Ulams

Ulam is a two-player game played on a grid, typically a square grid of any size. The game board is usually empty at the start. Players take turns placing their marks, traditionally X and O, on the grid. The objective of the game is to be the first player to get a certain number of their marks in a row, either horizontally, vertically, or diagonally. The number required for a win is usually specified before the game begins and depends on the size of the grid. For example, on a 5x5 grid, the goal might be to get five in a row.

Ulam is a game of pure strategy, meaning there is no element of chance. It is a solvable game, which means that with perfect play from both sides, the outcome can be predetermined. Theoretical analysis suggests that the first player can always force a win if the grid is sufficiently large and the winning line is short enough relative to the grid dimensions. However, for common board sizes and winning conditions, games can often end in a draw if both players play optimally. The complexity of the game increases significantly with the size of the grid and the length of the winning line. It is a popular game for computer AI research due to its deterministic nature and the challenge of developing optimal strategies.