 A strategy for a player is a set of rules that describe exactly how that player should choose, depending on how the two players have chosen at earlier moves. Mathematically, a strategy for \(\forall\) consists of a function which takes each position \(\mathbf{a}\) with \(\tau(\mathbf{a}) = \forall\) to an element \(b\) of \(\Omega\); we think of it as an instruction to \(\forall\) to choose \(b\) when the game has reached the position \(\mathbf{a}\). (Likewise with a strategy for \(\exists\).) A strategy for a player is said to be winning if that player wins every play in which he or she uses the strategy, regardless of what the other player does. At most one of the players has a winning strategy (since otherwise the players could play their winning strategies against each other, and both would win, contradicting that \(\W_{\forall}\) and \(\W_{\exists}\) have no plays in common). Occasionally one meets situations in which it seems that two players have winning strategies (for example in the forcing games below), but closer inspection shows that the two players are in fact playing different games.