your hand range compared to the alternative of calling and evaluating on the river.
As we saw previously in this book, if your opponent has bet, then your bluffing hands should come from the top end of your folding range. The free showdown raise is incorrect because it turns a hand that could call into a bluff. This is illustrated in Figure I below where in the “free showdown raising” portion of the graph, we can see that this strategy leads to too much folding and too little calling.
Figure I: Optimal
Bluff-Raising Versus Free-Showdown-Raising optimal bluff raising
For both strategies, the relative sizes of each raising range are fixed by keeping the bluffing ratio constant. (See “Appendix B: Game Theory” starting on page 383.) But when free showdown raising, the bluff-raising region comes out of the calling region, and in terms of your overall hand range, this leads to too little calling and too much folding compared to optimal bluffing.
So in the above hand, if the pair of sixes is not strong enough to call, then raising the turn with intention to check the river or fold to a 3-bet would be correct. The trouble with how the hand is played is that the 6♣6♥ in this spot is good enough to call the turn bet, and can call on many river cards as well. Therefore, in this case, bluff-raising the turn with hands worse than the sixes allows you to extract more value from your entire range.
Hand No. 16: Detecting an Imbalance (2)
(I played this hand online.)
Game: $25-$50 limit hold ’em — 5 Players with blinds of $12.50
and $25.
Preflop: Hero is on the button with the 2♦2♠.
Action: The first two players fold. Hero raises, the small blind folds, and the big blind calls. There is now $112.50 in the pot.
Flop: T♦7♠3♥
Action: The big blind checks. Hero bets and the big blind calls. There is $162.50 in the pot.
Since I raised from the button, checking behind on the flop is also worth considering. However, because my opponent is weak and passive, it’s my opinion that betting is a better exploitive play.
Turn: 8♣
Action: The big blind bets and Hero calls. There is now $262.50 in the pot.
The big blind, a poor player, bets the turn. He could be doing this with a large range of hands, either he has a hand of value or is randomly bluffing.
River: A♦
Action: The big blind bets and Hero calls.
The ace on the river is a bad card for my hand and the big blind bets again. However, it’s my opinion that my opponent will be scared enough by it to check his lower pairs. Because he’s unlikely to balance his bluffs and value bets, this tilts his range towards too many bluffs. Therefore, I call even though the river card has decreased the absolute value of my hand’s strength, because my opponent’s strategy is likely unbalanced.
Final Pot: $362.50. Hero shows the 2♦2♠ (one pair, deuces). The big blind shows the 6♣4♠ (no pair, ace-high). And Hero wins the $362.50.
Hand No. 17: Metagame Implications
(In this hand, the Hero posted it online for advice on his river play.)
Game: $10-$20 limit hold ’em — 5 Players with blinds of $5 and $10.
Preflop: Hero is the small blind with the J♥8♥.
Action: The first two players fold and Hero calls. The big blind raises. Hero 3-bets and the big blind calls. There is now $60 in the pot.
The preflop call heads-up against the big blind is fine. If I’m using a first-in calling strategy from the small blind, my strategy is to never reraise; preferring to wait until the flop to check-raise.However, when using a limp-reraising strategy, a suited hand like this is good to balance your reraises with.
Flop: A♠Q♥8♦
Action: Hero bets. The big blind raises and Hero calls.
Turn: J♣
Action: Hero checks. The big blind bets. Hero raises. The big blind 3-bets and Hero calls. There is now $220 in the pot.
River: 6♣
Action: Hero checks. The big blind bets and Hero folds.
On a stand alone basis, this fold seems reasonable. The big blind has raised both preflop and on the flop, and has 3-bet the turn. Given these levels of aggression, one pair is not a plausible hand for him to be raising for value. If he has at least two pair by the turn, then his hand must be better than Hero’s holding (since Hero has the bottom two pairs). Therefore, Hero can only beat a bluff, and it’s reasonable to assume that many players in the big blind’s shoes would be bluffing less than one time in twelve.
However, I think that Hero should call, not because I believe the odds of the big blind bluffing are necessarily sufficient, but because of the implications that these folds have on the rest of your strategy in limit poker. (In big bet poker, you will more often make value bets and then fold to a raise due to shorter pot odds.) What this means is that if you regularly press hard with strong hands and then fold to further action, this can reduce your Went to Showdown (WtSD) statistic. And when a good player sees that you showdown with a below average frequency, he’s much more likely to raise several streets on a bluff, especially if you take unusual action such as limp-reraising preflop or check-raising the turn (when many strong hands would be reraising on the flop).
So when you are facing up against the same good players on a regular basis, these are important calls to make because folding gives them the potential to make very profitable bluffs. If you were up against a player who seldom bluffs, who you will never play again, or is someone who won’t react by exploiting your strategy, then folding is fine and probably the best play. This would be known as making an “exploitable fold.” To finish, note that these conditions don’t often hold in online games at the midstakes and up, where the player pool is relatively small and the collation of statistics means that frequent folds against Player A could be noticed and exploited by Player B.
Hand No. 18: Balancing Play
(Polaris played this hand.)
Preflop: Polaris is the big blind with the 8♥5♣.
Action: Matt raises and Polaris calls. There is now 4 small bets in the pot.
Flop: 9♣6♠6♦
Action: Polaris checks. Matt bets. Polaris raises and Matt calls. There is now 4 big bets in the pot.
Turn: 9♠
Action: Polaris bets. Matt raises. Polaris 3-bets. Matt caps and Polaris folds.
A key part of GTO play is balancing every value bet with a corresponding ratio of bluffs. When a number of bets have gone into the pot, the pot size gets big relative to the size of the bet, and this reduces the optimal bluffing frequency. Also, on this board, only a large full house or four of a kind is strong enough to reraise the turn for value. (Remember, the optimal bluffing frequency is related to the number of hands you are betting for value.) This will make an expensive bluff infrequent; but it’s still something you should occasionally do.
