DisCoMath Seminar: Numerically Balanced Dice
Discrete & Computational Math Seminar (DisCoMath)
Numerically Balanced Dice
John Mooney
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This seminar may be attended in person in 3305 Gosnell Hall or online via Zoom.
Abstract:
Dice can only be fair in theory due to various physical imperfections that inevitably occur during manufacturing processes. A die is considered numerically balanced despite physical imperfections when the numbers assigned to its faces satisfy sets of linear constraints to preserve a fair die's expected value. The existence of numerically balanced dice was first confirmed in Bosch et al. using integer programming techniques to find balanced numberings of the d20, d30, and d120. We explore how to answer questions regarding uniqueness (up to isomorphism) of some isohedra suitable for use as fair dice. In this talk, we discuss the combinatorics involved to make the problem more computationally tractable and as well as approaches that eliminate the need for computation altogether. We present 5 new non-isomorphic numerically balanced numberings of the d20 (regular icosahedron).
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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