Back at the Massachusetts Institute of Technology, I attracted attention in the cafeteria when, once a week, I cashed yet another $100 bill from my casino winnings. With the way our currency has depreciated since 1961, the impact then was almost the same as if I were to pay today with $1,000 bills.
Meanwhile, my two-year appointment at MIT would end June 30, just three months away. The department chairman, W. T. “Ted” Martin, encouraged me to stay a third year at MIT and told me how highly I was regarded by institute professor Shannon. There was a chance this could lead to a permanent position either then or at a later date. Whether to try for this was a difficult decision. MIT had become one of the world’s great mathematics centers, following its transformation by projects for the government during World War II from a technical school to a scientific powerhouse. Simply walking down the hall, I would chat with people like the prodigy Professor Norbert Wiener (cybernetics) and the future Abel Prize winner Isadore Singer. The C. L. E. Moore Instructorship program, of which I was part, had brought in new PhDs like John Nash, who later won the Nobel for economics, and future Fields Medal winner Paul Cohen. Though there’s no Nobel Prize for mathematics, the Fields and the Abel prizes have that status. Cohen had left a few days before I arrived; his name was just being scraped off his door.
I finally decided not to stay on. From a career standpoint, I thought I had the talent to keep up with the big boys but I felt I needed more mathematical background. I also hadn’t collaborated on research with a senior faculty mentor or other colleagues in my area of specialty, and such work with others often is key to advancing in an academic department. Instead, I had spent much of my time working on blackjack and on building a computer with Professor Shannon to predict roulette. However, my work with Shannon wasn’t part of any academic field. It wasn’t mathematics per se and had no constituency and no name. It couldn’t help my academic career. Ironically, thirty years later MIT had become a world leader in the development of what would be called wearable computers, and the time line placed on the Internet by its Media Lab credited Shannon and me with building the first one.
New Mexico State University was bidding for bright young faculty members and subsidizing an incoming supply of good graduate students. They had just received a $5 million post-Sputnik Centers of Excellence Grant from the National Science Foundation, an amount equivalent to more than $40 million today, with a mandate to build a PhD program over the next four years. They proposed to jump my pay, from the $6,600 that both MIT and the University of Washington offered, to $9,000 a year and promote me to associate professor with tenure. I would also have a six-hour-a-week teaching load consisting of my choice of graduate courses. It provided the opportunity I wanted to expand my mathematical background, learning through teaching, doing my own research, directing doctoral theses, and collaborating with my students.
The position in New Mexico seemed to me to be the best next career step, even though my colleagues regarded it as an ill-advised gamble at what had been a mathematical backwater. Most important, a move to New Mexico would take Vivian and baby Raun to a much better climate and closer to our families.
As I was making this decision I agreed to write a book about blackjack. This came about after I mentioned my successful casino test to a few of my friends. The MIT grapevine did the rest. Yale Altman, representing the academic publisher Blaisdell (then a subsidiary of Random House), invited me to propose a book. I gave him the ten chapter headings from an outline I was already sketching, and he accepted it enthusiastically.
My working title was Fortune’s Formula: A Winning Strategy for Blackjack. Then Random House took the project away from Blaisdell, over the strenuous protest of its president. They wanted to distribute the book directly as a trade book, and proposed the new title Beat the Dealer. It would appear in November 1962, giving me time to exploit my strategies in the Nevada casinos before publication, after which I expected to be given a hard time whenever I showed up to play blackjack.
During the next few months I wrote the book. Vivian and I packed up with Raun and spent that summer of 1961 in Los Angeles. It was a fury of writing, doing mathematics research, going to Nevada on another blackjack trip, preparing to move in the fall to New Mexico State University, working twenty hours a week on roulette with Claude Shannon, and getting ready for the birth of our second child, Karen. Looking back I don’t see how Vivian and I did it all.
