Combinatorial game theory (
CGT) is a branch of
applied mathematics and
theoretical computer science that typically studies
sequential games with
perfect information. Study is largely confined to two-player
games which have a
position in which the players take turns changing in defined ways or
moves to achieve a defined winning condition. CGT has not traditionally studied games randomness and imperfect or incomplete information (sometimes called
games of chance, like
poker), favoring games whose position is public to both players, and in which the set of available moves is also public (
perfect information). Combinatorial games include well-known games like
chess,
checkers,
Go,
Arimaa,
Hex, and
Connect6. They also include one-player combinatorial puzzles, and even no-player automata, like
Conway's Game of Life. In CGT, the moves in these games are represented as a
game tree.