= Solution
\b[<Minimax search> applies because this is a finite, deterministic two-player <zero-sum game> with perfect information.] Each move assigns a previously unassigned <Boolean variable>, so play terminates after exactly $N$ moves. Both players observe the whole partial <Boolean valuation>, and there are no chance moves. Give terminal positions <payoff> $+1$ when the <propositional formula> is true and $-1$ when it is false, measured for $A$. At an $A$-node take the maximum child value and at a $B$-node the minimum. <Backward induction> then computes the winner and a corresponding <winning strategy>.
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