In August I traveled from Los Angeles to Las Vegas to play blackjack at the invitation of “Junior.” I was writing my book and wanted to learn more about the tactics casinos might use to prevent my readers from winning. Junior (also known as Sonny) was a Harvard law student who had contacted me while I was at MIT. He started playing casino blackjack on his twenty-first birthday, using a method called end play, a system discovered and exploited by a few early players. The basic idea was to play single-deck games that were dealt all the way down. Even though players of that era with their imperfect strategies usually had the worst of it, sometimes the deck toward the end would get very rich in Aces and Tens. Canny players would then make huge favorable bets. They needed enormous bankrolls to withstand the wild fluctuations in capital that followed. Although the casinos might win big, they also might lose a lot, so they did not like these players. Junior, for instance, had been widely barred, cheated, or reshuffled on, so he went to a Hollywood makeup artist who recast him to look Chinese. With his hair dyed black and his hairline carefully revised with a razor, he sat down at a Las Vegas blackjack table. Wearing a bulky body shell under his Chinatown outfit, he looked like a different person. Then the pit boss pointed at him, laughed, and said, “Look at Junior, all dressed up like a Chinese.”
Vivian had helped me train for this trip by dealing hands at high speed, blowing cigarette smoke at me, and engaging me in complicated conversations. Meanwhile, I was keeping track of the cards, calculating the percent advantage and my bet size, then playing out my hand using strategies that varied depending on the count. The key was to take it one step at a time, adding a new difficulty only after I became comfortable and relaxed with what I was already doing. What had seemed daunting finally became easy.
Junior backed my play with a modest $2,500 bankroll, equivalent to about $20,000 today. He followed me around Vegas with one eye open for cheating and another eye on his bankroll. While I was playing in the Sands, a pit boss who knew Junior told his friends that the kid was in town. Casino management saw that whenever Junior was around, I was playing nearby. Then my dealers stepped up the reshuffling and cheating. There was so much crooked dealing that I worried about playing on my own in the future without an expert to watch for it and warn me off. After a modest win, I returned to Los Angeles. The following month, September 1961, Vivian, Raun, and I moved to Las Cruces, New Mexico, where I began my duties at New Mexico State.
Although I learned from Junior that cheating was a serious problem and could make me a loser instead of a winner, he didn’t show me how it worked or how to spot it. Meanwhile I was writing a book that might send thousands of gamblers to the tables thinking they could win. If dishonest dealers wiped them out, it would be a slaughter. I had to understand how the cheating was done and explain it to my readers so they would have a chance to spot and avoid it. That’s what led to my next visit to Nevada.
The opportunity arose because I had been corresponding with Russell T. Barnhart, a magician and gambling scholar, who contacted me after my Washington, DC, talk in January 1961. We became acquainted while I was still at MIT and met in his apartment near Columbia University to talk about gambling and magic. As a treat Russell invited Percy Diaconis, a seventeen-year-old prodigy. Percy astounded me with card sleight of hand for an hour or so, then at Russell’s suggestion we talked about Percy’s future. What did I think about an academic career in mathematics as a professor versus being a professional magician? What advice would I give?
I told of the glories of the life of the mind, to be able to think about interesting problems as much as you wanted, as long as you wanted, to interact with intellectually challenging colleagues and students, to learn about any subject you chose, to have a lot of discretionary time with summers to travel and do research. Whether or not our conversation influenced Diaconis, he eventually became a full professor of mathematics at Harvard and also was awarded a MacArthur Foundation “genius” grant. He studied the theory of card shuffling, and the popular press widely reported his conclusion that seven fairly thorough shuffles was enough for practical purposes to randomize any deck of cards.
After the trip with Junior, when I told Russell of my problem with casino dishonesty, he proposed that I take him and his friend Mickey MacDougall on a blackjack foray. Mickey was perfect, being both a magician and a well-known card detective. His book Danger in the Cards describes his adventures detecting swindles in private games. He also had worked as a special consultant to the Nevada Gaming Control Board for several years. This led to the board citing several small casinos for cheating. Russell solved the bankroll problem by raising $10,000 from anonymous backers, with any profit—after our expenses had been paid—to be shared.
We met in Las Vegas in January 1962, during the year-end academic break at New Mexico State. Russell was a high-strung thirty-five-year-old bachelor and Mickey, a sixtyish fun-loving extrovert.
When we picked a casino and I found a seat I liked at the blackjack tables, our plan was for me to bet modestly until I got the go-ahead from Mickey. Following this, I would raise the scale of my betting and play for an hour, stopping sooner if I was warned off by Mickey or Russell. Stopping after an hour gave me a break during which I moved to another casino. Changing casinos after each session and varying the shifts on which we returned limited the time we were observed by any one casino employee. To further avoid notice, I stopped playing in any session before my wins became large, and I also stopped after a moderate loss to limit the impact in cases of cheating that we hadn’t detected. Mathematically, interruptions didn’t matter, because my lifetime of playing was just one long series of hands, and chopping it into sessions and playing them at various times and in various casinos should not affect my edge, nor the long-run amount I could expect to win. This principle applies in both gambling and investing.