When launching these expensive bluffs you want one of two things: blockers or a hand with some equity against another bluff. In this spot, because the ranges are so wide, not many hands can operate as blockers. For instance, if your opponent was raising from an early position in a full game, you would want to bluff with a hand like ten-eight since many people play hands like ten-nine suited and nine-eight suited. But when blockers aren’t really an option, you want a hand such as Polaris’s gutshot that has some equity versus your opponent’s bluffs. (This is a case of bluffing with an undominated hand.)
Man Machine, pseudo human being
Man Machine, super human being
— Kraftwerk
This chapter is a summary of the findings from the July 2008 heads-up limit hold ’em match between the poker robot Polaris and Matt “Hoss_TBF” Hawrilenko, plus a look at how some other poker robots play. It’s an interesting match to look at as each of them is attempting to play in an unexploitable (GTO) way. We can look at the similarities in their play, and when we see them doing something similar, we will have two independent data points that point to a good strategy.
Hawrilenko has been very successful at this form of poker. Polaris’s results are also impressive although it’s curriculum vitae is a little more complicated.
Polaris used five distinct strategies in its series of matches against the humans — one GTO strategy (Hyperborean08-Equilibrium) and four mildly exploitive strategies primed to take advantage of humans’ mistakes. The exploitive strategies were designed by either adding or removing an arbitrary amount to the pot, making Polaris either more or less aggressive. Polaris switched between strategies based on its dynamic view of which one should maximize its expectation against its opponent. The GTO strategy went undefeated in the 2008 Annual Computer Poker Competition (ACPC).81
Poker robots are becoming stronger all the time, so it’s likely that most of the GTO robots in the 2009 and 2010 ACPC are even better. For example, one of the robots submitted by the Computer Poker Research Group at the University of Alberta in 2009 had a statistically significant edge of 
over the 2008 version of Polaris. One caveat is that having an edge over another near-GTO strategy does not necessarily make your strategy closer to equilibrium; it could just be that you happen to greatly exploit whatever errors the other player makes more than that player exploits your errors.
An important element of unexploitable strategies is that of being balanced: playing many hands the same way prevents opponents from exploiting you. The easiest way to achieve balance is to exclude certain strategic options from consideration: never call first-in, never cold-call in six-max, never cap heads-up, always continuation bet the flop after reraising preflop, and always check to the raiser on the flop. Additionally, the rule of never reraising preflop is incredibly effective against opponents who always bet the flop (when you don’t reraise).
Using these rules significantly simplifies the game, and evidence from poker robots indicates that doing so comes at little theoretical cost as most poker robots do not frequently use other strategies. For instance, Polaris only caps around 16 percent of the time it has the opportunity to do so in my sample, and the capping strategy that it uses is highly nuanced. Polaris rarely calls first-in, and this strategy seems to be for the benefit of the few hands right on the border between raise-or-fold, plus sometimes calling with stronger hands for balance. On the flop, Polaris rarely bets into the raiser, and seldom checks the flop out-of-position as the preflop raiser, indicating not much is lost by ignoring these options, which are surely difficult to properly implement in a balanced strategy. The times it does use them appear to be related to how different flops improve the two players’ asymmetric ranges, providing interesting food for thought on how we could potentially include these options into our game. When Polaris does use all of these extra options, its play is incredibly well balanced across both the hands it doesn’t use the option with and the hands it does.
Some other elements of Polaris’s game are similar to Hawrilenko’s. Both players play more hands out of the big blind than on the button, and they both 3-bet a wide range of hands preflop. They raised a similar frequency of hands on the button, and as already noted, Polaris called very rarely. Also, they both used a similar strategy of almost always waiting until the turn to raise postflop when on the button. Although these two play similarly, there are probably many other GTO strategies we could use.
Here are Sonia’s preflop statistics at six-max limit hold ’em at a table with one copy of herself in each seat:82
Notice how close together Sonia’s VPIP and PFR are in all of the non-blind seats. This indicates that Sonia will rarely call first-in or cold-call, and on the few occasions that she uses these options her strategy will be highly balanced. Most of the spread is accounted for by first-in calls in early positions; she cold-calls only 0.2 percent of the time (and the 1 percent difference between VPIP and PFR in UTG must be entirely accounted for by first-in calls). This provides confirmation for the theory that frequently calling first-in is an error when it lets two or more opponents cheaply into the pot: Sonia is fond of calling a huge chunk of her range in heads-up games (as you can see in the tables below).
When Sonia is in an early position, there seems to be an opposite effect occuring: raise-or-fold forces her to be too tight, so she responds with a very few balanced limps. (Remember that when Sonia is at a table against copies of herself, the strategy she eventually converges on will be her estimate of unexploitable play.) It would be interesting to see how Sonia plays in the big blind against an early position raise. My guess is she would rarely 3-bet and would almost always wait until the flop to check-raise.
Sonia’s heads-up strategy against herself is very different than Polaris's heads-up strategy, and involves a lot of calling on the button (as indicated by the spread between VPIP and PFR in the SB):
One advantage of using this near-GTO strategy is its unusualness. Calling 27 percent of the hands on the button is not a strategy any winning human would consider, and so you could get a lot of action from other (worse playing) professionals. The strategy that Sonia uses to exploit Polaris is fairly different, although these shifts are worth only a tiny amount of EV 
Sonia’s VPIP in the big blind against herself is very different from the same statistic against Polaris because Polaris raises a lot more on the button than Sonia does. Sonia limping also decreases Polaris’s VPIP in the big blind. Polaris probably continuation bets the flop around 90 percent of the time in position, and it’s interesting that Sonia exploits this by vastly decreasing her preflop raise statistic in the big blind. (Part of the difference is that Polaris almost always raises on the button, whereas Sonia often calls from this position.)
