impartial game
game in which the allowable moves depend on the current position and not on which of the two players is currently moving
en-US/ˌɪmˈpɑɹʃəl ˈɡeɪm/
en-GB/ɪmˈpɑːʃəl ˈɡeɪm/
game in which the allowable moves depend on the current position and not on which of the two players is currently moving