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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, …

Here is one possible answer. An essential feature of any board game, in the way I am thinking about it, is that there are only finitely many game states that are realizable on the board. This fact, co …

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 …

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 …

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 question arises from what I find interesting in the recently asked question What is a chess piece mathematically? My answer to that question was that mathematically, game pieces are in general e …

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 …

The decidability of the special case of the won-position problem, restricted to positions having only short-range pieces, remains open to my knowledge. Nevertheless, as you suspected, one can use the …

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 …

This question spins off of Gil Kalai's recent question on Conway's game of life for a random initial configuration. There are numerous configurations in the game of life that are known to be stable …

I claim that Player A has a winning strategy in your game, and furthermore, it is a winning strategy for her simply to play the smallest available number. Let me consider the game along with several …

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 …

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 …

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 …

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 …