When Mickey and Russell signaled that I had been cheated, I quit and went off with them for a lesson in how it was done. Mickey would demonstrate, first slowly then at casino speed. When I could see it or, more typically, infer it from what poker players call tells, we would return to the same dealer and resume play, briefly and for low stakes, so I could get better at spotting the crooked dealing at the table.
I saw this done with great skill at what had become my favorite strip hotel casino. We had several winning sessions on this trip, bringing my lifetime total to fifteen winning rounds, no losses. As I began session number sixteen, the pit boss walked up and asked us how we were doing. Mickey replied, “Up and down, like an elevator.” Twenty minutes later, a man hurried through the front door of the hotel, rushed to the table, and replaced our dealer. Suspicious, I reduced my bets to the minimum, lost a couple of hands, and was signaled by Mickey to leave. Back in our rooms, Mickey showed me the virtually undetectable peek and second-card dealing that the new man had used.
This, a common technique, was to peek at the next card to be dealt, the so-called top card. Then, if that card was good for the player, deal the card just below it instead, the second card, in the likelihood it was worse. On the other hand, if the dealer was giving a card to himself, he would take the top card if it was good for him, and otherwise deal himself the second. The dealer who does this is a heavy favorite to beat the player. An expert cheat or magician does this so well that even when you are told in advance and are watching close up, you can’t see. It’s also nearly impossible to prove it ever happened. Cheating was so relentless during those days in Las Vegas that I spent as much time learning about the many ways it was being done as I did playing. Everywhere we went, we reached a point where we were cheated, barred from play, or the dealer reshuffled the cards after every hand.
For the last couple of days, we flew to the Tahoe-Reno area, where we visited Mickey’s contact at the Nevada Gaming Control Board. Invited to tell our story, we recounted for two hours the litany of second dealing, stacked decks, missing or marked cards, and more.
We named dozens of casinos and described the dealers and their methods. Of course, our accusations ranged in authority from “dead certain” down to “circumstantial but strongly suggestive.” Although the gaming control board official repeatedly invited us to guess or speculate, we made clear which statements were facts and which inferences. I had the uncomfortable feeling that we were being encouraged to speak carelessly and make exaggerated claims. I wondered at the time if this might be natural impatience with my academic habit of being careful and precise, or whether the board official was trying to get evidence to discredit what was in effect our damning indictment of the board itself.
After hearing our marathon account of rampant cheating, Mickey’s contact at the board claimed he wanted to talk about additional consulting work, and suggested that in the meantime I take the opportunity to play blackjack. For some reason Russell didn’t come with me. When I balked at playing without my cheating protectors, Mickey’s contact assigned one of the gaming control board’s agents to watch over me. Mickey thought this was a good idea, and had told me earlier that the dealers knew all the people the board used, so whenever they showed up the cheating stopped until they left.
I started at the Riverside Hotel in downtown Reno (years later the casino addition where I played was demolished, to my silent cheers), betting a cautious $5 to $50. It was uncrowded and I sat down alone in the middle of an empty table. My “protector,” pretending not to know me, wandered in a minute later and sat down to play also. Our dealer, a young woman with a low-cut blouse and heavily freckled skin, won the first few hands against each of us. On the next hand I was dealt a “stiff” (10, 6) versus a dealer’s upcard of 9 or 10. I hit and, to my amazement the card meant for me emerged from the deck and stuck twanging, held by its edge between the top card and the rest of the deck. The dealer froze and blushed bright red from cheeks to décolletage. The pit boss, watching the action from the end of the table to my left, literally asked me if I wanted the top card or the second! I could see that the second was a face card, which would bust me like it was supposed to. So that the gaming control board agent could hear me even if he were nearly deaf, and blind as well, I said loudly and distinctly, “The second busts me so I’ll take the top card.” It was an 8 and busted me anyhow. I cashed in my chips and left.
