I am new to combinatorial game theory, and I have a question about terminology. As far as I can tell, in order for a game to be a combinatorial game, the game must eventually end. That is, having a finite number of moves is part of the definition of a combinatorial game. Is there a term to describe combinatorial games that don't necessarily end? I want to study such games (like the Angels and Devils game), but I'm having trouble searching since I don't know what to call them. Thanks.
2026-03-31 10:58:46.1774954726
combinatorial game terminology
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A combinatorial game that doesn't necessarily end is called "loopy". However, the game in Conway's Angel problem wouldn't usually be called a loopy combinatorial game. The issue is that its win condition is different than the standard win conditions (either you win when your opponent can't make a move, or when you can't).
In standard combinatorial game theory, if play goes on forever, the game is said to be "drawn" (neither player wins). That said, if one player can force at least a draw, that's still notable.
But in the Angel problem, infinite play is a win for the angel, the angel being unable to move is a win for the devil, and the devil being unable to move is impossible.