Simple model for dice loading

Details Simple model for dice loading Simple model for dice loading

Mar 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010njph...12c3016n&link_type=abstract

New Journal of Physics, Volume 12, Issue 3, pp. 033016 (2010).

Physics

1

Scientific paper

Dice tossing is commonly believed to be random. However, throwing a fair cube is a dissipative process that is well described by deterministic classical mechanics. In Nagler and Richter (2008 Phys. Rev. E 78 036207; featured in 2008 Nature 455 434), we proposed a simplified model to analyze the origin of the pseudorandomness: a barbell with two masses at its tips with only two final outcomes. In order to keep things simple, we focused on the symmetrical case of equal masses. Here, we complete the picture by considering the general asymmetric case of unequal masses. We show how, depending on the initial conditions, dissipation during bounces, and mass asymmetry, the degree of unpredictability varies. Our analysis reveals, for the simplest possible non-trivial dice throwing model, the effect of dice loading. A surprising consequence of dynamical resonances is that an experienced player may benefit sometimes more from an unloaded than from a loaded barbell. In addition, we investigate the influence of loading on the symmetry breaking process causing one mass to come to rest earlier than the others.

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