When will (game) wars end?
Combinatorics
2024-03-01 v2
Abstract
We study several variants of the classical card game war. As anyone who played this game knows, the game can take some time to terminate, but it usually does. Here, we analyze a number of asymptotic variants of the game, where the number of cards is , and show that all have expected termination time of order . This is the same expected termination time as in the game where at each turn a fair coin toss decides which player wins a card, known as Gambler's Ruin and studied by Pascal, Fermat and others in the seventeenth century.
Cite
@article{arxiv.2302.03535,
title = {When will (game) wars end?},
author = {Manan Bhatia and Byron Chin and Nitya Mani and Elchanan Mossel},
journal= {arXiv preprint arXiv:2302.03535},
year = {2024}
}
Comments
10 pages, improved presentation, added background and examples