The (s, t)-Wythoff's Game under Misère Play Convention

Abstract

A.S. Fraenkel introduces a new (s, t)-Wythoff's game which is the generalization of both a-Wythoff's game and Wythoff's game. Fraenkel determines all P-positions of (s, t)-Wythoff's game under normal play convention. In this paper, the (s, t)-Wythoff's game under the misere play convention is investigated. Both the set of all P-positions and optimal strategies are given. Our results also provide answers to a-Wythoff's game and Wythoff's game under the misere play convention.