Betting On Physics: Researchers Use Math To Predict Dice Rolls

A group of scientists from the Technical University of Lodz in Poland and the University of Aberdeen in Scotland have created a three-dimensional model to describe a die roll. In a paper forthcoming in the journal Chaos, they describe how it is possible to predict the outcome of a dice roll.

 "Generally, it is assumed that when we toss a coin, throw a die or run a roulette ball this condition is fulfilled and all predictions have to be based on the laws of large numbers," the authors write. "In practice, the only thing one can tell with a given degree of certainty, is the average outcome after a large number of experiments."

But, the researchers say, the dynamics of a coin, die or roulette ball can actually be described by equations of motion.

All you need to know are some of the initial conditions before the toss is made: how viscous the air is, what the friction of the table is, and a figure representing the acceleration of gravity -- which until Richard Branson opens a low-orbit casino will pretty much always be 9.8 meters per second squared. Add a bit of chaos theory, and voila!

Lead author Marcin Kapitaniak and his colleagues created a 3-D model of a die throw -- using some rather complex mathematical equations -- and compared theory to reality, using a high-speed camera to take video of actual die throws.

In their model, the researchers found that the die tends to land on the face that was lowest at the beginning of the throw. They also found that a bouncing die is much more difficult to predict which way it will roll than one that lands on a soft surface.

But before you rush out to catch that flight to Vegas or Monaco, a bit of caution. Translating theory into a sure-fire strategy for beating the house is a difficult prospect since the math may be perfect, but your aim probably isn't.

"Theoretically the die throw is predictable, but the accuracy required for determining the initial position is so high that practically it approximates a random process," Kapitaniak said in a statement Wednesday. However, "only a good magician can throw the die in the way to obtain the desired result."

SOURCE: Kapitaniak et al. "The three-dimensional dynamics of the die throw." Chaos in-press.