The Eudaemonic Pie

by Thomas A Bass

  Sitting next to Doyne on his tour of the Montana card rooms was his friend Dan Browne, former motorcycle smuggler and Idaho Muscovite, who had originally lent him the copy of Morehead and convinced him there was money to be made in rambling and gambling. Browne is a natural card room talker. Give him silence and he’ll fill it up. A chess player, clarinetist, and undergraduate physics major at the University of Idaho, he worked his way through college by commuting on weekends to poker games in Spokane, where he cleaned out the house in time to make it back to Moscow for an eleven o’clock class Monday morning.

  Before walking into the Oxford, Browne and his protégé agreed on a strategy. “You can’t tell someone you’re a physics student,” Browne said. “They just won’t play with you.” Sporting a vest and wool cap, he reassumed the childhood pseudonym of George “Bug” Browne, Bug for short. Complete with straw hat, suspenders, and southwestern twang, Doyne rechristened himself “Clem.” Strolling into the Oxford, they sat on either side of a woman in a low-cut black dress. She tittered when Browne told her his name was Bug and then burst out laughing when Doyne introduced himself as Clem. He looked her straight in the eye and said, “Whatsa matter, lady? You don’t like something about my name?” She blushed and quickly made her apologies.

  “New Mexico Clem then settled down to some serious gambling,” said Browne. “To look at him, you would’ve taken him for a veritable mark. He fumbled the cards and spilled his chips. He didn’t know how to shuffle, and he dealt like someone just learning how to count. One and two and three and four. To the chagrin of everyone present but me, Clem turned out to be a pretty sharp player. After all, he knew every word that Morehead had ever written about poker, and he put it to good use.”

  After their nights at the Oxford, Clem and Bug drove to Lolo Hot Springs for a dip, some transcendental meditation, and a look at the sun coming up over the Rockies. “Everything grew timeless,” Browne recalled, “as all we did was eat, sleep, and play poker.” But a near disaster brought their tour to a sudden end.

  Although Clem played a good game of poker, he had yet to acquire Bug’s subtlety in disguising his winnings. “When I was starting out as a poker player,” said Browne, “I used to bet only when the odds were on my side. But when you’re taking money out of other people’s pockets, they can get a little upset. I got thrown out of a card room once for playing too tight, which was actually a good thing for my game. It made me loosen up, get into the bantering and joking, gamble once in a while when the odds were even, throw a card against the wall and call it, buy everyone a round of drinks. When I started playing in Spokane after that I became one of the regulars, a good old boy who they would never think of throwing out of the room.”

  His last night at the Oxford, not even a monosyllabic drawl had escaped from New Mexico Clem as he sat on his cards for two hours straight. The hand he finally played was a wheel, 1-2-3-4-5, which is the best you can do in low poker. He raked in a sizable pot and headed straight for the bank. There was grumbling around the table about “card sharps” and “mechanics” when an ex-professional wrestler by the name of Emo leaned over and picked up the nine of clubs from underneath Doyne’s chair. “I have no idea where it came from,” said Browne, “but it took a lot of explaining to make that card look less than mortal. It was time to head back to school anyway.”

  Norman Packard had also lit out for a summer of gambling, and he too was playing by the book—Edward Thorp’s Beat the Dealer, which outlines a card-counting system that Norman and a partner were implementing down at the blackjack tables in Las Vegas. After discussing the project with Ingerson and calculating the probabilities, Norman expected in two months’ play to clear a cool ten thousand dollars.

  The power of Thorp’s card-counting system lies in its comprehensiveness, which Thorp had obtained through extensive use of computer simulations. While teaching at MIT, he had programmed a mainframe IBM 704 to calculate the shifting probabilities of winning at blackjack as the deck is dealt down from top to bottom. “It would have taken roughly ten thousand man-years to do the same calculations with the aid of a desk calculator,” wrote Thorp of a machine that did the job for him in three hours.

