Combinatorial game theory is a branch of mathematics that studies strategic games where players take turns making moves. The games are typically defined by a finite set of positions and rules, allowing players to analyze possible outcomes based on their choices. This theory helps in understanding optimal strategies and predicting the winner in two-player games with no chance elements. In combinatorial games, each position can be evaluated using concepts like N-positions and P-positions. An N-position is one where the next player can force a win, while a P-position is one where the previous player can secure victory. This framework applies to various games, including chess, checkers, and nim.