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Consider the game of infinite Hex, where two players Red and Blue alternately place their stones on the infinite hex grid, each aiming to create a winning configuration. Red wins after infinite play, ...

This question originates from the paper On the Axiom of Determinateness by Jan Mycielski, section 7. Given a set $X$ and an ordinal $\alpha$, the author defines a transfinite game of length $\alpha$ ...