As my protector followed me outside, I said, “Did you ever see a second card like that before?” He replied, “Second? What second?” This agent had been sitting just three feet from the dealer. He saw everything and pretended to see nothing. Realizing he was there to finger me for the casinos, I used the restroom excuse to lose him and went to play at another casino. I was doing well and a small crowd gathered, but eventually my dealer, and only my dealer, was replaced. Looking around, I saw my now unwanted escort in the crowd. I played hide-and-seek with him for another two and a half hours.
The following morning, it was time to go home. The three of us barely escaped from Reno. Heavy snow closed the local airport, but there was a plane leaving from a nearby air force base runway that was still open. We caught it, learning later that it was the last plane out for eleven days. Afterward I learned that our backers were William F. Rickenbacker, one of two adopted sons of the famous flying ace Eddie (who, as the first man to drive faster than a mile a minute, was the original “Fast Eddie”), and other staff members of the National Review.
This trip taught me that while playing well, even with experts to warn me of dirty dealing, I could no longer openly win a significant amount. On future visits, I would need to change my appearance, be low-key, and generally avoid drawing attention to myself. Mickey MacDougall told the gaming control board that he saw more cheating in Nevada casinos while watching my eight days of play than he had seen in all his previous five years of working for the board. After his damning report he was never again asked to consult by them. Russell Barnhart became fascinated with gambling and went on to write several books on the subject.
I was beginning to realize Las Vegas had a scary underside. It has evolved over the years. In 1947 mob elements, reportedly unhappy with his management of the Tropicana casino, gunned down fellow gangster Bugsy Siegel in Southern California. In 1960, the El Rancho Vegas mysteriously burned to the ground two weeks after a well-known mobster was forcibly ejected. When I played in the early 1960s, tens of millions of dollars in cash were being taken from the counting rooms without being tallied. The hidden profit avoided taxes and funded mob operations throughout the nation.
Not long after I played, as numerous card counters began to appear, they were jailed on pretexts, their money was taken, and some were beaten in back rooms. A gang of employees at one strip casino robbed drunks in their spare time. The 1970s weren’t as bad but, as portrayed in the nonfiction book Casino, by Nicholas Pileggi—later a movie of the same name—they were bad enough.
Since then, Nevada has been dramatically transformed from mobster Bugsy Siegel’s dream of a Disneyland for the mafia to a mainstream entertainment destination run by corporations. Las Vegas now enshrines the old days with a mob museum open to the public. The current consensus among professional blackjack experts seems to be that cheating has become rare in the older established areas like Nevada and Atlantic City, but players should be careful in the smaller, less regulated, and more remote casinos in the United States and abroad.
Beat the Dealer came out in November 1962. It sold briskly to favorable reviews, and continued to show strong, steady sales, with a spurt after minor bits of publicity. Readers were excited and enthusiastic. I believed that it might really take off if there were some way to publicize it more widely.
Ralph Crouch, chairman of the Mathematics Department at New Mexico State University, knew the science editor at Life magazine, and suggested they do a story. A mathematical system for beating blackjack had both scientific and public interest, and they enthusiastically agreed on a piece. But the story was evergreen, meaning not time-sensitive, so they had no schedule. Meanwhile David Scherman at Time Life’s associated publication Sports Illustrated got permission to do a piece in advance of the Life article.
As time passed, blackjack players faced escalating casino countermeasures in Nevada. Management watched us through the “eye in the sky,” a system of one-way mirrors above the tables. Our faces were checked against a book of photos of undesirables. Honest card counters were treated like player cheats and other criminals. When a casino spotted an undesirable, it passed the word around.
Countermeasures included reshuffling the pack of cards by the time half or fewer of them had been played. This not only limits the card counter’s chances to make favorable bets, but is also costly for the casino because it slows the game down, fleecing the ordinary players more slowly and reducing casino profits. If one likens a casino to a slaughterhouse for processing players, then more time spent shuffling means less efficient use of plant capacity.
