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The infinitary guessing-box puzzle is amazing — see here. In the basic form, the Guessing-box Hall has infinitely many wooden boxes, each containing a real number, and there are 100 mathematicians wh …

I am currently writing an essay on hat puzzles, and for the warm-up section I introduce some of the standard finite hat puzzles. One of these proceeds as follows: You and two friends are each given a …

No, the negative a game is simply the game in which the player's roles are swapped, hereditarily. You can see this in the definition you provided $$-G=\{ -G^R\mid -G^L\}$$ since the left options in $- …

This is a great question — definitely enjoyed. Assuming the axiom of choice, then the answer is yes. Theorem. Assume there is a well ordering of the real numbers. If player I has a winning strategy, t …

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, …

Here is a complete winning strategy for the Justice game. One wins the Justice game simply by following the usual Nim strategy, with all the same winning positions and moves (except if the position is …

I have a question about the Chocolatier's game, which I had introduced in my recent answer to a question of Richard Stanley. To recap the game quickly, the Chocolatier offers up at each stage a finite …

My question is which player has a winning strategy in the two-player version of the Killing the Hydra game? In their amazing paper, Kirby, Laurie; Paris, Jeff, Accessible independence results for P …

Consider the following two-player pebble game. We have finitely many stones on a finite linear track of squares. We take turns, and the allowed moves are: move any one stone one square to the left, …

To prove that this is a metric, consider the following theorem. Theorem. If the second player can survive for $n$ steps in the $(\Gamma_1,\Gamma_2)$ game, and for $m$ steps in the $(\Gamma_2,\Gamma_3 …

I am not sure what you imagine, but once one makes the move to games with infinite play, then various set-theoretic issues come to light, and the subject becomes more set-theoretic and less like combi …

Thanks for your kind words about my blog. In the general-size square Sudoku board, you have an $\kappa\times\kappa$ array of $\kappa\times\kappa$ local blocks for some (possibly infinite) cardinal $\ …

This is a really great question! Previous attempts to make sense of infinite Go have sometimes had problems because it wasn't clear how to define the winner of a game of Go after transfinite play. T …

For even $n$, I claim that nobody has a winning strategy, and therefore both players have drawing strategies. To see this, observe first that by the fundamental theorem of finite games, we know that …

Consider the Sudoku Solver-Spoiler game, a natural variation of the Sudoku game recently appearing in the question Who wins two-player Sudoku? posted by user PyRulez. In that game, the players attempt …