 It is only for mathematical convenience that the definition above expects the game to continue to infinity even when a player has won at some finite position; there is no interest in anything that happens after a player has won. Many logical games have the property that in every play, one of the players has already won at some finite position; games of this sort are said to be well-founded. An even stronger condition is that there is some finite number \(n\) such that in every play, one of the players has already won by the \(n\)-th position; in this case we say that the game has finite length.