$m$-Modular Wythoff

Abstract

We introduce a variant of Wythoff's Game that we call $m$-Modular Wythoff's Game. In the original Wythoff's Game, players can take a positive number of tokens from one pile, or they can take a positive number of tokens from both piles if the number of tokens they take from the first pile is equal to the number of tokens they take from the second. In our variant, we weaken this equality condition to one of equivalence modulo $m$. We characterize the P-positions of our $m$-Modular variant as a finite subset of the P-positions of the known P-positions of the original Wythoff's Game.