No matter how powerful a gambling system may be, there still remains the question of how best to employ it. “If you have a system that really makes forty percent, you still have to ask yourself, ‘How should I play it?’ There’s a lot of literature on optimal systems for favorable games, and the answer is not immediately obvious. Even if you have an advantage, it’s clear you don’t bet all your money at once. Because what if you lose? You’re wiped out. But on the other hand, if you bet too conservatively you may never make any money. So somewhere in between is the right way to play a winning system.”
As any gambler knows in his bones, if not in theory, you can have a crushing advantage over the house and still get cleaned out of a game. The theoretical analysis of such disasters is known as the probability of ruin. In any contest against Fortuna, favorable odds exist only in the long run, while in the short run statistical fluctuations can appear that look like vengeance incarnate. As Tom Ingerson wrote in one of his epistles to the Eudaemons, “If you’re placing $100 a shot bets while looking for a 35 to 1 payoff once in 25 rolls, the statistical fluctuations in the payoffs and the amount of money sunk into investments can get scary. You could easily get into the hole to the tune of $10,000 or $20,000, before seeing any sign that the odds, in the long run, are in your favor.”
A chart devised by Allan Wilson, the previously mentioned specialist in biased wheels, and printed in his book The Casino Gambler’s Guide nicely summarizes the probability of ruin for various games played at different advantages. Posted at the entrance to all Las Vegas casinos, Wilson’s diagram might give pause to would-be gamblers. Labeled “Chances of Success and of Ruin in Attempting to Double Your Bank on Flat-Bet Play in an Even-Payoff Game,” the chart offers a simple way to calculate how much money you need to start with, and how you should deploy it, if you want to win a game with a predetermined certainty of success.
Figure 1. A gambler’s probability of ruin.
To see how the chart works, take as an example the average Thorpian card counter who plays blackjack with a 1 percent advantage over the house. Find the curve on Wilson’s diagram representing this player’s edge of + 1 percent. Now let’s say the card counter wants to play blackjack with an 80 percent certainty of doubling his money. (He is willing to expose himself to statistical fluctuations that give him a 20 percent chance of losing his shirt.) He calculates his proper bank-to-bet ratio by locating the intersection of the + 1 percent curve and the horizontal 80 percent success line. He then drops down to the bottom of the graph to see that he should divide his bank into 70 units. A gambler betting all his money on the first draw would be playing with a bank of one unit, while a more conservative player might wish to extend Wilson’s curve and play with a bank divided into more than a hundred units.
When you look more closely at Wilson’s chart, certain aspects of it become unnerving to the professional gambler. To gain only an 80 percent certainty of success, the Thorpian card counter has to divide his bank into seventy units, and even a bank divided into a hundred units leaves him exposed to being wiped out more than once in every ten games. Unless you have a lot of money burning up your pocket, bank-to-bet ratios as low as these slow down the game, reduce the chances for a “big win,” and prove altogether uninteresting to the high roller ignorant of probability theory, and proud of it. The problem for roulette players is worse still. As Wilson’s chart pertains to “flat-bet play in an even-payoff game,” bettors playing roulette—which is not an even-payoff game—need to multiply their required banking units by thirty-five.
Wilson’s diagram becomes truly unnerving when one looks at the curves for games played at a negative advantage—which includes virtually every game played in a casino. Note in particular the curve for roulette, where the house holds an advantage over the average player that looks positively usurious. On reading a player’s probability of ruin—this time from the left side of Wilson’s chart—a startling fact comes to light. The more units into which the average roulette player divides his bank, and the longer he tries to stay in the game, the greater his probability of ruin. This leads to the following conclusion: “If you want to double your bank on an American roulette wheel,” says Wilson, “there is one and only one best bet. You must take all the money that you intend to risk at roulette during your whole life and shove it all down on one spin of the wheel on one of the even-money propositions.”
A computerized roulette player with an advantage of 40 percent can approach the game with more creative leeway, but even an edge as large as this entails a slight possibility of having the odds run against you long enough to wipe you out.
