Restrictions of a-Wythoff's Game

Abstract

A.S. Fraenkel introduces a new a-Wythoff's game which is the generalization of Wythoff's game. Fraenkel determines all P-positions of a-Wythoff's game under normal play convention. In this paper, we introduce two new restricted versions of a-Wythoff's game, Odd-Even Wythoff's Game and Odd-Even a-Wythoff's Game. Both new games are investigated. All its P-positions under normal play convention are given, and the corresponding wining strategies are also presented.