Polaris’s VPIP in the small blind here is slightly lower than in the match against Hawrilenko, showing that the exploitive versions of Polaris respond to typical humans’ mistakes by playing slightly looser and by calling more often than the GTO version on the button. (GTO Polaris only limps 0.5 percent of the time, much closer to raise-or-fold, whereas Polaris limped 2.4 percent in my sample.) I agree that the average human is too tight in the big blind compared to being too loose, and Sonia exploits a number of humans by calling many hands on the button. (But it’s my opinion that calling on the button is a difficult exploitation for humans to use, so it’s not something I would recommend except against all but the worst opponents.) Marv Anderson’s poker robots give us another interesting data point that provide confirmatory evidence for the strength of the raise-or-fold and never-cap rules on the button.83 Anderson’s robots have performed well in the 2009 and 2010 ACPC, they raise-or-fold on the button, never cap, and their preflop hand selection closely approximates the guidelines set out in this book and used by other top players:
Table I: Anderson’s Robot
Opening Range from the Button (82.2%)*
Table II: Anderson’s Robot
Folding Hands in the Big Blind (8.1%)*
Table III: Anderson’s Robot
Reraising Hands in the Big Blind (29.6%)*
Table IV: Anderson’s Robot Checking
Hands in the Big Blind After Call (33.5%)*
Table V: Anderson’s Robot Raise-Call
Hands in the Big Blind After Call (59.1%)*
Table VI: Anderson’s Robot Raise-Cap
Hands in the Big Blind After Call (7.4%)*
The robot raises 82.2 percent of the time on the button (Table I) exactly the same as the 2008 GTO version of Polaris. It folds only 8.1 percent of the time in the big blind (Table II): a number similar to Polaris (which calls nine-deuce offsuit in the 2008 GTO version). It reraises 29.6 percent of the time out of the big blind (Table III): a high number similar to Polaris, raising predominately with suited hands and pocket pairs. It also attacks first-in calls incredibly aggressively, raising with 66.5 percent of the hands (59.1 percent of the hands raise-call (Table IV) and 7.4 percent of the hands raise-cap [Table VI]), implying that the robot believes that mostly below-average hands should be calling on the button. Anderson’s reraising strategy is similar to Polaris’s (Table VII),84 the main difference being that Polaris utilizes a mixed strategy with some offsuit hands, whereas the Anderson robot (Table III), uses almost all pure strategies — a few hands are mixed but they are shown as pure in the table.
Table VII: Polaris’s
Reraising Strategy in the Big Blind
Notice that (almost) only reraising with suited hands and pairs is a sophisticated strategy since it allows you to balance your starting hands in both your calling and reraising ranges without resorting to mixed strategies on individual hands. For example, this strategy allows the robot to represent the specific hand jack-ten in both its calling and reraising range which could be important on certain board textures. The Anderson robot is a great demonstration of how to hide information without using mixed strategies on any individual hands in both the small blind because it never calls and never caps, and the big blind. Since I advocate these types of strategies for humans, it’s encouraging to see my views replicated by a computer.
As computer processing power and optimization algorithms become ever better, poker robots will become an increasingly important avenue for poker theorists both as a check on existing theories and as a way of further improving our play. The small sample of Polaris’s play that I have analyzed in this book has thrown up a number of interesting facts; looking at larger samples from the best robots of today should throw up further discoveries.
As an example of all of this, here is a spot where we could implement Polaris’s strategy of betting out on certain flops. Say the cutoff raises first-in, the next two players fold, we use a call-or-fold strategy in the big blind and call, and the flop comes the
This flop hits our hand range relatively hard even though the cutoff has the stronger preflop range. However, if we always check to the raiser on this flop, then a lot of control of the hand is given to the cutoff who can then check a number of hands and correlate the size of the pot with the strength of his hand. But, we can pre-empt this by betting out a balanced range on the flop, say hands like 33, x2, and a range of bluffs with backdoor draws and pair outs. This strategy would give the cutoff some incredibly hard decisions with hands like the
that haven’t improved.
There are also a huge number of situations like this where we could use more of our strategic options to improve our overall strategy. On other flops, such as the
our play would be the normal strategy of always checking to the raiser since this board hits his range so hard that it’s in his interest to always bet. But betting on the flop has the advantage in that it allows the big blind to see the type of flop before committing further action (unlike reraising preflop), and it prevents the preflop raiser from having the luxury of always checking behind when it suits him to do so.
No-limit hold ’em is the most popular form of poker today. Even though we have mainly been discussing its cousin, limit hold ’em, many of the same ideas apply. This is the benefit of taking a theoretical approach to poker strategy.
We have already briefly considered some elements of preflop no-limit hold ’em in “Analyzing the Opening Round in Other Forms of Poker” starting on page 79. When your stack size is very small, correct strategy can be approximated by restricting your play to either moving all-in or folding. But play becomes more complex as your stack size grows: implied odds lengthen and the cost of reraising with many hands increases since it allows opponents to make a big reraise that you cannot call. Both of these factors make it correct to cold-call many raises in deep stack no-limit, whereas in limit, you should either raise or fold especially when the pot has been raised and you have players left to act.
“End Play” starting on page 93 showed a neat way of approaching the river in limit hold ’em, and the same method can be used for no-limit. First, you visualise your hand range as a continuous line, with the strongest hand you can hold at one end and the weakest at the other. Then, split your range into sections: usually betting and raising with your best hands, calling with intermediate hands, and folding or bluffing your worst hands. Finally, decide which section your current hand belongs to, and take the required action.
The ordering of each action region is the same in no-limit —raise your best hands for value and call with intermediate hands with the only difference being the relative size of each region. In limit hold ’em, the bet size on the river is usually small in comparison to the size of the pot. This means you should call
much more than you fold, and your proportion of bluffs should be small relative to the amount of value bets. Additionally, in limit hold ’em, you should call a raise with a majority of your value bets, as the size of your opponent’s raise is usually small compared to the pot.