  Thorp’s system relies on the fact that a player’s chances of winning at blackjack vary according to the cards already dealt in previous hands. The house will win more often, for instance, if the aces have been exhausted from the deck. Allowing players to take advantage of these shifting probabilities, Thorp devised a “point-count system” and “basic strategy” of optimal responses. With perfect recall and faultless play, Thorp’s card-counting strategy “is enough to give the player a comfortable 3 per cent edge!”

  Thorp promoted his book in the early 1960s with much hoopla. Using capital supplied by professional gamblers, he had sat down at the blackjack tables in Las Vegas with reporters from Time and Life at either elbow. “A Prof Beats the Gamblers” announced an article in The Atlantic Monthly, although Scientific American was less sanguine in its appraisal of Thorp’s achievement. “The system will benefit only the idle rich,” it declared. “The edge it gives the player is so small that he needs a large initial capital and a lot of time to run up substantial winnings.” Apparently, there were enough “idle rich” in the world to turn Thorp’s book into a best seller and make the casinos take precautions against card counters. The owners introduced play with multiple decks, reshuffled cards after every deal, and forcibly ejected anyone suspected of card counting—Thorp included.

  Norman knew that implementing Thorp’s system in Las Vegas would be “a nontrivial problem.” He discussed it with Len Zane, Ingerson’s brother-in-law and a successful card counter, who also happened to be chairman of the physics department at the University of Nevada in Las Vegas. Zane passed on to Norman an enhanced card-counting system, written by the pseudonymous Lawrence Revere, which was specially tailored for payability in the casinos. “How to interact with pit bosses, how to win without antagonizing the management, these,” advised Zane, “are crucial elements in any scheme.” He helped Norman develop a costume that kept his bearded face masked by sunglasses and a straw hat with pink hatband.

  As system players, neither Norman nor Doyne thought of himself as a gambler. They were scientists taking advantages of stochastic fluctuations. A gambling system, properly conceived, is anti-en-tropic. It locates fluctuating probabilities—shifts in the advantages or disadvantages of a game in play—and stores them up in small but consistent winnings.

  “When you’re operating a system,” said Norman, “you can’t be gambling. Any hint that you are means you’re not playing the system. That’s why to gamblers this approach is boring, pointless, stupid, and takes the fun out of the game. The thrill for them comes in being lucky, while for a system player there is no stroking your rabbit’s foot and getting a big kick when you win. Your behavior is completely predetermined. You should play like an automaton.”

  Norman and his partner in Las Vegas, a classmate from Reed named Jack Biles, graphed their daily progress in the casinos. “There were amazing fluctuations,” Norman discovered. “For five days straight the winnings graph would go up. We would shift to high stakes, and then the graph would go up even faster! But then invariably it sank in a slow but steady decline.”

  Near the end of the summer they visited the Gambler’s Book Club and “bought everything we could on playing cards in Las Vegas. We gradually came to the conclusion that we were being cheated. You can spot cheating by characteristic maneuvers on the dealer’s part, and when we knew what to look for we found all the telltale signs.

  “In our final tally we barely broke even. This means that our system was working to some extent, because a typical blackjack player goes to the tables and loses at a twelve percent rate, which is huge. We weren’t losing that fast, but we weren’t winning either.”

  Despondent over their bad fortune, Norman and Jack played their last hand and stopped for a drink at one of the casinos on the Strip. They sat at the bar and talke
d about the possibility of beating games other than blackjack. A bespectacled Texan with gold-rimmed glasses, Biles blinks and stutters with excitement over new ideas. Promiscuous with his suggestions, loving and leaving them without a thought, he declared, “I bet you can beat roulette using physics.” There was a long pause during which Norman stroked his beard. “You’re right,” he finally said. “Use Newton’s laws and find a way to enter initial data. It’s classic physics.”

  “In the back of his book,” Norman remembered, “Thorp announces in a cryptic sentence or two that he devised, but failed to implement, a system to beat roulette. I thought on reading this that it was utter hogwash. Roulette is a random game. You can’t devise any betting scheme that will win. But on rereading Thorp, we realized that you might be able to develop a predictive scheme, and that that’s what he was talking about.”

