“The gambling is all run by the Mafia, and it’s their best business. Who knows what makes people do it? It’s an animal instinct, an atavistic trait, a disease. Sitting there in the middle of it is like being on Forty-second Street at Grand Central Station. You see every kind of person in the world. They drop all pretense. They mouth their incantations over the roll of the dice or the card on top. It exceeds all other levels of reality. It’s naked reality. I mean the casinos are so bad and greedy—screaming about every nickel they lose, while cheating and robbing people blind—that to beat them at their own game is a white knight operation.”
After Reagan moved up to national politics, Abraham returned to California. “I’m a contactee, an astral projector into alternate realities, a listener to radios from other planets, and it was a bit odd,” he said, “being back at the university. My specific goal is to revolutionize the future of the species. Mathematics is just another way of predicting the future.”
The three of them later became good friends, but Doyne and Norman hesitated before talking to Abraham about the Project. Who knew what alternate reality he might make of it? Indeed, their first meeting went rather badly. “I studied their algorithm, and it looked like it would do,” said Abraham. “I reviewed their statistics, the fatigue factor, the equipment they’d put together, and it too looked like it would work.
“But they had no concept of casino security. They thought they could swap battery packs and equipment in the hotel toilets, which are monitored, of course. I thought the consequences could be severe if they were caught. Ken Uston was in the hospital at the time, having reconstructive surgery done on his face.
“I tried to warn them in that first meeting about the dangers of detection. They said their technology was too sophisticated. I believed they’d give themselves away. They thought I was paranoid. I thought they were conceited. I told them their best bet was to sell the computer to somebody who knew what he was doing.”
5
Debugging
Things are not as simple as they at first seem.
Edward Thorp
After a year of building computers, transmitters, receivers, shockers, and the biofeedback device, Eudaemonic Enterprises paused for a spring party also meant to celebrate Letty’s graduation from Stanford Law School. Entitled “Come as You Are in 1997,” the party was projected as the twentieth class reunion for the Class of 1977—a time warp into which costumed participants would slip for a peek at themselves on the brink of the third millennium.
Norman made a 1997 calendar to hang in the hall and unfurled a “Welcome Class of 1977” banner over the front door. (The banner drew several confused participants from off the street.) All the rooms in the house were made over and dedicated to one form or another of pleasure. The living room was wired with strobe lights and turned into a discotheque. A movie room showed nonstop Abbott and Costello films and abstract color field productions by Larry Cuba. An R&R room was lit with candles, and another chamber had been converted into a tactile room modeled on the Exploratorium in San Francisco. Completely darkened and lined with mattresses, the room and its walls were covered with everything from salami to fur.
Doyne’s bedroom, renamed the Neural Stimulation Room, was converted into a shrine commemorating the excesses of the 1960s. Set up on an altar surrounded by signs referring to the days “when hippies used to sear synapses and pulverize pain with mind-expanding drugs” was a Jacob’s ladder, with electric current arcing up it, and a bowl full of Kool-Aid punch.
The Neural Stimulation Room also featured Doyne’s biofeedback device, which was appearing in public for the first time as a reflex tester. Set up on a bicycle wheel and operated by hand rather than toe switches, it otherwise employed the KIM computer and the same system of photocells wired into an electronic circuit.
Other equipment from the Project surfaced during the party. Dressed as a 1997 hipster, a bearded Norman wore a red headband, a burnoose that floated around him like a dress, and an LED necklace made from flashing diodes and a prism. “That’s an example of an idea from which I could have made millions,” he said. “But, alas, it’s just one of those things I never got around to marketing” Appearing as Tom Terrific, Doyne sported a red leotard and cape, with a Peruvian medallion around his neck and a metal funnel for a hat. A light bulb on top of the hat, activated by one of the Project’s toe-operated microswitches, lit up whenever he had an idea.
Many people pictured themselves in 1997 with extra organs and mutations. One guest showed up with a fully developed third eye made from a roulette ball. The first photosynthetic human came covered with green veins and leaves. Wearing a loincloth and burlap sack, with fetishes decorating his neck, Dan Browne arrived as a post—World War III cave man. Letty zipped around on jet-powered roller skates. Bruce Rosenblum, a physicist at the university, wore a Mexican cut-away jacket and a cone on his head covered with Maxwell’s equations. Another professor, aged with charcoal creases and false breasts, came as Tiresias. Juano, dressed in a white robe and carrying a silver wand topped by a flashcube, kept himself enveloped in a cloud of gaseous nitrogen.
Many danced until dawn, while others emerged sheepishly from the tactile room late the following day. In the course of the evening, the reflex tester flunked everyone. “There was no doubt,” said Norman, “that a lot of stuff consumed at the party was bad for your motor coordination.”
“After Doyne finished programming the computer,” Norman confided, “we thought it would be a matter of weeks before the money started rolling in. Once the program was finished, let’s face it, that’s the main thing. The Project was done in principle.”
