# Combinatorial game theory facts for kids

**Combinatorial game theory**, also known as **CGT** is a branch of applied mathematics and theoretical computer science that studies combinatorial games, and is distinct from "traditional" or "economic" game theory. CGT arose in relation to the theory of impartial games, the two-player game of Nim in particular, with an emphasis on "solving" certain types of combinatorial games.

A game must meet several conditions to be a combinatorial game. These are:

- The game must have at least two players.
- The game must be sequential (i.e. Players alternate turns.)
- The game must have perfect information (i.e. no information is hidden, as in Poker.)
- The game must be deterministic (i.e. non-chance). Luck is not a part of the game.
- The game must have a defined amount of possible moves.
- The game must eventually end.
- The game must end when one player can no longer move.

Combinatorial Game Theory is largely confined to the study of a subset of combinatorial games which are two player, finite, and have a winner and loser (i.e. do not end in draws.)

These combinatorial games can be represented by trees, each vertex of which is the game resulting from a particular move from the game directly below it on the tree. These games can be assigned game values. Finding these game values is of great interests to CG theorists, as is the theoretical concept of game addition. The sum of two games is the game in which each player on her/his turn must move in only one of the two games, leaving the other as it was.

Elwyn Berlekamp, John Conway and Richard Guy are the founders of the theory. They worked together in the 1960s. Their published work was called *Winning Ways for Your Mathematical Plays*.

## See also

In Spanish: Teoría de juegos combinatorios para niños

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