Combinatorial Game Theory
Combinatorial Game Theory is a branch of mathematics that studies strategic games where players take turns making moves. The games are typically zero-sum, meaning one player's gain is another's loss. This theory focuses on determining winning strategies and analyzing the positions of the game, often using concepts like Nim, Sprague-Grundy theorem, and impartial games.
In these games, players often have perfect information, meaning they know all possible moves and outcomes. Combinatorial Game Theory helps in understanding complex games by breaking them down into simpler components, allowing players to devise optimal strategies and predict their opponents' moves effectively.