  Setting out to verify their hunch that roulette is a predictable game, Jack and Norman borrowed a tape recorder and stuffed it in a plastic bag. Standing next to roulette wheels in various casinos, they tapped the microphone on the tape recorder at each revolution of the ball in front of a fixed point. After transcribing these clicks onto graph paper, they found that the ball did indeed decelerate, fall off, and land in a regular way. Excited by their discovery, they thought with hindsight that blackjack and poker playing were naïve propositions. Roulette was clearly the game to beat.

  “I was supposed to rendezvous with Norman at the end of the summer and compare notes on our gambling experiences,” said Doyne. “When I met him at the Greyhound bus station in Portland he was still wearing his straw hat and card counter’s outfit. Rather than being despondent about his blackjack losses, all he could talk about was beating roulette. I told him it was a waste of time but he was so persistent he finally convinced me to think about it myself.

  “I imagined a person eyeballing the wheel and making a click as the ball passed a fixed point. I assumed a tenth of a second as a fair guess of human accuracy. Then I made some back-of-the-envelope calculations to see what error this gives in predicting where the ball will fall off. The angle of error spreads out over time, but much to my surprise, the calculations looked good. It was theoretically possible to predict the final position of the ball within a few numbers. This realization was what first got me interested in roulette.”

  Norman, Jack, and Doyne spent three days working on the problem. How were they going to clock the ball and input data? Would they keep their hands in their pockets on a switch, or use their toes? Could they get a laser to throw an infrared beam across the path of the ball? Would ultrasonic sound follow it with a kind of Doppler effect? “We tossed out a lot of schemes,” Doyne recalled, “and tentatively decided to go ahead with the project.”

  In the early division of labor, Jack and Norman undertook to build an electronic clock that would analyze their tape-recorded data. Back in Santa Cruz, Doyne and Dan Browne would study the project’s feasibility. Their initial research centered on the problems of scatter and bounce. Scatter results from the fact that roulette balls, after dropping from orbit, sometimes find their trajectory interrupted by metal diamonds attached to the sloping side, or stator, of the roulette wheel. Bounce refers to the problem of balls hopping from cup to cup on the central disk, or rotor, before finally coming to rest. Bounce and scatter tend to randomize the game, and either one, if exaggerated, could put a wrinkle in Doyne’s otherwise encouraging calculations.

  To look more closely at wheels in play, Doyne and Dan Browne drove from Santa Cruz to South Lake Tahoe. “On our maiden trip to the casinos,” remembered Browne, “our main goals were, one, to find out exactly what went on at the roulette table in a casino and, two, to make some observations—rough data taking, if you will, on the dispersion of the ball. How many cups did it tend to jump over before coming to rest? So with our notepads in hand, we stole from casino to casino, watching roulette wheels and taking down data. Doyne recorded exactly where the ball struck the numbers, and I noted which cup it actually landed in. Then we switched roles and repeated the process, until finally one or both of us had seen so many spinning wheels, red and black numbers, and little white balls, not to mention keno girls, that we couldn’t see straight.”

  “Being paranoid about collecting data in the casinos,” Doyne said, “we would remember a string of ten numbers and then duck into the toilet to write them down. Later we realized that lots of people were standing around with notebooks calculating mathematical systems, and that we looked even more suspicious running in and out of the toilet.”

  When they graphed their findings back in Santa Cruz, they discovered the possibility of gaining a clear advantage over the house. The ball is randomized by scatter and bounce, but not so randomized that predictability is eliminated. Many balls pass uninterrupted through the diamonds on the stator. Others land in a cup with nary a hesitation. Even the balls whose trajectory is altered are still fairly predictable.

  “Though crude,” said Browne, “these first data were very important. They showed that the ball bounced on average no more than a quarter or a third of the way around the wheel. If we could build a machine that could predict when a spinning ball would leave a circular track—a straightforward, although difficult, physics problem—we could beat roulette. Mind you, we were miles away from actually coming up with such a machine, but we knew it existed, at least in the realm of possibility.”

