One can prove that for any first-order sentence \(\phi\), interpreted in a fixed structure \(A\), player \(\exists\) has a winning strategy for Hintikka’s game \(G(\phi)\) if and only if \(\phi\) is true in \(A\) in the sense of Tarski. Two features of this proof are interesting. First, if \(\phi\) is any first-order sentence then the game \(G(\phi)\) has finite length, and so the Gale-Stewart theorem tells us that it is determined. We infer that \(\exists\) has a winning strategy in exactly one