Greedy Galois Games
Combinatorics
2011-10-07 v1
Abstract
We show that two duelers with similar, lousy shooting skills (a.k.a. Galois duelers) will choose to take turns firing in accordance with the famous Thue-Morse sequence if they greedily demand their chances to fire as soon as the other's a priori probability of winning exceeds their own. This contrasts with a result from the approximation theory of complex functions that says what more patient duelers would do, if they really cared about being as fair as possible. We note a consequent interpretation of the Thue-Morse sequence in terms of certain expansions in fractional bases close to, but greater than, 1.
Cite
@article{arxiv.1110.1137,
title = {Greedy Galois Games},
author = {Joshua N. Cooper and Aaron M. Dutle},
journal= {arXiv preprint arXiv:1110.1137},
year = {2011}
}
Comments
7 pages