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Cuboidal dice and Gibbs distributions

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Abstract

What are the face-probabilities of a cuboidal die, i.e. a die with different side-lengths? This paper introduces a model for these probabilities based on a Gibbs distribution. Experimental data produced in this work and drawn from the literature support the Gibbs model. The experiments also reveal that the physical conditions, such as the quality of the surface onto which the dice are dropped, can affect the face-probabilities. In the Gibbs model, those variations are condensed in a single parameter, adjustable to the physical conditions.

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Acknowledgments

The authors thank Robert Allin for valuable discussions about an earlier version of this paper. D.O. acknowledges the discussions with Nick Jones.

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Authors and Affiliations

  1. Zentrum für Lehrerbildung Köln, August-Bebel-Str. 80, 50259 , Pulheim, Germany

    Wolfgang Riemer

  2. Institut für Stochastik, TU Bergakademie Freiberg, 09596 , Freiberg, Germany

    Dietrich Stoyan

  3. International Centre for Radio Astronomy Research, M468, University of Western Australia, 35 Stirling Hwy, Crawley, WA, 6009, Australia

    Danail Obreschkow

Authors
  1. Wolfgang Riemer
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  2. Dietrich Stoyan
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  3. Danail Obreschkow
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Corresponding author

Correspondence to Dietrich Stoyan.

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Riemer, W., Stoyan, D. & Obreschkow, D. Cuboidal dice and Gibbs distributions. Metrika 77, 247–256 (2014). https://doi.org/10.1007/s00184-013-0435-y

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  • DOI: https://doi.org/10.1007/s00184-013-0435-y

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