I don’t know what pains me more: Walking through a Las Vegas casino on a Friday night, seeing hundreds (thousands?) of piteous losers attached to slot machines like so many intensive-care patients on a morphine drip; or watching ABC on Sundays, Tuesdays, and Thursdays, seeing dozens (hundreds?) of otherwise very smart people make one costly gambling mistake after another.

The pop-culture sensation known as “Who Wants to Be a Millionaire” is missing a question mark in its title. The vast majority of contestants who appear on the show seem to be missing the boat.

What I see night after night is the equivalent of someone taking two large handfuls of $100 bills and throwing them into the middle of the Strip. (Naïve slot players do the same thing, but their willingness to leave money laying in the street is expressed in far less dramatic fashion. They just piss it away a nickel or a dime or a quarter at a time. The contestants on “Millionaire” blow their money grandly, operatically, epically. And on national television.

Yes, blow their money.

I’m not talking about someone who valiantly works his way up the ladder of questions to the $250,000 level and then answers incorrectly. I’m talking about those silly players—and there are surprisingly plenty of them—who don’t answer at all, who “take the money and run” when the right thing to do is venture a guess.

What these contestants don’t realize is that from an expected-value perspective, far from “taking the money,” they’re actually dashing off prematurely, leaving a good portion of what’s rightfully theirs behind in host Regis Philbin’s manicured fingers.

This happens, I assert, because the very smart people who make it through the long-odds screening process and into the “hot seat” know infinitely more about otherwise useless trivia questions than about a few basic gambling concepts. I would have thought that anyone bright enough to pass the phone test, win the phone playoff with other qualified entrants, and beat nine other smarty-pants types to make it into the money-chair would have taken a moment or two before their trip to New York City to analyze how to best use their lifelines. And how to make educated guesses. And, most importantly, when to guess and when to walk.

Strangely, with an alarming regularity that reminds me of slot players, the knowledgeable contestants on “Millionaire” consistently prove that their heads have been too inextricably buried in almanacs and oceanic maps to have considered the very real possibility that they might get to a certain level in the game and not know the correct answer. Or at least not be utterly sure of it. Based on observing almost every episode of the show, exactly three contestants have demonstrated that they know the right thing to do when they’re less than 100% positive that they know the winning answer.

I say “the right thing to do” instead of “best thing” or “safest thing” or “most telegenic thing” because “Millionaire” has an immutably correct “basic strategy” that yields for the player the highest expectation against the game. Just as there is one mathematically best play for every combination of player total and dealer upcard in blackjack, there is one best decision for every situation on “Millionaire.” Hunches, suppositions, and fanciful theories proposed by your Uncle Jed (the one the casinos treat like visiting royalty) do not obviate “Millionaire’s” blunt mathematics. If you make the right play, you optimize your “return on investment”; if you don’t, you cost yourself money.

To quickly review: Players on the show answer multiple-choice questions with prize values that roughly double at each succeeding step. Miss a question and you’re reduced to one of two plateau levels: $1,000, which is locked in after answering five questions correctly; or $32,000 which is locked in after answering 10 questions correctly. Each contestant gets three “lifelines,” a trio of diverse and extremely helpful methods of getting an answer a player does not otherwise know. (On “Who Wants to Be a Millionaire,” being really good at trivia helps, too. But as numerous players have proven, even without much more than average skill, judicious use of lifelines can earn an otherwise dull contestant a spectacular payday.)

From a gambling-odds perspective, the “50/50” lifeline, which removes two wrong answers, is the most reliable of the trio; the “phone-a-friend” lifeline, which allows the contestant to call a smart colleague (who, if he’s really smart, should be sitting in front of a high-speed computer surrounded by a roomful of smart cohorts), is probably the next most powerful tool; and the “ask-the-audience” lifeline, which allows the contestant to poll 200 strangers, is the least powerful.

