Stalement is a position in which neither player can ever move again. Technically, stalemate is not possible in backgammon. Here is a rough explanation why: • To have a stalemate, each player would have to be blocking the other. Perhaps they each have prime in front of the other player’s checkers. • Both players cannot hold their primes forever unless they are stuck on the bar. • If the players are both on the bar, one of them will eventually reenter unless both players are closed out. • So the only possibility for stalemate is both players on the bar and both players closed out, like this: But this position can’t happen. If it could, what was the position before the last hit? A player who was on the bar and closed out cannot hit his opponent. Stalemate might be possible, though, if one of the players makes an illegal play. See this post by Bob Johnson.