## New games related to old and new sequences (2003)

Venue: | Heinz (Eds.), Proc 10th Advances in Computer Games Conference (ACG-10 |

Citations: | 2 - 2 self |

### BibTeX

@INPROCEEDINGS{Fraenkel03newgames,

author = {Aviezri S. Fraenkel},

title = {New games related to old and new sequences},

booktitle = {Heinz (Eds.), Proc 10th Advances in Computer Games Conference (ACG-10},

year = {2003},

pages = {367--382},

publisher = {Kluwer, Academic Publishers}

}

### OpenURL

### Abstract

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.