[1] A key property of a strategy-stealing argument is that it proves that the first player can win (or possibly draw) the game without actually constructing such a strategy.
But then, roughly speaking, after making an arbitrary first move – which by the conditions above is not a disadvantage – the first player may then also play according to this winning strategy.
[2] However, Nash did not publish this method, and József Beck credits its first publication to Alfred W. Hales and Robert I. Jewett, in the 1963 paper on tic-tac-toe in which they also proved the Hales–Jewett theorem.
In the game of Sylver coinage, strategy stealing has been used to show that the first player can win in certain positions called "enders".
There is a class of chess positions called Zugzwang in which the player obligated to move would prefer to "pass" if this were allowed.
Since the 1930s, however,[6] the second player is typically awarded some compensation points, which makes the starting position asymmetrical, and the strategy-stealing argument will no longer work.
This approach may be defeated using ladder tactics, ko fights, or successfully competing for control of the board's central point.
For games with a finite number of reachable positions, such as chomp, a winning strategy can be found by exhaustive search.