Cheating, on the other hand, not only makes money faster but can capture profits the house would otherwise miss. I saw this happening one night when I walked into the lounge of a packed Las Vegas Strip hotel casino about 10 P.M. Louis Prima, a famous musician of that era, and his lead singer, new wife Gia Maione, were entertaining, and the adjacent blackjack tables were packed, with crowds of players waiting. I had come to play blackjack and as I checked all the tables, hoping to get a seat, I noticed that the players at every table were losing at an astonishing rate. The dealers were all wearing glasses with the same yellow-orange tint, through which they could see identifying marks on the backs of the cards. If the card on top was good for the player, the dealer dealt him the next card, or “second,” instead. Since players were wiped out faster, with their vacated seats being immediately refilled, profits soared. As a result, many who would have been discouraged by the wait and taken their money elsewhere left it at this casino instead.
Often, a suspected card counter was simply barred from playing blackjack. Apparently this was legal under Nevada law. Ironically, many innocent non-counters found themselves barred, along with incompetent would-be card counters. To get around this, I experimented with disguises, including contact lenses, sunglasses, a beard, and drastic changes of wardrobe and table behavior. This bought me extra playing time. Once, when I returned from a trip still in my disguise, my children didn’t recognize me. Frightened by the bearded stranger, they burst into tears. Though just five and three at the time, Raun and Karen still remember this. It didn’t bother baby Jeff, who was only a year old.
I tested one such disguise in Reno, where I had arranged through mutual friends to meet a couple who would keep an eye on me in the casinos in return for the fun of watching me play. We had never met and they didn’t know what I looked like. When I introduced myself at dinner, they saw a bearded fellow wearing a brightly patterned Hawaiian shirt, wraparound sunglasses, and jeans. Afterward, we headed for one of the big hotel casinos, where I settled into a higher-limit table on the quieter second floor. I chose the best seat for a card counter, known as third base, which is farthest to the left as viewed from the player’s side of the table.
Sitting there, I was the last to act, so I would benefit by having seen more cards when it was time to play my hand. Flashing a roll of bills, I bought a heap of chips. Seeing the money, my dealer, an attractive young woman, found me interesting. As we chatted and the casino offered drinks, which I accepted not to relax me but to relax them, she told me her shift was over at 2 A.M. and maybe we could “do something” afterward. Meanwhile, my steady winnings attracted the attention of the pit boss. He eventually decided I was a card counter, after which a parade from management came to watch. By 1 A.M. they had had enough and told me, to the astonishment and disappointment of my dealer, that I was no longer welcome at the tables. They evidently spread the word. Wearing the same disguise, I was barred from play the next day at several casinos.
That afternoon, I decided to put my disguise to the acid test. Before meeting my companions for dinner, I shaved off the beard, replaced the prescription sunglasses with contact lenses, and combed my hair differently. A sports jacket and tie—cocktail attire—completed the transformation. Opening their door to my knock, my companions, showing no signs of recognition, said, “Yes-s-s?” Their astonishment was my delight.
After dinner, I went to the same casino and took the same seat I had the night before. The same dealer looked up as I put a few chips from my pocket on the table in front of me. She saw no cash roll and I was now wearing a wedding ring—not a person of interest. To avoid being given away by my voice, I didn’t talk. When the cocktail waitress offered me a drink, I said in a barely audible hoarse whisper, “Milk.” I won again and all was well—for a while.
Then the pit boss came to watch as before, followed by the same management parade as on the previous night. But instead of me, they were focused on a player cheat who—worse luck—was seated next to me. After betting and receiving his first two cards, if he liked his chances he would add to his wager, and take some of the bet back if he didn’t. For an hour or so, they scolded him repeatedly, and when he wouldn’t either stop cheating or leave, they escorted him out. With my pile of chips growing steadily, I played on undisturbed. The next day I had no problem playing in the establishments that had barred my bearded self just the day before.
It was becoming clear that there was more to beating blackjack than counting cards and keeping cool as your bankroll went up and down. The green felt table was a stage and I was an actor on that stage. A card counter who wanted to be allowed to continue playing had to put on an effective act and present a nonthreatening persona. There are as many ways to do this as there are to portray characters in the theater. You can be the drunken cowboy from Texas or the wildly animated lady from Taiwan who can’t wait to get her next bet down. You can be Caspar Milquetoast, the nervous accountant from Indianapolis who has already lost too much down the street. Or Miss Spectacular, who draws all the attention to herself, not to how she bets and plays.
Dave Scherman’s full-length piece, “It’s Bye! Bye! Blackjack” appeared in the January 1964 issue of Sports Illustrated—and Beat the Dealer sold out everywhere. Two months later Life ran a nine-page story and the book moved onto the New York Times bestseller list.
