= Combinatorial game theory
= CGT
{c}
{synonym}
<Combinatorial game theory> studies positions in alternating-move games with fully specified legal moves, usually perfect information and no chance. A position can be defined recursively by the positions available to each player. Under the <normal-play convention>, a player with no legal move loses.
An <impartial game> gives both players the same moves; <Nim> is the standard example. A <partizan game> allows different moves for Left and Right. The <disjunctive sum> lets a player move in exactly one component on each turn, making it possible to study how game positions combine algebraically. Infinite play or <misère play> requires additional conventions; normal-play results do not automatically transfer.
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