How random is dice tossing?

@article{Nagler2008HowRI,
  title={How random is dice tossing?},
  author={Jan Nagler and Peter H. Richter},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={78 3 Pt 2},
  pages={
          036207
        }
}
  • J. Nagler, P. Richter
  • Published 2008
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
Tossing the dice is commonly considered a paradigm for chance. But where in the process of throwing a cube does the randomness reside? After all, for all practical purposes the motion is described by the laws of deterministic classical mechanics. Therefore the undisputed status of dice as random number generators calls for a careful analysis. This paper is an attempt in that direction. As a simplified model of a dice a barbell with two marked masses at its tips and only two final positions is… Expand

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References

Vulovi ć and R . E . Prange
  • Phys . Rev . A Phys . Rev . A Phys . Rev . A Phys . Rev . E Chaotic Dynamics . An Introduction Based on Classical Mechanics
  • 2006