“Under the best of all possible conditions,” said Doyne, “the computer’s advantage in roulette is something like a hundred percent. You can predict where the ball will come off the track three revolutions ahead and almost always pick the right half of the wheel on which it’s going to land. A hundred percent advantage means you have a two-to-one edge over the house. If your prediction allows you to eliminate half the numbers on the wheel, the number you’re betting on is twice as likely to appear as ordinary, and you thereby double your money.
“Because of bounce and scatter and other conditions that are less than optimal, the computer’s real advantage is more like forty percent, which means that we’re shadowing, or eliminating, eight unlikely numbers from the wheel. In normal play this is a fair guess of what actually happens, and it agrees with what Thorp and Shannon found.”
The greatest possible advantage in roulette, which comes from predicting with absolute certainty one of its thirty-six numbers at each play of the game, equals thirty-six times one hundred, or 3600 percent. “Only the ultimate roulette scheme would give you a thirty-six-hundred percent advantage,” said Doyne. “That’s where you’re using a psychic, who can peer into the future and then roll time backwards.”
Intending to spend the summer in Las Vegas playing roulette, the Projectors devoted the spring of 1978 to debugging equipment and testing the system. They planned to work in rotating shifts. Having learned a lesson from the debacle of their recent trip to Reno, they would keep these groups small, well equipped, and highly trained. “We had our eyes fixed on the Nevada lettuce patch,” said Norman, “but we were going to be very crafty about getting in there to eat out of it.”
“Once the equipment was working reliably,” said Doyne, “we wanted to test the boundaries of the program so that we knew exactly how far we could push the computer. We were going to explore the envelope. The idea was to go to Las Vegas with a number of trained data takers, increase our stakes, and play the thing out.”
Scheduled to leave Santa Cruz as soon as the term ended, the Projectors were delayed nearly a month while debugging equipment. Dave Miller, a new recruit to roulette madness, came from Silver City to help out with what everyone had taken to calling “the hardware wars.” A college engineering major and former member of Explorer Post 114, Miller had gone on to achieve local fame as New Mexico’s motocross champ.
Having last seen them in Las Vegas, Tom Ingerson also arrived during the hardware wars to find his former Explorers possessed by roulette. Even while jogging along the San Lorenzo River, all they could talk about was computers and gambling. “He wasn’t what I expected,” Ingrid said of her first meeting with Ingerson. “Instead of a young, dynamic person—a real initiator in getting people to do things—he seemed like anyone else in his forties. Lonely and a little bit insecure, he was starting to develop the habits of older people. Things had to be a certain way. He got nervous around messes. He was put off by the house feeling like a camp or a football team, with everyone getting psyched up to go out there and meet the enemy. We were all using the same jargon and had the same glint to our eyes. He couldn’t get us to talk like normal people and show respect.”
Ingerson helped Norman fine-tune the receivers, while other visitors to the Riverside house got drafted into Eudaemonic service debugging and testing computers. “By the end of the hardware wars we had worked
ourselves up into a pretrip frenzy,” said Norman. “This was mingled with an exhaustion that rotted judgment.”
In the middle of June, Alan, Ingrid, Doyne, and Norman, composing the “first wave” of summer roulette players, loaded three vehicles with five computers and set out from Santa Cruz to cross the mountains and desert to Las Vegas. For transportation, they had Alan’s Triumph, along with the Blue Bus and Dave Miller’s VW van, both of which were packed to the ceiling with roulette gear and all the pots, pans, and other utensils needed for spending the summer in Las Vegas. For computers, they had Harry, Patrick, Renata, and Cynthia, as well as the KIM and its PROM burner, in case any last-minute changes were required in the program.
Heading due east from Monterey Bay into the Sierra Nevada, they spent the first night camped in the Motherlode along the Merced River. “Then we marched across the Sierras in a little caravan,” said Norman. “It was my first trip to Yosemite, and we spent a beautiful second day driving up to Tuolumne Meadows. Green and filled with mountain streams, it felt like a fairyland on top of the world.”
