The usual way of viewing a game of roulette is as a game with a specific number of potential outcomes all of which have an equal chance of happening. There are 37 numbers including zero on a European roulette wheel (38 on the American version which has a double zero as well as a single one) and that means that, on every spin of the wheel, there is a one in thirty seven chance of any number coming up regardless of the history of the previous spins.

The famous Gambler’s Folly is to think that because a number has not come up for some time it is overdue and the likelihood of it coming up in the future will be increased. Of course that is a fallacy, but could there be more to the game than meets its simplistic statistical analysis?

Enter quantum mechanics. If you have ever watched the progression of the roulette wheel’s spin with its contrary rotating ball, then you might have been impressed of the initial smoothness of the ball’s trajectory as it is subjected to Newtonian forces until, on gradually loosing momentum and height, its descending trajectory causes it to collide with those pesky little studs designed to bring the spin to an early end.

Suddenly order descends into chaos. The ball bounces around in apparently random motion until eventually it comes to rest in one of the numbered slots.

We believe that this has an analogy in quantum mechanics. The ball in motion on the wheel may be represented by a wave function with a superposition of 37 possible states. Like Schrodinger’s cat, it is in all of the final possible states at the same time. When it collides with the first stud it is, in the quantum sense, ‘observed’ and so the wave function collapses and the ball’s value in terms of its resting slot is determined.

Of course knowing this will not help you win any more often but it does underpin that the Gambler’s Folly is indeed a folly – avoid it.

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