When Will (Game) Wars End?
Name
When Will Game Wars End .pdf
Description
Published version
Size
719.78 KB
Format
Adobe PDF
Checksum (MD5)
79d7ad8db42cefaf367e116fc210bc37
Author(s)
Bhatia, Manan
Chin, Byron
Mani, Nitya
Mossel, Elchanan
Date Issued
January 2, 2026
Journal
The American Mathematical Monthly
Publisher
Taylor & Francis
Citation
Bhatia, M., Chin, B., Mani, N., & Mossel, E. (2026). When Will (Game) Wars End? The American Mathematical Monthly, 133(1), 35–46.
Version
Final published version
Abstract
We study several variants of the classical card game war. As anyone who has 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 n, and show that all have an expected termination time of order 𝑛2. This is the same expected termination time as the game where at each turn a fair coin toss decides which player wins a card, known as Gambler’s Ruin and was studied by Blaise Pascal, Pierre de Fermat and others in the seventeenth century.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivatives
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/00029890.2025.2572283