From there they made their way over Tioga Pass and began the long descent into the desert. Leaving behind the pine trees and meadows, they dropped down the arid flanks of the eastern slope toward Mono Lake, whose reflection glimmered on the horizon like a vast inland sea. With the sun burning overhead, they were looking forward to stopping for a swim. But the blue mirage kept receding in front of them, and when they finally reached the shore, they found only the pathetic remnant of a lake long ago sucked dry by Los Angeles. “It was nothing more than a mud flat with a little puddle in the middle full of brine shrimp,” said Norman. “But we were hot and tired, so we parked on the edge of the mud flat and walked out to the puddle to go swimming.”
Afterwards Ingrid felt sick. In the past few days she had been falling asleep at odd times and forgetting things. The Bus was already halfway to the Nevada border when she remembered leaving her wallet at Mono Lake. They turned back, only to discover later that the wallet had been in Ingrid’s backpack all along. “I got angry,” said Doyne. “I thought her being sick was psychological. I was feeling the pressure again, thinking to myself, ‘Are we ever going to get over the hump and do it?’ I was slave-driving everybody as hard as myself.”
Out in the desert on the outskirts of Tonopah, Dave Miller’s van threw a rod. It was night, and no stores were open to buy even a chain or a tow bar. At a Chinese restaurant in Tonopah, Doyne found some cowboys wearing snap-button shirts and ten-gallon hats. They didn’t have any proper rope, but one of the cowboys sold him a lariat. It was really too short for towing, except in a pinch. Norman voted to spend the night in Tonopah. Alan Lewis was noncommittal. Ingrid was asleep. Doyne insisted they shove on. After tying the van to the Blue Bus with the lariat, he and Norman worked out a system of signals for slowing down and stopping. Maybe Doyne saw the signals and ignored them, or maybe the lights of the van were too close to be seen from the Bus, but he maintained a steady sixty-five miles per hour towing Norman at the end of a five-foot lariat against his will through Scotty’s Junction, Lathrop Wells, Indian Springs, and on south through the Sonoran Desert to Las Vegas. When they stopped on the Strip, Norman’s face was white with anger.
“Usually when you make decisions with Doyne he appears to be completely rational. But this time he was just imposing his will.”
Arriving in the early hours of a June morning, they found the temperature in Las Vegas within striking distance of a hundred. They drove to Len and Jeri Zane’s house—on loan for two weeks while the Zanes were out of town—and unloaded their gear.
“In no time,” said Norman, “we had the living room and the rest of the house transformed into a junkpile of electronic parts.” When not working on the reflex tester or tweaking up equipment, the Projectors studied casinos for likely wheels. They compiled tilt histograms. They sketched floor plans and inserted them in the black three-ring notebook with separate entries for each casino. They mapped the location of bathrooms, exits, cameras. They recorded shift changes and made notes on the style of individual croupiers.
For sauntering around town, Norman bought a polyester leisure suit. “We had a problem,” he said, “in needing sports coats and sweaters to hide the computer, but here we were in the desert in the middle of summer, and it was a hundred degrees in the shade. We solved the problem by affecting the classic Las Vegas look: the leisure suit, consisting of a lightweight polyester jacket with matching pants in pastel colors. Alan Lewis already had a polyester wardrobe, but the rest of us had to scavenge through Goodwill and the secondhand shops.” Doyne sported a Mexican wedding shirt and a pair of purple knit pants inherited from Norman. Ingrid once again did her best to look alluring in her floral-print rayon blouse worn with ratted hair, makeup, and computer-padded bra.
Like other professional gamblers, the Projectors breakfasted after noon and arrived at “work” by the cocktail hour. A typical day might begin with a ninety-nine-cent breakfast special at the Golden Gate, followed by a stroll through the casinos on Fremont Street to eyeball wheels and jot notes on those that looked promising. Because it simplified the process of roulette prediction, choosing the best from among the town’s many nicely tilted wheels was worth the effort.
