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Predicting a die throw

Date:
September 12, 2012
Source:
American Institute of Physics (AIP)
Summary:
By combining chaos theory and high school level mechanics, scientists reveal that the random probability of a die throw can be determined and predicted, if you precisely understand the initial conditions.

Vegas, Monte Carlo, and Atlantic City draw people from around the world who are willing to throw the dice and take their chances. Researchers from the Technical University of Lodz, Poland, have spotted something predictable in the seemingly random throw of the dice.

By applying chaos theory and some high school level mechanics, they determined that by knowing the initial conditions – such as the viscosity of the air, the acceleration of gravity, and the friction of the table – it should be possible to predict the outcome when rolling the dice.

The researchers created a three-dimensional model of the die throw and compared the theoretical results to experimental observations. By using a high speed camera to track the die’s movement as it is thrown and bounces, 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 landing on any other face. This suggests that the toss of a symmetrical die is not a perfectly random action.

“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,” said Marcin Kapitaniak, a Ph.D. student at the University of Aberdeen, Scotland. “Only a good magician can throw the die in the way to obtain the desired result.”

These results suggest that randomness in mechanical systems is connected with discontinuity as the die bounces. “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,” Kapitaniak said.


Story Source:

The above story is based on materials provided by American Institute of Physics (AIP). Note: Materials may be edited for content and length.


Journal Reference:

  1. Marcin Kapitaniak, Jaroslaw Strzalko, Juliusz Grabski, Tomasz Kapitaniak. The three-dimensional dynamics of the die throw. Chaos, 2012; (accepted)

Cite This Page:

American Institute of Physics (AIP). "Predicting a die throw." ScienceDaily. ScienceDaily, 12 September 2012. <www.sciencedaily.com/releases/2012/09/120912083526.htm>.
American Institute of Physics (AIP). (2012, September 12). Predicting a die throw. ScienceDaily. Retrieved July 31, 2014 from www.sciencedaily.com/releases/2012/09/120912083526.htm
American Institute of Physics (AIP). "Predicting a die throw." ScienceDaily. www.sciencedaily.com/releases/2012/09/120912083526.htm (accessed July 31, 2014).

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