Strategy-stealing Argument

In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many games, that the second player cannot have a winning strategy (i.e., a strategy that will always win the game for them, no matter what moves the first player makes).

The strategy-stealing argument applies to any symmetric game (one in which either player has the same set of available moves with the same results, so that the first player can "use" the second player's strategy) in which an extra move can never be a disadvantage. Examples of games to which the argument applies are hex, chomp and the m,n,k-games such as gomoku. In hex ties are not possible, so the argument shows that it is a first-player win.