Obviously, the core of no-limit is that bet sizing is up to the players, and is not rigidly dictated by the rules of the game. However, in general, bet sizes are a much larger fraction of the pot. Typical bet sizes in no-limit might range from a quarter pot to twice the pot. And the general rule is this: The larger the bet size is relative to the pot, the more often the first player should bluff, and the less the second player should call. For example, for a pot-sized bet, the GTO bettor should have one bluff for every two value bets, and the caller should call half the time since the bettor is receiving odds of 1-to-1 from the pot. (These relations are driven by the optimal bluffing ratio. See “Appendix B: Game Theory” starting on page 383.) This means it’s much more common to see someone make a marginal value bet and then fold to a raise in no-limit. However, since the penalty (a larger bet) is more in no-limit than limit, it becomes correct to make less value bets on the end with marginal hands.
Variable bet sizes allow for many more possible passages of play in no-limit. All games can be represented by a game tree: a diagram which represents each player’s possible action as an individual branch, and grows in a sequential fashion to represent each possible sequence of play. The tree grows as the number of strategic options and betting rounds increase, leading to a much thicker tree in no-limit. But with a few simplifications, it’s possible to create a world class heads-up limit hold ’em robot by getting a computer to search through the tree to find a good approximation to an unexploitable (GTO) strategy.
However, at the time of this writing, no-limit hold ’em robots are much worse than the best human players. This is because the current robots need to vastly simplify the number of betting options to reduce the tree to a manageable size. In theory, you should be able to consider betting any possible fraction of your stack in a given situation. But this leads to far too much branching of the tree, and so robots have to reduce the number of possible bet sizes into a computationally feasible number.85
For instance, a robot might consider only these four options: call, fold, raise the size of the pot, and raise all-in. This leads to two problems. First, the robot is unable to use a different bet size which might be more appropriate for a given situation. Second, the robot will always have to consider its opponent’s bet as one of these options. So if its opponent bets the minimum, then the robot will have to consider it as a pot size bet, will act accordingly, and will hence make some big errors in its play. The best no-limit robots are able to consider a finer granularity of bet sizes, but the game tree grows exponentially as you include more options, and hence they are still a long way from beating the best humans.
This problem will likely affect GTO no-limit robots for the foreseeable future. In my opinion, exploitive no-limit robots have a much better chance of soon challenging the best humans. This is because exploitive robots do not need a fixed strategy for every possible branch of the game tree; most of their computational power goes into building an accurate model of how their opponent plays — allowing them to maximize EV on a hand-by-hand basis as new situations arise. Of course, building an accurate model of your opponent is more difficult in no-limit given the large number of strategic options, but this should be easier than building a GTO robot. Furthermore, playing this exploitive robot against itself should then give you an approximate Nash equilibrium in heads-up no-limit hold ’em.
Exploitive play is also important for humans. Again, this is because finding good GTO strategies is very hard. The general method for finding a GTO strategy is recursive. First, you set an initial strategy for one player: say, raising to three times the big blind with 60 percent of the hands on the button. Then you find a strategy for the big blind that maximizes EV against that initial strategy — this would no doubt involve a fair amount of calling and reraising. Then you go back to the first player, and make any refinements to the overall strategy to improve EV against the big blind. This goes back and forth until neither player wants to make any further changes and an approximate Nash equilibrium is reached.
You might spend a lot of time devising a strategy in the big blind that does well against someone who plays raise-to-three-big-blinds-or-fold on the button. But what if your opponent does something else, such as min-raising or raising to 5x? If your overall strategy is fully GTO, this won’t be a problem: GTO strategies will at least break even regardless of your opponent. However, full GTO solutions aren’t even known in limit, let alone no-limit, so there are no guarantees your approximation will do well against a different opening sequence. When devising strategies, it’s common to spend most of your time trying to counter the strategies you come up against most often; unusual strategies are more likely to unearth any errors in your thinking.
So if you want to play exploitively in no-limit, do so by putting your opponent in situations that he hasn’t encountered much before and there should be a number of opportunities for this given the vast size of the game. Also, it’s interesting that some high stakes no-limit players refuse to play against opponents who don’t raise to three times the big blind, indicating that this method has some merit.
Continuing on, I’m not saying GTO play is useless in no-limit, just that the balance that you should use between exploitive and GTO play is slightly more tilted towards exploitive moves. GTO play is still incredibly important: First, it makes it easier to spot exploitable errors, and second, having a theoretical underpinning allows you to react to new situations (such as unusual bet sizes).
We have already seen how refusing to use certain strategic options can benefit your limit hold ’em game. But in no-limit, things are slightly messier: not only because certain actions such as cold-calling are much more attractive, but also because the ability to choose your bet size gives you a vastly higher amount of strategic options to choose from. Some authors address this problem by first deciding on a bet size for a given situation, and then deciding whether to bet — betting the same amount with each hand that bets.86 And once a bet size has been found, this strategy has the benefit of reducing the effective number of strategic options down to the same number as in limit, and betting the same amount in a given situation will prevent you from revealing information by your choice of bet size. But is it correct?
We cannot know the answer to this question until heads-up no-limit hold ’em is fully solved, which will not be for many years, but we can try and get an indication by looking at some models of no-limit poker. Most often this is done by using the U[0,1] game which we have previously examined in detail or with a game known as three card poker where the deck is reduced to only three cards. (See “Appendix B: Game Theory” starting on page 383 for a simple implementation of this model).
The trouble with this is that the optimal betting strategy is dependent on the model in use. In one model of three card poker, it’s indeed correct to bet the same amount with each hand: This amount happens to be
, or about 41 percent of the pot.87
Things are radically different in a different version of the U[0,1] game: Here every value hand bets a different fraction of the pot.88
Even though this directly reveals information, it doesn’t lead to any exploitable opportunities because each value bet is matched with a correct fraction of bluffs (and in this model the first player is unable to raise).
In some games with multiple betting rounds, the correct betting strategy is to bet an equal fraction of the pot on each round so that you are all-in by the final bet (known as betting the geometric growth of the pot).89 This last model applies best to the earlier betting rounds; the first two models are really simplifications of the river. This last model means that the larger your effective stack size, the more you should bet on early rounds to give yourself a better chance of getting all-in by the river.