The Projectors scheduled two gambling sessions a day, one in the late afternoon and the other from midnight to three in the morning. This was a particularly good time to play roulette, as the casinos were relatively quiet, while a lot of wheels that would stop with the graveyard shift were still in play. Shift change times varied from casino to casino, and information such as this was carefully recorded in the black notebook. “Ideally,” said Norman, “we didn’t want to play too long on one shift, to avoid drawing attention to ourselves. So we played an hour or two on one shift and then took a break before playing the next.”
The two-person system was now perfected. Wired with the data-taking computer and transmitter, Doyne, Alan, or Norman would approach a wheel and start clocking the ball and rotor with toe clicks. Stopping along the way to adjust the program’s variable parameters, they required roughly twenty minutes to drive the computer around the mode map. They then clicked into the “play” mode.
Having given the data taker a head start, Ingrid or another bettor would arrive at the table wearing the second computer and receiver. The two players were connected primarily by radio link, but they also “talked” to each other by means of signals on the layout. A chip placed on red or black, odd or even, or the various side bets in the game might mean “take a five-minute walk,” “sit down and play,” or “raise stakes.”
It was now second nature for the four of them to walk around town wired from head to toe with microswitches, antennas, battery packs, and computers. While pumping their toes and counting solenoid buzzes on their stomachs, they could still manage to crack jokes and flirt with croupiers and hostesses. Doyne in particular was a master of casino disguises, adept at keeping his face as wide open and ingenuous as the prairie out of which he must have come. Under normal conditions, this face was animated with thought, but here in the casinos it was cleansed of expression, and those parts of it that were slightly akilter—a chipped tooth, a nose bent at the base from having been broken three times, a lopsided smile—were used to construct an impenetrable mask. Doyne resumed his southwestern twang and slipped back into the persona of New Mexico Clem, the poker sharp last seen at the Oxford Card Room in Missoula, Montana.
The Eudaemonic system demanded role playing from opposite ends of the spectrum. The data taker, while standing next to the wheel, made only insignificant bets and developed other techniques for self-effacement. The bettor, standing farther down the layout, never looked at the wheel and placed high-stakes wagers straight up on individual numbers. Between these simple differences lay an immense psychological gulf. “There is a sharp distinction here,” wrote Dostoyevsky in The Gambler, “between the kind of play that is called mauvais genre and the kind a respectable person can allow himself
. There are two kinds of gambling, one that is gentlemanly and another that is vulgar and mercenary, the gambling of the disreputable.… A gentleman, for example, may stake five or ten louis d’or, rarely more; he may however stake as much as a thousand francs if he is very rich, but only for the sake of gambling itself, for nothing more than amusement, strictly in order to watch the process of winning or losing; he must by no means be interested in the winnings themselves. When he wins he may, for example, laugh aloud, or pass a remark to one of those standing nearest to him, and he may play again, and then double his stake once more, but solely out of curiosity, to observe and calculate chances, not out of any plebeian desire to win.”
According to Dostoyevsky’s model, the Eudaemonic data taker seemed a disreputable, if harmless, player of mauvais genre, while the Eudaemonic bettor displayed only the most “gentlemanly” of attributes, including an aristocratic disdain for the spinning wheel and workings of the game. The data taker actually operated under an altogether different and, in fact, paradoxical set of constraints. His plodding attentiveness to the wheel had to be exaggerated, so that the drudgery of it appeared as something stupid or harmless.
Three kinds of people in Las Vegas stare at roulette wheels: (1) rubes off the Great Plains, (2) people who have never before played roulette, and (3) system players. Doyne, in his virtuosity, could look like any or all of the above. He could stand next to a wheel for two hours with a computer tucked under his armpit and be completely ignored by croupiers, wheel spinners, bankers, pit bosses, floormen, and cocktail waitresses—people trained expressly not to ignore anyone. Looking like the Son of Sam tuned in to voices from other planets, Doyne was an obvious case of someone with a screw loose. At other times he affected the look of a system player. He would take a pencil from behind his ear and doodle numbers in a notebook, thereby joining the well-respected company of those ignorant of the fact that no mathematical system for beating roulette exists.
The Eudaemonic Pie Page 17