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.

   

Article: “The three-dimensional dynamics of the die throw” is accepted for publication in Chaos.

Source: American Institute of Physics