A Generalization of Wythoff's Game*
Ian G. Connell · Canadian Mathematical Bulletin · 1959
W.A. Wythoff [1] in 1907 defined a modification of the game of Nim by the following rules: (i) there are two players who play alternately; (ii) initially there are two piles of matches, an arbitrary number in each pile; (iii) a player may take an arbitrary number of matches from one pile or an equal number from both piles but he must take at least one match; (iv) the player who takes the last match wins the game. If, after his move, a player leaves one match in one pile and two in the other he can force a win; for if his opponent takes one match from the pile containing two he can take both remaining matches; and similarly for the other possibilities.