Editing Strategy-stealing argument (section)

== Example ==
A strategy-stealing argument can be used on the example of the game of [[tic-tac-toe]], for a board and winning rows of any size.<ref name="b"/><ref name="hj"/> Suppose that the second player (P2) is using a strategy ''S'' which guarantees a win. The first player (P1) places an '''X''' in an arbitrary position. P2 responds by placing an '''O''' according to ''S''. But if P1 ignores the first random '''X''', P1 is now in the same situation as P2 on P2's first move: a single enemy piece on the board. P1 may therefore make a move according to ''S'' – that is, unless ''S'' calls for another '''X''' to be placed where the ignored '''X''' is already placed. But in this case, P1 may simply place an '''X''' in some other random position on the board, the net effect of which will be that one '''X''' is in the position demanded by ''S'', while another is in a random position, and becomes the new ignored piece, leaving the situation as before. Continuing in this way, ''S'' is, by hypothesis, guaranteed to produce a winning position (with an additional ignored '''X''' of no consequence). But then P2 has lost – contradicting the supposition that P2 had a guaranteed winning strategy. Such a winning strategy for P2, therefore, does not exist, and tic-tac-toe is either a forced win for P1 or a tie. (Further analysis shows it is in fact a tie.)

The same proof holds for any [[strong positional game]].