For an impeccable optimist like Norman, Project Rosetta Stone was already a fait accompli with roulette wheels knocked off all the way from Monte Carlo to Macao. “It took us a while after that before we actually got in the casino, but as far as our state of mind went, all we had to do were a few little things and tsweeet“—he makes a noise with his tongue expelling air through his lips—“we’d be in there, no prob.”
Doyne was equally buoyed, until he became suspicious late in the spring that something somewhere was not working right. Word having gone out that a trip to Nevada was imminent, Jack Biles had come down from Oregon for a marathon session of hardware building. But beyond the usual problems in getting hardware soldered together and running, Doyne began to suspect that something might be wrong with the computer program itself.
“The big push during the spring and summer,” he said, “was to get the program to predict roulette in real time.” He went back to plotting histograms, filling sheets of paper with graphs showing the frequency with which the computer’s predictions matched the ball’s actual behavior. “I remember sitting there and taking histogram after histogram and not having any advantage. I got worried enough at that point to develop three alternate systems for prediction.”
Doyne thought the problem with the computer program might lie in the fact that roulette wheels possess varying degrees of tilt, some being relatively flat, most being tilted several degrees, and others resembling the Andrea Doria ten minutes after the final call to abandon ship. He wrote algorithms to cover these varying conditions and programmed the KIM to play roulette with three different sets of equations.
Unbeknownst to Doyne, two of these three algorithms had already been identified by Edward Thorp when he and a partner—mysteriously left unnamed for many years—tried but failed to implement a computerized roulette system in the early 1960s. One reason for his difficulties lay in the fact that Thorp’s system possessed a limited number of adjustable parameters. The player, for instance, had to guess the exact number of revolutions remaining before the ball fell off the track. Another reason for Thorp’s disappointment—one entirely beyond his control—stems from the fact that the microprocessor had not yet been invented. Carrying pre-cursor technology into the casinos, Thorp had had to work with approximations rather than precise equations, which, even if they had been known to him, would have
been unsolvable by his computer.
Although Thorp’s roulette system had been mentioned earlier in Beat the Dealer, its details were first revealed in a technical paper published in 1969 in the Review of the International Statistical Institute. This is not a journal commonly read by either physicists or gamblers, and few among the latter would have understood Thorp’s equations anyway. So even after this breach of secrecy, the theory of roulette remained esoteric knowledge.
“Our basic idea,” wrote Thorp—referring to himself and his unnamed partner—“was to determine the initial position and velocity for the ball and rotor. We then hoped to predict the final position of the ball in much the same way that a planet’s later position around the sun is predicted from initial conditions, hence the nickname ‘the Newtonian method.’”
As too many variables in the game lay beyond the scope of Thorp’s linear approximations to its nonlinear equations, he and his partner abandoned the Newtonian method and developed an alternate approach that they called the quantum method. This took advantage of imbalanced roulette wheels and the fact that even a slight amount of tilt greatly simplifies one of the variables in roulette prediction: locating the point on the track from which the ball will fall and begin its spiral down to the rotor. On tilted wheels the ball races around the track at varying velocities. It alternately slows down and speeds up as it approaches and passes the high side of the wheel. Under these conditions the ball tends to come off the track when slowed for its climb up to the high side. Once over the hump and gaining in velocity, it hugs the track through a stretch Thorp called the forbidden zone.
The presence of tilt in a roulette wheel also adds a neat twist to the physics of the game. It allows for quantizing, or clumping into discrete sets of values, the position and velocity of balls coming off the track. Thorp explained the logic of the quantum method as follows: “Suppose the ball is going to exit beyond the low point of the tilted wheel. Then it must have been moving faster than a ball exiting at the low point, so it reaches its destination sooner. But it has also gone farther, and the two effects tend to cancel.”
With these differences offsetting each other, Thorp realized that balls exiting from a discrete section—or quantum—of the track will all tend to strike the rotor at the same point. The more tilted the wheel, the “more sharply bunched or focused” will the balls be when they hit. Estimating that more than a third of the roulette wheels in Nevada had the required tilt of at least two degrees, Thorp calculated an advantage for the quantum method of over 40 percent. This is a tidy return on an investment that can be made and paid off every minute and a half!
Because of its relative obscurity, Doyne read Thorp’s essay—on learning about its existence from Ralph Abraham—only after developing his own roulette algorithms. Having independently arrived at the same conclusions, including the importance of tilt for predicting the outcome of the game, Doyne nonetheless adopted Thorp’s terminology. He appreciated how nicely it recapitulated the history of physics. “In the Newtonian method you assume there is a continuum of positions from which the ball can come off the track. Newton thought that all of physics could be described by such continua. When quantum mechanics overthrew the Newtonian picture, you could no longer assume the existence of a continuum, and what you had instead was matter broken up into quanta, or indivisible chunks.”
By the time he read Thorp’s article, Doyne had already organized the Newtonian and quantum methods into equations, which he solved for the first time with the aid of the Project’s digital computer. He had also developed a third differential equation for describing roulette. Called the post-Newtonian method, it was meant for use on wheels intermediate in tilt between the flat and the rakish.