Which out of the two river models should we prefer? You can’t go too far wrong by always betting the same amount, but in my view, this is a little too rigid to be a truly theoretically optimal strategy. I’m basing this on my knowledge of limit hold ’em robots who are capable of using a full range of strategic options that a lot of humans would consider bad, but they do so in a way that is highly balanced and are unexploitable. So betting different amounts makes sense to me: Stronger value bets will usually want to make larger bets, while weaker value bets want to bet smaller
amounts as this entices weaker hands to call and costs less when wrong. Of course, stronger value bets will be required to mix it up by sometimes making the smaller bet and vice versa. If this is done in the correct amounts, then it shouldn’t result in any exploitable opportunities.
You also need to consider position when bet sizing. It’s my view that out-of-position bets should on average be smaller than in-position bets, and betting small amounts out-of-position is similar to the concept of a “blocking bet,”90 the idea being that betting a small amount can dissuade your opponent from making a larger bet himself. When out-of-position, you are in somewhat of a bind; your opponent can always choose to escalate the pot whatever you choose. Given this fact, making small stabs at more pots allows for making thinner value bets and gives more opportunity to win pots without a showdown.
Against weak players, I think you could take this concept to the extreme by making min-bets instead of checking when out-of-position in large pots. This is because the min-bet forces them to choose from (fold, call, or raise), instead of (check or bet). When a bad no-limit player is faced with the option of folding, they might do so with too many hands, particularly against a min-bet in a large pot where hands as weak as eight-high could theoretically be correct calls. Note that min-betting in-position would be incredibly dangerous because it reopens the betting with little potential reward.
Two strategies from limit hold ’em are also worth noting: playing call-or-fold out-of-position in the big blind, and never four-betting heads-up. The opportunities to use call-or-fold will be more limited in no-limit since this strategy works best when your opponent always continuation bets the flop. This is less likely in no-limit, as the cost of getting reraised makes it less profitable to value bet in-position, and hence leads to more checking behind.
The strategy works best when your opponent’s range is so strong that he should almost always bet the flop which is most likely when your opponent raises from an early position, or against a tight player. It can also work as an exploitive strategy if your opponent has a high flop continuation bet statistic.
Never four-betting heads-up is slightly more interesting, and it’s a tactic used by some high stakes no-limit players. It’s very much a GTO play in limit; in no-limit, I think it’s more exploitive. Never four-betting allows you to benefit more from being in-position. When you four-bet, the effective length of the hand shortens; things tend to get settled preflop by either an all-in reraise or a fold. When you don’t four-bet the pot grows more gradually, and so you have more opportunities to use your positional advantage. Also, four-betting is very much the norm; this is what most 3-bettors expect, and a player who four-bets will have a much weaker calling range than a player who never-four bets. This means that most 3-bettors are used to having a vastly superior range when they 3-bet and get called, allowing them to value bet and bluff aggressively. They should react to you never four-betting by acting more cautiously postflop, and if they don’t, you might be able to pick them off. This tactic should be reserved for when the stacks are extremely deep, allowing for more postflop play to implement your positional edge.
The nature of no-limit hold ’em means you shouldn’t go about restricting too many strategic options from your game. It’s very much a dynamic game where one card or one bet can radically alter a hand. This means you should use the full spectrum of strategic options: reraising out of the big blind preflop and then using a balanced range of checks on boards that are poor for your range; putting aggressors to the test by betting out into them, particularly on scary boards that miss a lot of their range; betting all the way and then going for a check-raise on the river; going for a check-raise on the turn after the flop was checked behind.
A little bit of creativity helps with making these plays, but they can also be arrived at analytically. Think about how the board hits each players’ range: Do you want to always continuation bet after raising preflop? If not, it’s best to check a variety of different hands, and when out-of-position, you will have to use all of your available compound options: check-fold, check-call, and check-raise — using a variety of hands with each option (even the hands you check-fold should in theory be varied in case your opponent gives you a free card). A combination of practice and study makes the necessary skill of quickly performing this process at the table much easier.
Hand Examples
Let’s look at some hands from the sixth series of High Stakes Poker to illustrate some of the differences and similarities between limit and no-limit hold ’em.
Hand No. 1
Game: No-limit hold ’em — 7 players with blinds of $400 and $800, plus a $200 ante. There is now $2,600 in the pot.
Action: The first two players fold, Tom Dwan calls, the next two players fold, Phil Ivey calls, and Andreas Hoivold checks. There is now $3,800 in the pot.
Tom Dwan calls first-in from two seats off the button with the Q♠ T♠ . Players frequently call first-in in this game from early positions. That’s because the game is playing very deep which increases implied odds and makes it attractive to play more hands and calling allows you to do exactly that despite a positional disadvantage. An alternative would be to min-raise: this is still a cheap way to enter the pot, but it has the advantage of forcing the blinds to put more money in (which could have lead to Dwan winning this hand).
Flop: A♠J♦4♠
Action: Ivey and Hoivold check. Dwan bets $2,700, Ivey calls, and Hoivold calls. There is now $11,900 in the pot.
Dwan’s flop bet gets called by both players. Ivey’s call needs some explaining: Ivey and Dwan are playing with effective stack sizes of over 600 big blinds and so there is going to be a lot of posturing between them when the pot is small, so Ivey calls despite having close to nothing.
Turn: 4♣
Action: Ivey bets $8,000, Hoivold folds, and Dwan calls. There is now $27,900 in the pot.
The four on the turn is the perfect card for Ivey to launch the bluff that his speculative flop call was in preparation for. Ivey can have a four here given the earlier action. If he did have a four, then betting out is better than check-raising because a lot of Dwan’s flop value bets will now check the turn given the danger of reopening the betting. And Ivey’s turn bet is an example of correlating your bluffs and value bets.
River: 9♣
Action: Ivey bets $25,000 and Dwan folds.
Ivey’s river bluff highlights a difference between no-limit and limit hold ’em. He holds king-high, and with an ace on board the bluff can only work if it makes Dwan fold a pair or better. In limit hold ’em, this would be a very bad bluff since the high pot odds would mean that all better hands will call while making your opponent fold worse hands doesn’t do you much good. Therefore, you might require a hand as weak as ten-high to bluff this river in limit hold ’em.
