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arXiv · 2201.07004

Snakes and Ladders and Intransitivity, or what mathematicians do in their time off

Gregory B. Sorkin
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Abstract

This recreational mathematics article shows that the game of Snakes and Ladders is intransitive: square 69 has a winning edge over 79, which in turn beats 73, which beats 69. Analysis of the game is a nice illustration of Markov chains, simulations of different sorts, and size-biased sampling. Connecting this to "intransitive dice" illustrates the power of a name, and the joy of working with colleagues. When draws do not count, we show a minimal example of intransitive dice, with one die having just a single "face" and two dice each having two faces.

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Gregory B. Sorkin. 2022-01-13. Snakes and Ladders and Intransitivity, or what mathematicians do in their time off. https://arxiv.org/abs/2201.07004

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