Combinatorial Game Theory
Combinatorial Game Theory is the study of turn-based games where both players can see all the pieces and no luck is involved.
Think of it this way
Two players take turns moving checkers on a board. Each player sees every piece and knows every rule — no hidden cards, no dice. The player who runs out of moves loses. Every spot on the board is either a win or a loss, based on whose turn it is.
Explaining combinatorial game theory by grade level
Think of a game where you take turns picking up stones from a pile. You can see all the stones. There is no dice or luck. The way you win is by thinking ahead about what the other player will do next.