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In terms of mathematical analysis and combinatorial game theory, the essence of any game is captured by its game tree, the tree whose nodes represent the current game state, and to make a move in the …

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 …

Consider the following open knight's tour on a $5\times 5$ board, starting at position $1$ and then touring the $5\times 5$ board in the indicated move order. The final position is $25$, from which th …

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 …

Update. (Oct 28, 2015) See below, for a position with game value $\omega^4$. This is a great question, which I have been pondering for some time. I have just completed a joint article Transfinit …

Update. I made a blog post about Infinite Sudoku and the Sudoku game, following up on ideas in this post and the comments below. I claim that the second player wins the even-sized empty Sudoku boa …

There is a positive solution for the decidability of the mate-in-$n$ version of the problem. Many of us are familiar with the White to mate in 3 variety of chess problems, and we may consider the na …

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 …

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 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 …

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 …

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, …

Consider the arithmetic progression game, a two-player game of perfect information, in which the players take turns playing natural numbers, or finite sets of natural numbers, all distinct, and the fi …

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, …

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 …