Small recorded on a computer the times at which the ball and a specific part of the roulette wheel passed a fixed point on the frame supporting the wheel. The pair tested their model on a standard casino roulette wheel installed in Tse's laboratory. "Then we make a guess as to what portion of the wheel the ball is likely to land in." "We extrapolate that prediction to the point where the ball hits one of the deflectors - the raised bumps in the wheel's rim that are added to increase the random bouncing of the ball," Small explained. They wrote down equations to predict the path the ball would take once the croupier releases it. Small and Tse used high-school calculus and physics - specifically, the branch known as classical mechanics - to develop their model. substantially enhance returns," the two researchers reported in the journal Chaos. "A very slight slant in the roulette table, could. But for gamblers it presents the obvious problem of how to conceal the equipment in a security-conscious casino.Īnd yet another factor increased the chances of beating the house even further. The other approach, using a digital camera mounted above the wheel to obtain the same data, provided better predictions. casinos, the odds tilt further in the house's favor because the wheel contains one extra space. In experiments on a roulette wheel in a laboratory, the method produced predicted earnings of almost 20 percent instead of the expected loss of about 2.7 percent for a European-style wheel. The simpler method the pair tested involves careful observation and recording of the initial conditions by an individual or team of players. "In some cases you can beat them quite significantly." "Knowing the initial conditions allows you to beat the odds," said Michael Small, a statistician at the University of Western Australia in Perth, who carried out the study with Chi Kong Tse of Hong Kong Polytechnic University. The key, the modelers found, is knowing the precise location of the ball and the relative speeds of the ball and wheel when the croupier - the casino worker in charge of the game - sets the wheel in motion and releases the ball.
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