Some of the small (but costly) mistakes contestants make involve the use of these aids. For example, although a plurality of the audience is right about 80% of the time, they’re typically polled only on easy questions. The audience is a good barometer for the low-level pop-culture-type questions, but you wouldn’t want their help on, say, a Shakespeare question. Nonetheless, anyone with a rudimentary grasp of probability should realize that when a random group of people who ostensibly have no special knowledge of a subject return their votes, the percentages for each answer should be 25%. Now, if one of the answers gets more than 50% of the vote and the other three hover around 17%, this is a strong indicator that they have a (collective) handle on the subject. In other words, the audience might be mistaken, but they probably aren’t. Thus, this lifeline has served its purpose—highlighting what is likely to be the right answer. (Conversely, if two choices get nearly 50% of the vote or three get 33%, then the results should be dismissed.) Despite being furnished with such strong mathematical evidence, I see countless contestants ignore the audience vote because, the contestants often feebly explain, they were “hoping for a more convincing majority.”

Similar gaffes include using the phone-a-friend to confirm a choice the contestant is already “pretty sure” (80% certain) about, thereby diluting the full value of the lifeline; using the phone-a-friend after narrowing the choices to 50/50, thereby diluting the full value of two lifelines; burning any lifeline on the “free” $64,000 question when it’s more than 50% probable that you know the answer; and wasting the audience lifeline on subject matters other than popular culture or any other subject that would be familiar to a population that is more likely to subscribe to People magazine than Atlantic Monthly.

These are all small errors, the equivalent of not hitting a 16 versus a dealer’s 10-up in blackjack. Other mistakes on “Millionaire” are much worse.

The most egregiously wrong thing to do on this show is to not take full advantage of the guaranteed money plateau at $32,000. Even if you’re out of lifelines, everyone—even Regis—knows that when faced with the $64,000 question, you should take a guess. It’s a $32,000 free-roll. Get it right and you’ve won $32,000 more than you previously had. Get it wrong and you still leave with $32,000. You’re risking $0 to win $32,000.

It’s at the next level, the $125,000 question, where I see the most money being squandered by the show’s contestants. Granted, people get nervous when the very real prospect of winning a six-figure prize looms before them, but here are the facts.

By rule, if a contestant has won $64,000, the smallest amount he can leave with is $32,000. Thus, a wrong answer at the $125,000 level costs the player only $32,000. If, on the other hand, he gets the question right, he wins an additional $61,000—nearly twice as much as he stands to lose. In odds terms, you’re getting 2-1 on your money. (Technically, it’s not exactly 2-1; that would require the 12th question to be worth $128,000, which, I suppose, doesn’t seem quite as elegant to the producers as $125,000. But it’s pretty close.) To break even on this proposition, a player would have to answer the question correctly one out of three times. If he’s able to answer the question correctly one out of two times—being right as often as he is wrong—he’s getting an enormous “overlay,” as gamblers like to say.

“Millionaire,” you may recall, poses questions in a multiple-choice format, providing contestants with three incorrect choices and the correct one. Even with no knowledge whatsoever of a subject, a contestant who guesses will do so correctly one out of four times. (Remember, at the $125,000 level, players need only answer correctly one out of three times to break even.) If, however, he’s able to eliminate one or more incorrect choices, he’s drastically improved his chances. Indeed, with the help of the 50/50 lifeline, which eliminates two wrong answers, leaving one wrong answer and the correct one on the board, the player has an even-money (1-1) shot to pick the winner.

In this case, the correct play is clearly to guess. Flip a coin. Play eeny-meeny-miney-moe. Whatever. It doesn’t matter how the choice is made—just so long as a choice is made. Being paid 2-1 on an even-money shot is about the best proposition you’ll find in the gambling universe.

Looking at the $125,000 question from a purely mathematical perspective, when the contestant has narrowed the choices to 50/50, a guess is clearly warranted. But what of the emotional and practical perspectives?