“At one point I contemplated writing an article on roulette algorithms and the physics of roulette balls for Physics Today. I imagine,” he said with a smile, “that I’m the world’s expert on the subject.”
Working with the KIM computer in his bedroom, where it was set up on the picnic table next to the roulette wheel, Doyne began to get worried when he could get none of his three equations to work well in real time. They looked good on paper, but up against the wheel they gave only a slender advantage.
“I was being overly ambitious,” he said. “I wanted to beat every possible roulette wheel. Some are going to be very tilted, some flat, and a lot in between, and the idea was to walk up to any one of them and be able to play.
“But I began to realize how long this thing was dragging on. I couldn’t afford to spend months developing fancy algorithms to predict roulette when I didn’t even have one that would work on highly tilted wheels, which are the easiest of all. Late that spring I got really nervous that the whole thing was just not working, that there was a flaw in the basic idea that we weren’t taking account of. Maybe the ball was bouncing around on the track too much. It was jittery and somehow blowing the predictability.
“We still had data stored in the campus computer; so I went up to the university to try out the algorithms. No matter how I fiddled with the equations, the data on campus just didn’t seem to work right. I did several experiments and got really depressed. It looked as if it might have been a fluke that we had gotten any advantage at all. At that point, I knuckled down and said, ‘O.K., let’s just go for the simplest thing. Tilt the wheel like hell, enter two clicks, and see if we can predict where the ball is going to fall off.’”
Doyne spent the entire summer reprogramming algorithms that failed to beat the roulette data stored in the campus computer. The Project at this point came to resemble an intensive language course in cuneiform. Written in floating-point binary arithmetic—the machine language understood by the KIM computer—Doyne’s roulette program had grown to four thousand instructions. Reproduced longhand, it took fifty pages of binary numbers to label every location in the program. Each label, or address, in this string of numbers represented eight bits. The on-off orientation of a bit can also be represented by an electronic tone sounding either “high” or “low,” which allowed Doyne to store these fifty pages of numbers in a tape recorder. When played back, these tones, sounding like the gibberish of a speed freak gone astral, filled ten very long minutes of tape.
Without high-level languages or other aids for traversing the fifty pages of a machine code program, Doyne struggled through them on guts alone. In the beginning he had had no choice. Fresh from the factory, the KIM got programmed in machine language, or not at all. Software tools known as compilers and assemblers can gather together machine code instructions and greatly simplify the process of programming a computer, but by the time hackers had developed them for the 6502 microprocessor, Doyne, strapped for money, decided against the investment.
On passing the bar exam, Letty took a job in Los Angeles at the Center for Law in the Public Interest, where she was offered the chance to work on the environmental and political cases that interested her. “We drove to Los Angeles and stayed with friends for a few days,” Doyne said. “We wanted to check it out and decide if human beings could survive there. And then later in the summer I drove Letty down with all her belongings and helped her find a place to live.”
On returning to Santa Cruz, Doyne sat down to look again at the roulette program. It was still not working right. Something, somewhere, was preventing it from attaining the accuracy it theoretically possessed.
At Ralph Abraham’s suggestion, Doyne phoned Edward Thorp, who was then teaching at UC Irvine. They discussed casino security, and not the technicalities of the program itself, but this was the first of several brief encounters that Eudaemonic Enterprises would have with Thorp.
“Ralph convinced us,” said Norman, “that Thorp was basically on our side in wanting to see the casinos beaten. He wouldn’t give us away; he wasn’t a casino man. Ralph also thought that if there were other systems being developed, Thorp would be the most likely person to know about them. We were interested in finding out if we had any competition. We also wanted to hear why Thorp had quit, i
f he had quit, and what the story was.”
Thorp reassured them that a system such as theirs was workable in the casinos and that he himself had not met with any undue suspicion while using his computer in Las Vegas. He briefly discussed the reasons for his limited success, which he ascribed to hardware problems. “But he was vague,” said Doyne, “about whether he or other groups were working on roulette—quite vague.”
Back from his year in Chile and a trip around the world, Tom Ingerson showed up in Santa Cruz late that summer. While jogging several miles a day on the levees along the San Lorenzo River, he and Doyne talked about bugs in the program and other problems in getting the radio receivers to work properly. Ingerson came up with several helpful ideas, including a scheme for making the computer program “smart” enough to filter errors out of its signals. But his relationship to the Project was basically ambivalent. His sister and brother-in-law lived in Las Vegas, and he had spent a fair amount of time with them out in the desert. He had watched Len Zane dabble in card counting and then lose his nerve one day when a pit boss at the Sahara put his hand on Zane’s shoulder and said he should take his business elsewhere. Like Ralph Abraham, Ingerson thought the consequences could be serious for someone discovered in the casinos wearing a computer.
In the meantime, Doyne was spending long days laboring alternately on the KIM and the university’s PDP 11/45. “By the end of the summer,” he said, “I still couldn’t get the program to work right.”
He went back to look again at the feasibility studies done the previous summer. These measurements of the game in play had been fed into the university computer and then modeled into the simulations on which he had based his algorithms.
The Eudaemonic Pie Page 11