New Games Related to Old and New Sequences

We define an infinite class of 2-pile subtraction games, where the amount that can be subtracted from both piles simultaneously, is a function f of the size of the piles. Wythoff’s game is a special case. For each game, the 2nd player winning positions are a pair of complementary sequences, some of which are related to well-known sequences, but most are new. The main result is a theorem giving necessary and sufficient conditions on f so that the sequences are 2nd player winning positions. Sample games are presented, strategy complexity questions are discussed, and possible further studies are indicated.

• Type: Conference
• Year: 2003
• Where: ACG
• Authors: Aviezri S. Fraenkel
• Keywords: 2-pile Subtraction Games, ACG 2003, Complementary Sequences, Computer Graphics, Player Winning Positions