Many trivia mavens are hesitant—if not downright ashamed—to admit they don’t know an answer, and even more loath to answer wrongly. If you’re brave enough to exhibit your vast store of knowledge on national television, you probably have a positive opinion of your mental powers and would hate to do anything that appears to diminish your trivia omniscience. But as most successful poker players, blackjack professionals, backgammon champions, golf hustlers—anyone who gambles for a living—will testify, there’s little room for such emotion in an arena where rationale and logic carry the day. In other words, you probably have no business attempting to win the $1 million top prize on “Who Wants to Be a Millionaire” if you cannot divorce your heart from your head. Because your heart invariably won’t let your head win.

Practically speaking, a lot of very smart people invoke a concept called “utility theory” to justify less than optimal decision-making. Utility theory basically says that if the money you stand to lose could be better used in your real life than in a highly positive gambling proposition (where, despite a big advantage, you could very well lose your stake), then it’s better not to gamble at all. My position is this: Either you believe in the concept of expected value or you don’t; it doesn’t apply only when you’re comfortable. Utility-theory apologists say, “The thirty-two thousand I could lose would pay for my kid’s college education. I really shouldn’t be gambling with it!” Expected value advocates say, “The hundred thousand or so you’re refusing to accept could pay for that education and a lot more!”

Yes, $100,000 or more.

By not taking a shot at the $125,000 question, a player is not merely costing himself $14,500 (the difference between the expected value of guessing with a 50/50 chance, and simply walking with $64,000). He’s costing himself tens of thousands in future equity, which is a term gamblers use to describe financial potential.

Here’s why. A player who correctly answers the $125,000 question gets to look at the $250,000 question. Even without any remaining lifelines, he has a very real chance of knowing the answer, particularly if he’s knowledgeable enough to have gotten this far already. The $250,000 may be about a subject dear to him or a piece of information he recently saw in a newspaper article or something he remembers from high-school biology class. Or he may be able to deduce the correct answer by throwing out the ones he knows to be incorrect. In that case he gets a free look at the $500,000 question. In fact, the equity consideration is so strong, it’s worth guessing at the $125,000 question if you can only narrow it down to three answers, where the expected value of a guess is just $63,000 (a grand less than the locked-in $64,000).

Basic strategy also dictates that a player guess at the remaining levels, assuming the field can be narrowed to two choices. Thanks to the guaranteed $32,000, he’s getting a reasonable overlay—and, again, the equity is huge. While there’s an argument to be made that equity also makes it proper to guess in one-out-of-three situations further down the line, a precipitous drop in expected value (at levels above $125,000) likely justifies stopping when a player is less than 50% sure.

Setting aside questions of a player’s intelligence or knowledge or deductive powers, these informed (and narrowed-down) guesses represent great gambling propositions. It’s similar to certain arbitrage opportunities that sometimes occur in sports betting. For example, with no handicapping knowledge whatsoever, without even an understanding of the rules of the game, someone who is offered the opportunity to lay 2.5 points on the favorite and take 3.5 points on the underdog in NFL football will show a tidy profit at season’s end, since, historically, the final result lands on 3 in the NFL games in which the line is 3 far more often than the one-out-of-20 times necessary to break even. Similarly, even if you know absolutely nothing about NBA basketball, if you couldn’t tell the difference between a zone defense and an end zone, getting 3 points and laying 2 on the same game will turn a slim profit (even after the bookie’s take).

In “Millionaire” you don’t have to know anything—other than how to say “That’s my final answer”—to take advantage of the game’s favorable gambling opportunities. You just have to have the heart (and wisdom) to know you’re doing the right thing.

Now, those who do know something do, of course, enjoy a great advantage. A photographic memory and an insatiable appetite for learning otherwise useless esoterica comes in handy on this show. But equally important is approaching the game as if it were a gambling tournament, where the money must be thought of merely as “chips” and each decision made must be considered solely in terms of expected value. If the answer to the show’s eponymous rhetorical question is indeed “everyone,” then contestants would do well to think more like wiseguy gamblers and less like degenerate slot machine junkies.