But the bets are much larger in no-limit hold ’em; Ivey has bet just under the size of the pot. This allows the aggressor to turn slightly stronger hands into bluffs, and given the strength of the hands Ivey is betting for value, king-high could easily fold out some better hands.
Hand No. 2
Game: No-limit hold ’em — 7 players with blinds of $400 and $800, plus a $200 ante. There is now $2,600 in the pot.
Action: Dario Minieri raises to $3,000, Eli Elezra calls, the next three players fold, Tom Dwan calls, and Antonio Esfandiari calls. There is now $13,400 in the pot.
Flop: 5♥4♠2♣
Action: Dwan checks, Esfandiari checks, Minieri checks, and Elezra checks.
Tom Dwan’s attempted check-raise fails to come through.
Turn: K♥
Action: Dwan checks, Esfandiari checks, Minieri checks, and Elezra checks.
Undeterred, Dwan goes for a check-raise again. This is a good play; don’t be fooled by its failure to come off. The K♥ gives Dwan a flush draw to go with his two pair which reduces the danger of giving another free card, as any four, deuce, or heart will actually improve his hand. It’s important for the early position players to sometimes attempt these check-raises with no previous aggressor. Otherwise, late position players could exploit this by indiscriminately bluffing the turn when checked to, and the early position players would have no credible counter-threat.
River: 5♣
Action: Dwan checks. Esfandiari bets $9,000, Minieri folds, Elezra calls, and Dwan folds.
Antonio Esfandiari takes a stab at the river with nothing. Bluffing the river with nothing is generally a good play, but I don’t like it in this instance. The most important factor when bluffing is that you must always balance your bluffs with value bets, and it’s hard to see how Esfandiari could have a possible value bet in this spot.
Esfandiari’s most likely value bets are fives and kings. But in order to have a five, he must have checked it to the raiser on the flop, and then be too scared to bet on the turn when the king comes. So I don’t believe he could have bet with a five on the flop. Plus, two more reasons to have bet earlier are that this probe bet would give him information and it would prevent a free card on a very dynamic flop.
I also think a bet on the turn makes sense: Yes, someone could have a king, but so could Esfandiari, and a turn bet is unlikely to get raised by just a pair of kings. In addition, Esfandiari would have almost certainly bet a pair of kings on the turn.
Eli Elezra makes the same deduction when he calls with ace-high. But Dwan decides his hand isn’t worth an overcall, and makes a debatable fold given the cards that are out. Dwan’s play is generally right: You usually need a stronger hand to overcall the river than to just call. But then again, since Esfandiari’s bet is especially suspicious, Elezra can call with some very weak hands (and Elezra is unlikely to hold much given the river paired the top card on the flop and he checked in last position on two
No-Limit Hold ’em: Applications and Extensions 249
streets). Therefore, Dwan should consider his pair much stronger than normal.
This is the exception that proves the rule about overcalling: If the initial bettor has no credible value bets in his range, then overcall as frequently as you would make an initial call; otherwise, overcall with fewer hands. I’ve made a number of similar folds like Dwan’s play here, and in fairness to him, he did immediately comment that he had made a mistake.
Final Pot: $31,400. Antonio Esfandiari shows the T♣8♣ (one pair, fives — king-ten-high). Eli Elezra shows the A♦9♠ (one pair, fives — ace-king-high). And Elezra wins the $31,400 pot.
Hand No. 3
Game: No-limit hold ’em — 8 players with blinds of $400 and $800, plus there is a $200 ante. There is now $2,800 in the pot.
Action: Phil Ivey straddles to $1,600 and the next two players fold. Gus Hansen raises to $5,600, the next four players fold, and Ivey calls. There is now $14,000 in the pot.
Flop: J♥J♠5♥
Action: Ivey checks. Hansen bets $6,800 and Ivey calls. There is now $27,600 in the pot.
Gus Hansen’s flop bet isn’t really a value bet (since weaker hands won’t call) or a bluff (since better hands won’t fold). Mostly, it’s a continuation bet that reflects the strength of his distribution (given his position), and the weakness of his opponent’s — Ivey straddled and was receiving great pot odds given all of the antes and blinds. Also, continuation bets like this are entirely logical when you hold a vastly superior hand range.
Turn: 5♣
Action: Ivey checks. Hansen bets $13,200 and Ivey calls. There is now $54,000 in the pot.
Hansen’s intentions are clarified by the turn: His hand is now very much a bluff. He clearly isn’t expecting worse hands to call, so his bet must be intended to make better hands, such as small and medium pocket pairs, fold.
This hand highlights an interesting difference between the two games. It would be very common to see exactly the same sequence of action in limit hold ’em, only the bettor’s intentions would be entirely different. If a preflop aggressor bet this turn in limit hold ’em with ace-high, then it would always be a value bet. This is because most better hands, such as a medium pair, would check-raise the flop, and so ace-high is now likely the best hand. However, it would also make sense for the blind to continue calling with hands such as king-high because the aggressor can still have a number of weaker hands. And he could also win by pairing one of his cards.
River: 7♠
Action: Both players check.
Hansen decides to give up on his bluff — likely an accurate read.
Final Pot: $54,000. Phil Ivey shows the 8♥8♣ (two pair, jacks and eights). Gus Hansen shows the A♠K♥ (two pair, jacks and fives). And Ivey wins the $54,000 pot.
Hand No. 4
Game: No-limit hold ’em — 8 players with blinds of $400 and $800, plus a $200 ante. There is now $2,800 in the pot.
Action: Tom Dwan raises to $3,200. Antonio Esfandiari reraises to $11,000, the next six players fold, and Tom Dwan calls.
Tom Dwan is notorious for opening the pot and calling reraises with a wide range of hands.
Flop: T♦7♣5♣
Action: Dwan bets $14,700 and Esfandiari folds.
