Combinatorial games: selected short bibliography with a succinct gourmet introduction

Summary

In this instalment of the Games Bibliography, Richard Nowakowski joined as a coauthor. Unlike previous instalments, this one is restricted, mainly, to new entries of the last few years that did not appear in previous versions, such as in “Games of No Chance 3” and the Electronic J. of Combinatorics (Surveys). We apologize profusely that due to lack of time, this version does not include all the new game papers we are aware of, and also lacks some unifying editing and polishing.

Roughly speaking, the family of combinatorial games consists of two-player games with perfect information (no hidden information as in some card games), no chance moves (no dice) and outcome restricted to (lose, win), (tie, tie) and (draw, draw) for the two players who move alternately. Tie is an end position such as in tic-tac-toe, where no player wins, whereas draw is a dynamic tie: any position from which a player has a nonlosing move, but cannot force a win. Both the easy game of nim and the seemingly difficult chess are examples of combinatorial games. And so is go. The shorter terminology game, games is used below to designate combinatorial games.