Wythoff's game is a kind of 2-pile Nim game, which admits taking the same number of stones from both piles. It differs only a little from the 2-pile Nim game, but their winning strategies are quite different from each other. Amazingly the winning strategy of Wythoff's game is directly related to a real number, specifically the golden ratio. In this paper we add two restrictions to this game, and investigate the winning strategy of the revised game.
Aoki, Ryoma; Sawada, Junpei; Miyake, Yuki; and Fujiwara, Hiroaki
"Cold Positions of the Restricted Wythoff's Game,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 8.
Available at: http://scholar.rose-hulman.edu/rhumj/vol13/iss1/8