 One might be tempted to add to the description of a play: ‘player 2 chooses a value for \(\exists w\) in ignorance of the value for \(\forall x\).’ However, such a paraphrase would not clarify the conceptual situation. It makes no sense to speak of the independence of a move from other given moves with reference to a single play; this can only be done with reference to a multitude of plays. Quantifier independence can be conceptualized in game-theoretical terms making use of the notion of strategy. In the example, a strategy of player 2 is a set \(\{f, g\}\) of strategy functions, function \(f\) providing a value for \(\exists y\) depending on the value of \(\forall x\), and function \(g\) providing a value for \(\exists w\) depending on the value chosen for \(\forall z\) but not on the value chosen for \(\forall x\). The strategy \(\{f, g\}\) is, then, a winning strategy for player 2, iff \(R(a, f(a), c, g(c))\) holds in \(M\), for all values \(a\) chosen for \(\forall x\) and \(c\) chosen for \(\forall z\). One precise way of implementing the idea that player 2 is ‘ignorant’ of the move player 1 made for \(\forall x\) is to say that (a) strategy functions always only take as arguments the opponent’s moves, and (b) the strategy function corresponding to \(\exists w\) may not take as its argument the move player 1 made for \(\forall x\).