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This question is a kind of "dual" to an earlier one of mine. Although I don't know a reference for this, it's easy to show the following result: Suppose $G$ is a game in which neither ...

(Previously asked at MSE.) Let the determinacy number, $\mathfrak{g}$ (for "game"), be the smallest cardinal such that for every (two-player, perfect-information, length-$\omega$) game on $\...