How to pick your football team
Combinatorics
2026-05-06 v1
Abstract
Team captains Alice and Bob divide up footballers, each reduced to a real-valued score, into two teams of footballers each. On each turn, one captain plays picker, and the other chooser: the picker names a footballer yet to be selected, and the chooser decides which captain's team receives that footballer. Alice starts as picker, Bob as chooser, and roles alternate. The game ends as soon as either captain has a full team of footballers, at which point the other team receives all remaining footballers. The team with the larger sum of scores wins. Settling a problem raised by Eccles in 2015, we show that Alice cannot win.
Keywords
Cite
@article{arxiv.2605.04034,
title = {How to pick your football team},
author = {Bhargav Narayanan},
journal= {arXiv preprint arXiv:2605.04034},
year = {2026}
}
Comments
11 pages