This is a good flop for Dwan given that he’s the player with the much wider range, and both players know that he is capable of holding a hand like ten-eight suited in this spot. Furthermore, a large proportion of Esfandiari’s hands will be combinations that haven’t improved like AK, AQ, and AJ.
So this is a good spot for Dwan to bet out with hands that have improved, especially since Esfandiari will probably check his ace-high hands if given the chance. Remember from Hand No.1 how important it is to correlate your value bets and bluffs, and the
is a great hand for Dwan to bluff: It has six outs and can improve if called, but it’s too weak to call if Esfandiari makes an ordinary sized continuation bet.
Hand No. 5
Game: No-limit hold ’em — 8 players with blinds of $400 and $800, plus a $200 ante. There is now $2,800 in the pot.
Action: Patrik Antonius calls, the next three players fold, Tom Dwan calls, and Barry Greenstein calls. Phil Ivey raises to $7,000, the big blind folds, Patrik Antonius calls, and Dwan and Greenstein both fold. There is now $18,000 in the pot.
Patrik Antonius makes an early position call with a suited hand. Phil Ivey doesn’t necessarily need that strong of a hand to raise, this is known as a squeeze play, so Antonius calls given the large effective stack sizes.
Flop: 7♣4♦4♠
Action: Ivey bets $12,000. Antonius raises to $36,000 and Ivey calls. There is now $90,000 in the pot.
This flop, given the large stack sizes, tremendously impacts the strength of both players’ ranges. Phil Ivey is much more likely to have a big pocket pair, but the really important question on this flop is: Who holds the most fours? The answer is: Antonius does, as he has plenty of starting hands like six-four suited and five-four suited. With smaller stack sizes, or in limit hold ’em, Ivey would still be in the drivers seat as his strong average hand would overwhelm Antonius’s threat of holding more fours.
Turn: A♦
Action: Ivey checks. Antonius bets $42,000 and Ivey folds.
The turn card gives Antonius more outs, and it only improves Ivey’s hand enough to check-raise if he started with aces. This means the danger from reopening the betting is reduced, and so Antonius can make his in-position semibluff.
Hand No. 6
Game: No-limit hold ’em — 8 players with blinds of $400 and $800, plus a $200 ante. There is now $2,800 in the pot.
Action: The first three players fold. Barry Greenstein raises to $3,000. Phil Ivey 3-bets to $13,000 and the button folds. Patrik Antonius 4-bets to $36,400, the big blind and Greenstein fold, and Ivey calls. There is now $78,200 in the pot.
Flop: Q♠T♦J♥
Action: Both players check.
This is an extremely bad flop for both hands: they are now beat by AK, QQ, JJ, and TT. So it’s no surprise to see them both check with the large stack-to-pot ratio. Patrik Antonius can only beat the one premium hand his opponent is actually holding: kings. Ivey has the small consolation of a straight draw.
Turn: Q♦
Action: Both players check.
Other than further weakening both players’ hands, this turn card changes very little.
River: 9♣
Action: Antonius checks. Ivey bets $45,000 and Antonius calls.
Improving to a straight finally makes Ivey’s hand worth a bet. Antonius’s range is now very weak, but pocket aces are much too high up in his range to fold given the passive play on the earlier streets (since he wants to call enough hands to make Iveyindifferent to bluffing). Given the large bet, Antonius only needs to call a relatively small fraction of his bluff-catching hands, and pocket aces are certainly good enough given his generalweakness.
This hand would play differently in limit hold ’em. Each hand would comfortably reside in each players’ value region, and so a number of bets would go in on the flop and/or turn.
Final Pot: $168,200. Phil Ivey shows the K♥K♦ (straight — king-high). Patrik Antonius shows the A♦A♣ (two pair, aces and queens). And Ivey wins the $168,200 pot.
Hand No. 7
Game: No-limit hold ’em — 7 players with blinds of $400 and $800, plus a $200 ante. There is now $2,600 in the pot.
Action: Tom Dwan straddles to $1,600 and the next three players fold. Daniel Negreanu raises to $6,500 and both blinds fold. Dwan 3-bets to $23,600 and Negreanu calls. There is now $49,800 in the pot.
I don’t like Negreanu’s call. The trouble is, if he misses the flop, Dwan can always steal the pot with a bet, but if Negreanu improves, he will often make, as he does here, a second best hand.
Flop: A♥A♦J♥
Action: Dwan bets $28,200 and Negreanu calls. There is now $106,200 in the pot.
Turn: K♣
Action: Dwan bets $56,500. Negreanu raises to $138,600 and Dwan calls. There is now $383,400 in the pot.
Dwan finds himself in the great position of getting raised while holding the nuts. Calling Negreanu’s raise has a couple of advantages over reraising all-in. First, if Negreanu is bluffing (as it happens, Negreanu was bluffing), then calling gives him a chance to bluff the rest of his chips on the river. Second, calling also adds more balance to Dwan’s strategy: If his calling range is too weak, then Negreanu could exploit that fact by making thin value bets. Also, not only does Dwan have the absolute nuts, there is no danger of allowing Negreanu to draw out.
River: 9♣
Action: Both players check.
Final Pot: $383,400. Tom Dwan shows the A♠K♦ (full house —aces full of kings). Daniel Negreanu shows the J♦8♠(two pair, aces and jacks). And Dwan wins the $383,400 pot.
Hand No. 8
Game: No-limit hold ’em — 7 players with blinds of $400 and $800, plus a $200 ante. There is now $2,600 in the pot.
Action: Patrik Antonius straddles to $1,600. Daniel Negreanu raises to $6,000, the next player folds, Dennis Phillips calls, the button folds, and both Barry Greenstein and Patrik Antonius call. There is now $26,200 in the pot.
Flop: A♣K♠8♣
Action: Greenstein, Antonius, and Negreanu all check. Phillips bets $14,000, Greenstein folds, Antonius calls, and Negreanu folds. There is now $54,200 in the pot.
Negreanu refuses to continuation bet into three players, but Phillips decides to bet his top pair with the action checked around to him.
