“How Are You This Evening, Professor?” Asked the Roulette Croupier

When I was a graduate student doing research in experimental particle physics at the University of California in Berkeley in the 1968-74 period, I shared an office with another graduate student up on “the Hill” in Building 50B of the Lawrence Berkeley Lab.

Jerry, a sociable young researcher whose office was across the hall, was frequently at the center of conversations right outside my door. Jerry had a pretty loud voice, so I heard a lot about what he and his friends were up to. The talk might be about rock concerts or other recreational activities as well as physics shop talk. Sometimes people would go skiing, sometimes people would take a trip to the casinos in Reno, which wasn’t that far away.

At some point, Jerry and a few other junior physicists and grad students decided to apply their physics knowhow to the problem of beating the roulette tables at Reno. From my memory of Jerry’s hallway accounts, augmented a little by answers to questions I asked someone (Jerry, probably) at the time, I can sketch the outlines of how the project went.

As far as I know, they came up with their scheme independently from any previous attempts. Their idea was a sort of Gordian-knot-cutting approach that didn’t require a detailed analysis of the roulette ball’s motion. No equations of motion required!

YouTube has a collection of roulette wheel videos (mostly advertising ways to make money playing roulette!) for those of you as unfamiliar with how a roulette wheel works as I was until a few days ago or who would like to refresh your memory. The basics are the following. The croupier launches the roulette ball so that it races around a circular track that encompasses the rest of the roulette apparatus. The track is banked, and the ball is traveling along a section of the inside of a cone, but due to the ball’s high initial velocity, it hugs the wall and doesn’t start to roll downhill toward the center of the apparatus until it has slowed down substantially.

Frictional forces slow the ball down; at some point gravity has its way, and the ball rolls downhill, eventually coming to rest in one of the numbered compartments of the inner wheel. To make things more interesting the inner wheel rotates in the direction opposite to the way the ball travels around the outer circle.

I never knew the full details of their scheme, but I know that the basic premise of their method was that an essential parameter of the roulette ball’s motion followed an exponential decay law. The method depended crucially on the fact that roulette bets can still be placed for some time after the ball has been launched, which gave them a short time in which to make measurements and calculations and then place their bets based on the results.

Exponential decay of a certain variable occurs when the rate at which the variable decreases in time (decays) is proportional to the current value of the variable. The constant of proportionality is called the decay constant. For any fixed time interval (say half a second), no matter when the timer starts, the value of the decaying parameter will always be found at the end of the interval to have decreased by the very same percentage from what it was when the interval began.

The speed of the ball around the outer perimeter in the first part of the spin must have been the parameter they were focussed on, since it’s the only variable you could realistically hope to obtain in real time. What’s more, ball speed would be the crucial variable to know. If you know the value of an exponentially decaying variable (ball speed in this case) at any time, then the decay constant tells you what its value will be at any later time.

Exponential decay of the speed would imply that the the frictional force slowing the ball down was proportional to the speed. This wouldn’t have to be strictly true, just a sufficiently good approximation. Any detailed analysis of the ball’s motion would clearly be impossible in real time. Exponential decay would just be a hypothesis to test, and evidently, in the experience of Jerry and his friends, it was good enough to make money on.

They had no device for measuring speed directly. The requirement would be to time the position of the ball at three points and with sufficient accuracy to determine the decay constant. I assume a hidden programmable calculator would be used for all the calculations, since they would have had to use the measurements to solve for both the speed at some particular time and the decay constant. How they would have input this data into the calculator, I don’t know. I wish I had actually seen them in action, as it must have been fascinating. They would only have needed to determine the decay constant once for a given roulette wheel and ball combination. Then only two measurements would have been required during a spin to determine the speed at a known time.

I’m guessing that they would have used their speed formula to determine the point on the wheel at which the ball would lose contact with the outer rim and begin its descent, which would occur when the component of the gravitational force parallel to the cone’s surface became greater than the component of centrifugal force acting in the opposite direction. Yes, I know centrifugal force is not a “real” force; but, mathematically, it’s a convenient fiction for calculating when the gravitational force starts to make the path of the ball deviate more from the straight line it would follow (in the absence of wall or gravity) than it would deviate if the centripetal force exerted by the wall on the ball were acting alone.

To calculate this point would require knowledge of the angle that defines the interior conical surface on which the ball is moving, but that would either be standard or something they could calibrate from observing a few roulette spins, always assuming the method was reasonably sound. Once the descent has started, the motion is probably similar from one roulette spin to the next, even allowing for the possibility of hitting a deflector on the way down. Those occasional deflections aren’t going to make or break the method as a potential money-maker.

The roulette-beating team would have had to take into account the motion of the inner wheel as well, but that would be simply a matter of keeping track of a constant rotation. With all that knowledge they should have had an excellent chance at correctly identifying the sector (though not the exact number) the ball should end up in. They would have bet on some contiguous range of numbers, for I can’t imagine the method could have done better than that. Individual bets would not pay at long odds, but they could consistently win if they could predict the sector the ball would end up in.

After the team had advanced their technique sufficiently, they rented a roulette wheel for testing their method under realistic conditions. The method perfected, they set off for a dry run in Reno. The results of that expedition convinced them they could be making money at it even under the pressure of a casino environment. Perhaps they won a little money playing for low stakes.

I assume that on their next trip to Reno they were ready to make some real money, perhaps even to win an enormous jackpot, but I don’t know that for a fact. Inside the casino, it was soon apparent that things were not going to go well. Jerry was greeted with “How are you this evening, Professor?” Now even though this was not 100% correct about Jerry’s job title, it was enough to indicate some serious intelligence work on the subject of who he was, and it conveyed very adequately the desired message of “We know who you are and what you’re up to.”

Whether Jerry and his friends decided to leave on their own then or were escorted out, I can’t say. I do know that they were joined in the parking lot by some professional intimidators, who made it clear they had better not come back. So ended the story of the Lawrence Berkeley Lab roulette scheme, or at least the last I heard of it.

Jerry, if you should by some amazing accident stumble upon this article, I ask you to write up your experience, as I’m sure it would be very entertaining. Send it to me by email, and I will post it (without revealing your full name if you prefer) if you can’t think of a better outlet. Of course, Jerry may be the one with the magnificent Tuscan villa I imagined for Bob in my previous post, in which case he will not want to give away any trade secrets.

Also, if anyone makes a fortune from the secrets revealed in this post, please don’t forget to come back and make a donation. Just remember I don’t condone breaking any laws, and I believe there are now laws about using any sort of computer in a gambling casino, at least in the most up-to-date jurisdictions.

Finally, let me propose that the Department of Homeland Security could benefit from hiring a few people that work in casino security. They know how to identify suspicious characters and follow their moves to see what they are up to. And they don’t waste time with random searches.

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