News in Science

Physics unlocks the secrets of roulette

Shortening the odds Thinking like a physicist can improve your chances of winning at roulette, say researchers.

A paper in a recent issue of the journal Chaos shows how a computer program can be used to give an expected return of at least 18 per cent, instead of the usual -2.7 per cent.

"It's a fairly simple model that we're using and the result we get is the one you would expect to get," says lead author, mathematician Professor Michael Small of the University of Western Australia.

"What's interesting is showing it can be done and the extent to which you can make a profit from it."

In the game of roulette, a ball spins around on the rim of a wheel in the opposite direction to the direction the wheel is spinning.

Eventually it rolls out of the rim, hits one of a number of deflectors and starts chaotically bouncing about.

Small says knowing where the ball starts bouncing and which deflector it hits is key to narrowing down which of the 36 squares (in a casino-grade European roulette wheel) it will eventually come to rest in.

Over the years there have been reports of people using technology - from lasers to computers in the heels of their shoes - to detect the movement of a roulette ball and calculate its likely resting point.

But, says Small, this is the first scientific paper to demonstrate how such a method can work.

Roulette model

Small and colleague Dr Chi Kong Tse of the Hong Kong Polytechnic University developed a simple model for the motion of a roulette wheel and ball.

They showed that if you know the initial position, velocity and acceleration of the ball you can narrow down where it's going to land, thereby increasing the odds of winning.

Small says he developed his own "shoe computer" that could record (with the click of a button) every time the ball passed a certain point on the wheel.

This in turn could be used to predict when the ball would start bouncing and which subgroup of roulette squares it would end up in.

"As the wheel is moving at a constant angular velocity, the ball is decelerating the time interval between these passes at a particular point are going to get longer," he says.

"If you measure that three times you can estimate velocity and deceleration."

Improving the odds

Small says the odds are usually stacked against you when playing roulette.

"On average, you're going to lose money, which is what you would expect. Casinos make money because, on average, you lose money," he says.

But his system allows a player to improve the odds of winning.

"We demonstrate an expected return of at least 18 per cent, well above the -2.7 per cent of a random bet," says Small.

He says this means every time you bet $1, on average you will get $1.18 back instead of the standard odds of getting 97.3 cents back after betting $1.

"If you keep playing for long enough and you have got enough money you will come out ahead," says Small.

Small got even better returns in a bigger experiment using a digital camera and image processor to track the ball and wheel.

Small says the model would still need fine tunings and that it may even be possible that smart phone apps could even be used in the future.

But using such a device would raise the ire of a casino.

"I'm not a lawyer but in most jurisdictions it's not really a legal matter," says Small. "It's just a matter of you playing a game and breaking the rules that the casino would like you to be obeying."