  They made another trip to Nevada the following spring. “Doyne and I took off in my Opel station wagon and headed for Paul’s Gaming Devices in Reno. We had heard that Paul built professional roulette wheels and refinished old ones, and that his wheels were the standard models used in Reno and Las Vegas. We left Santa Cruz early, got to Reno around noon, and went straight to Paul’s workshop. We gave him a phony line about needing a roulette wheel for a local fraternity party. I doubt he was fooled, although I’m certain he had no inkling what the wheel was really for. He showed us everything he had, and then we pointed to the best of the rebuilt models and said, ‘We’ll take that one.’”

  Built in Detroit, inlaid with teak, ebony, mahogany, and other exotic woods, it was a B. C. Wills regulation roulette wheel. For the wheel, a top-of-the-line model newly refinished by Paul, and a wooden shipping crate, they paid fifteen hundred dollars in cash. “He thought we were odd,” Doyne recalled, “because all we cared about was the condition of the track.”

  “Paul gave us a long spiel,” said Browne, “about what a first-class wheel we had bought, about its heritage, precision tooling, and twelve kinds of African wood—although I still think for that kind of bread it should have come with four tires and a steering wheel.”

  Back in Santa Cruz they crated up the wheel and shipped it to Portland, Oregon, where Jack and Norman were going to study it with their electronic clock. The wheel got as far as Oakland when the trucking company phoned to say there was a problem with the delivery. On driving up to the Bay Area, Doyne was met at the loading dock by two FBI agents; they said the shipping of gambling devices across state lines was a matter of interest to them. Doyne protested that a roulette wheel like this, inlaid with twelve kinds of African wood, was nothing more than a collector’s item, and convinced them to let him take it back to Santa Cruz.

  Having passed his qualifying exams the previous spring, Doyne was supposed to be researching a dissertation in astrophysics. “I was trying to figure out the question of galaxy formation in the Hoyle-Narlikar cosmology. You start with a universe and it goes blooey. You then have matter homogeneously distributed throughout, which you want to clump into galaxies. But when you calculate how fast things should clump, they don’t clump fast enough. This is the big test of a cosmology, to see if it allows for galaxy formation without having to resort to something hokey, like primordial black holes.”

  The study of physics divides into various intellectual and temperamental domains. “If you want to be on the philosophical forefront of physics,” said Doyne, “you go into particle physics. It’s the esoteric bra
nch that is also intensely cutthroat and deeply established. It is not practical. The practical people go into solid-state physics.” The least practical and most romantic of all physical domains is cosmology. Doyne later in his career would have the chance to shift from romance to revolution. He and several colleagues at Santa Cruz would find themselves at the center of what Thomas Kuhn called a paradigm shift: a radical shakeup of the very categories used to think about physics. At the moment, though, not even romance was going well. Doyne was bored with school and distracted. Far more interesting to him than Hoyle-Narlikar was the question of galaxy formation in the roulette cosmos.

  As a preceptor at Cowell College, one of the affiliated schools scattered among the redwoods at UC Santa Cruz, Doyne lived in a two-room apartment attached to a dormitory. “A big problem with doing experiments in Doyne’s rooms,” said Browne, “was how to keep the wheel hidden. We didn’t want anyone finding out what we were up to. But with people wandering in and out, it was hard to disguise an ashtray three and a half feet in diameter.”

  The problem was further complicated when Doyne’s mother came to visit for a week from Fort Smith, Arkansas, where she and her husband had moved to open a pie shop meant to capitalize on her secret recipes and his innovations in culinary engineering. As one good talker appreciating another, Dan Browne characterized Mrs. Farmer as “a nice, friendly woman, crazy as a loon, sharp as a tack, who talks a blue streak, way up into the miniwavelengths; so we weren’t sure it was the right time to clue her in to the project, especially one as bizarre as this.”