Turn: 9♣
Action: Antonius bets $28,000 and Phillips folds.
Antonius’s bet is incredibly dependent on his exact hand and this specific board texture. Phillips’s most likely hand is just a pair of aces, whereas Antonius’s play fits the sequence of a draw and the flush has just come in. If Antonius checks, then Phillips will likely take a free card. So the best way for Antonius to get action on his two pair (or a low flush) is to lead out with a bet.
Antonius would likely check if all he had was a pair of aces— as now he can get a free card from Phillips’s stronger aces. If Antonius had two pair, but the turn card didn’t complete the flush, then Antonius would check and probably go for a check-raise.
Despite Phillips folding a pair of aces, I’m not saying that Antonius having two pair should be obvious to him. Antonius is an aggressive player, and can plausibly be making a play, especially since Phillips bet the flop in dead last position. In addition, Antonius has made a relatively small bet on the turn, just over half the pot, which is the right size to tempt Phillips into calling with one pair.
Hand No. 9
Game: No-limit hold ’em — 8 players with blinds of $400 and $800, plus a $20 ante. There is now $2,800 in the pot.
Action: Phil Galfond straddles to $1,600, Daniel Negreanu calls, and the next player folds. Tom Dwan raises to $8,000, the next five players fold, and Negreanu calls. There is now $20,400 in the pot.
Flop: A♥T♥7♣
Action: Both players check.
We analyzed this decision point from a limit hold ’em perspective in detail in “Checking Back the Flop” starting on page 116, and concluded that if your range is not strong enough to always continuation bet heads-up and in position, then you should check a balanced range, mainly comprised of mediocre draws and made hands.
This spot is very similar in no-limit hold ’em. The main differences are that you require a stronger hand to value bet, and due to the larger bet size you can turn more hands into bluffs.Therefore, it’s not surprising to see Dwan check back the flop with a gutshot since Negreanu could potentially make a large enough check-raise to prevent Dwan from calling. In the same session, Dwan also checked the 9♦ 7♦ on a J♦9♠ 2♠ flop, (a hand that would normally be strong enough to value bet in limit hold ’em).
Turn: 8♥
Action: Negreanu bets $14,000 and Dwan calls. There is now $48,400 in the pot.
Dwan’s checking range is quite weak, so he should call the turn bet with a pair of eights given that he is inducing a bluff from Negreanu with his flop play.
River: K♠
Action: Negreanu bets $42,000 and Dwan folds.
Hand No. 10
Game: No-limit hold ’em — 6 players with blinds of $400 and $800, plus a $200 ante. There is now $2,400 in the pot.
Action: The first player folds. Phil Laak raises to $3,900, Eli Elezra, Phil Ivey, and Daniel Negreanu all call. Tom Dwan raises to $28,900, Laak and Elezra both fold, Ivey calls, and Negreanu folds. There is now $70,700 in the pot.
Dwan makes a preflop squeeze play. If he can get Laak to fold, there is a good chance the other players will fold as well.
Flop: K♦Q♣T♦
Action: Dwan bets $45,800 and Ivey calls. There is now $162,300 in the pot.
This is a standard out-of-position continuation bet on a flop that strongly hits Dwan’s range.
Turn: 3♠
Action: Dwan bets $123,200 and Ivey calls. There is now $408,700 in the pot.
River: 6♣
Action: Dwan bets $268,200 and Ivey folds.
The turn and river are best analyzed in reverse. Dwan will have absolutely nothing on any non-eight, -nine, or -jack river. This makes Dwan’s hand a perfect candidate to bluff any river card that misses him. Given Dwan’s strong play on the earlier streets, he should have a lot of hands that will want to value bet in this spot. So from a GTO perspective, this makes Dwan’s bluff on this river card absolutely mandatory — if he didn’t bluff this hand, he would have no bluffs in this spot, and Ivey could exploit that. Since Dwan and Ivey are such regular and skilful opponents, any exploitive deviations they make from GTO play shouldn’t be too large, otherwise, the other player could counter-exploit them.
Now that we know what should happen on the river, we can analyze Dwan’s turn play. Earlier in this book, we saw that the hardest bluffing situation is out-of-position on an early round where the key variable is your opponent’s probability of checking behind. Here, the effective stack sizes are around $675,000 and the pot is $162,300. If Dwan checks the turn, then Ivey has to be wary — a check-raise would be an effective way for Dwan to get his full stack in by the river. This makes checking the turn a reasonable option for Dwan: He can hope that Ivey checks
behind, giving him a chance to improve his hand or to bluff at the river, but, critically, into a much smaller pot. However, Dwan is trying to represent a very strong hand range at this point, in which case betting a lot of hands, as either value bets or bluffs, makes sense. By the way, Ivey nearly called this river bet with just a pair of sixes, so perhaps Dwan had been bluffing a little too much in similar spots before.
I think that Tom Dwan has an intuitive feel-based approach to the game, but it’s interesting to note how closely his play follows game theoretic prescriptions: He puts hands into action regions, plays with balance, and plays every hand with a purpose that belies his loose and bluffy image. This confirms my suspicion from the “Two Schools of Poker,” that even if the best players don’t play in an explicit GTO fashion, they will evolve towards this style (in a version of the survival of the fittest ).
It’s interesting to note that Dwan’s biggest deviations from GTO play run counter to his image. Since people know he is always capable of bluffing, they attempt to exploit this by making loose river calls. But Dwan seems to realize this, and on at least three occasions in this series, he checked the river with a hand that had no chance of winning a showdown. On each of these occasions, he had a number of value betting hands in his range, so bluffing would be correct from a GTO perspective. But he seemed aware that since people were so liable to call, his best exploitive move was to refuse to bluff. It’s also interesting to note that he still bluffed the river against Ivey: his most regular and toughest opponent.
Anyway, as we have seen, being capable of a bluff in any situation is correct: The key to GTO play is to balance every value bet with an appropriate fraction of bluffs. Perhaps we can all learn something by studying Dwan’s most outrageous bluffs. 91