Snakes and Ladders and Intransitivity, or what mathematicians do in their time off
History and Overview
2022-01-19 v1 Probability
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.
Keywords
Cite
@article{arxiv.2201.07004,
title = {Snakes and Ladders and Intransitivity, or what mathematicians do in their time off},
author = {Gregory B. Sorkin},
journal= {arXiv preprint arXiv:2201.07004},
year = {2022}
}