The publicity brought both expected and unexpected consequences. For me, it was the pleasure of seeing my father’s silent pride in my fulfilling some of his hopes for me. In addition, there was a contact from my father’s younger sister, who had vanished from his life in 1904 along with his mother when their parents divorced. The Life story led his sister to him through me and he arranged to visit her in Iowa where she, her five children, and numerous grandchildren now lived. Separated when he was six and she was four, my father had dreamed for a lifetime that he would somehow find her again. But he never saw her. He died of a heart attack shortly before the trip.
After reading the articles, thousands of counters and would-be counters headed for Las Vegas. The Nevada Resort Hotel Association met in a secret emergency session. Twenty-nine years later, here is how longtime casino executive Vic Vickrey described that meeting.
“How the heck do I know how he does it? I guess he’s got one of them mathematical minds or photographic memories, or something.”
This was Cecil Simmons, the casino boss at the Desert Inn, talking on the phone with Carl Cohen, the Sands casino manager. It was the mid-1960s and they were discussing a book that would have a most profound impact on Las Vegas casinos and their approach to the game known as 21 or blackjack.
“All I know,” Simmons roared, “is he wrote a book that teaches everyone how to win every time they play blackjack. I’m just telling you, this book-learning SOB has ruined us…we’re out of the blackjack business.”…
Thorp’s book was the main topic of conversation whenever and wherever casino bosses gathered back during the ’60s…
…A meeting was called [to find] a solution…
We…gathered in…the Desert Inn. I still today do not know why the boys from Back East thought we had to be so damned secretive…I reminded them that this meeting was not exactly the same as their Appalachia meeting in up-state New York that had been raided by the feds years earlier.
…They could all have passed for actors who had just left an old George Raft movie set. They began talking out of the side of their mouths at the same time, with each one shouting out his remedy to the problem.
Hard-Knuckle Harry’s solution was quite simple: “Break a few legs…”
“No, Hard-Knuckles, no,” our chairman almost shouted. “We’re all legit now and we gotta think like legit businessmen.”
…It was finally agreed that a number of rule changes must be implemented…to thwart these card counters.
On April 1, 1964, April Fool’s Day—the Association announced the result: for the first time ever, it was changing the rules of blackjack. Pair splitting and doubling down would be restricted and the entire pack of cards would be reshuffled after just a couple of deals.
As part of an orchestrated PR follow-up, a Las Vegas Sun editorial of April 3, 1964, assured us that “Anybody who has been around Nevada very long knows that [casinos welcome] players with a system.” “Edward O. Thorp…obviously doesn’t know the facts of gambling life. There has never been a system invented that overcomes…the advantage the house enjoys in every game of chance.” And for the clincher: “ ‘Dr. Thorp may be qualified at mathematics, but he is sophomoric on gambling,’ is the way Edward A. Olsen, Gaming Control Board chairman, put it.” In a nonconfrontational vein, Gene Evans of Harrah’s Club explained that “…the club believes the player may have a better chance when the deck is shuffled every time, because all the Aces and face cards could come up on each deal.”
I told the press that the changes would hurt business badly and that skilled counters would still win. As Vic Vickrey reported, “Our regular 21 players who were not attempting to count cards…rebelled to such a degree that our 21 play began to decline at an alarming rate. [After several weeks] We had no choice but to reinstate the original rules which were more favorable to the player.” The casino bosses understood what their apologists denied. The mocking from a few weeks earlier was replaced by headlines like these: “Vegas Casinos Cry Uncle, Change Rules—Players Too Smart,” and “How Wizard of Odds Beat Las Vegas Cards.”
From a mathematical idea in my head, I forged a system for beating the game. Then I was ridiculed by the casino beast, which said that it sent cabs for fools like me. Thinking they played fair and that I was taking my secret weapon, a brain, to a sporting event, I found myself barred, cheated, betrayed by a representative of the gaming control board, and generally persona non grata at the tables. I felt satisfaction and vindication when the great beast panicked. It felt good to know that, just by sitting in a room and using pure math, I could change the world around me.
Rather than quit the field, I launched an army with Beat the Dealer. Thus continued the great blackjack war between the casinos and the players that still rages, more than fifty years after the invention of card counting.