A complete solution for the partisan chocolate game
Combinatorics
2023-10-23 v1
Abstract
The class of Poset Take-Away games includes many interesting and difficult games. Playing on an -dimensional positive quadrant (the origin being the bottom of the poset) gives rise to nim, wythoff's nim and chomp. These are impartial games. We introduce a partisan game motivated by chomp and the recent chocolate-bar version. Our game is played on a chocolate bar with alternately flavored pieces (or a checkerboard). We solve this game by showing it is equivalent to blue-red hackenbush strings. This equivalence proves that the values of game are numbers and it gives an algorithm for optimal play when there is more than one chocolate bar. The checkerboard interpretation leads to many natural questions.
Keywords
Cite
@article{arxiv.2310.13559,
title = {A complete solution for the partisan chocolate game},
author = {Tomoaki Abuku and Hikaru Manabe and Richard J. Nowakowski and Carlos P. Santos and Koki Suetsugu},
journal= {arXiv preprint arXiv:2310.13559},
year = {2023}
}
Comments
21 pages, 9 figures