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Theory

When a roulette ball is launched by the croupier it first spins around the rim of the wheel until gravity pulls it down from its track and it spirals into the spinning rotor, usually colliding with one of the vertical or horizontal vanes along the way. This last part of the journey, when the ball is scattered because of the deflectors and then bounces on the rotor before finally coming to rest in one of the numbered pockets makes the game of roulette appear totally random.

However, if we take a closer look at the skip=scatter+bounce behaviour of the ball we find that on most wheels there is some kind of structure. The above graph shows a typical skip-statistic obtained from 50 spins on our roulette wheel in the following way: for each spin we recorded the number N1 on the rotor which was under the ball at the moment the ball hit one of the deflectors. Then we noted the winning number N2 when the ball had come to rest in one of the pockets and calculated the skip distance as the number of pockets between the numbers N2 and N1. As can be seen on the above graph, there is a cluster between the skip distances of 8 and 20 pockets with a mean value of about 16 pockets.

Now, if we could have predicted with 100% certainty which number was under the ball at the moment the ball collided with a deflector and used the mean skip value of 16, we would have had the following favorable situation: if we would have bet 1$ on each number of a 5-number sector around the number predicted by this method, then in 50 spins we would have invested a total of 250$ and won 12 times 35$ = 420$, which amounts to a return on investment of 68%. This payout situation is typical for European casinos (where the bet of the winning number goes into the "tronc", i.e. is a compulsory tip for the croupiers).

If in practice we can only predict with 75% certainty the number which is under the ball at the moment of collision, then in the above example we would "only" win 9 times 35$ = 315$, amounting to a 26% return on investment.

In the (copyrighted) technical article RoulettePhysics (PDF-file) we describe the theory of physical roulette prediction and you can put our theory to the test with our roulette predictor program which you can download and run on your own system.

There is also a companion article with the title RoulettePhysics: Basic Insights and Sensitivity Analysis which explains in more detail some of the key issues of roulette prediction in order to obtain a working solution!