What is a combinatorial game?
Like the games you are most familiar with, combinatorial games have players, moves, rules, and winners or losers. In fact, here already we are departing from some games you know like chess, which do not always have a winner. The games we are interested in can not end in a draw. (Chess is clearly an interesting game, so combinatorial game theorists also extend what they think about to include games where draws are allowed.) Since sometimes it may not be easy to see that the game can not end in a draw, this immediately sets a mathematical challenge: to prove that there is a winner in a given game. Although combinatorial style games can have more than two players or only one (solitaires), we will restrict our attention to games with only two players. Furthermore, we will be interested in games which do not go on forever. Since the games that interest us can not end in a draw or last forever, one player wins and one player loses. It will turn out that there is a staggering variety of combi
