Researchers Say a Roll of the Dice is Not Truly Random, But Is Still Nearly Impossible to Predict

Posted on September 15, 2012

Researchers from the Technical University of Lodz, Poland and University of Aberdeen, Scotland, say a die throw is not random. They say a roll of the dice can be predicted using chaos theory and some initial conditions such as the viscosity of the air, the acceleration of gravity, and the friction of the table. This information is typically not something someone playing Dungeons & Dragons or craps at the casino will have at their disposal.

The researchers built a three-dimensional model of the die throw and compared the theoretical results to real world observations with a high speed camera. The camera tracked the die's movement as it was thrown and bounced. The researchers say they found "the probability of the die landing on the face that is the lowest one at the beginning is larger than the probability of it landing on any other face."

Inside Science reports that the researchers found the cameras found the dice frequently kept the same face even after bouncing. They also found that the "top face will always be more probable." The researchers say this suggests that the toss of a symmetrical die is not a perfectly random action.

Marcin Kapitaniak, a Ph.D. student at the University of Aberdeen, Scotland, said in a statement, "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. Only a good magician can throw the die in the way to obtain the desired result. When the die bounces on the table, it is more difficult to predict the result than in the case of a die landing on the soft surface."

Pips in the dice also play a role as previous dice rolling studies have shown. The video below is an automated version of W.F.R. Weldon's 1894 study where he rolled a set of dice 26,306 times. Take a look:

The article, "The three-dimensional dynamics of the die throw," by Marcin Kapitaniak, Jaroslaw Strzalko, Juliusz Grabski and Tomasz Kapitaniak, has been accepted for publication in Chaos.