Although \(\sc{TWO}\ \sc{PLAYER}\ \sc{SAT}\) is defined in terms of a very simple game, similar results can be obtained for suitable variations of a variety of well familiar board games. Consider, for instance the following variation on the standard rules of Go: (i) the game is played on an \(n \times n\) board; (ii) the winner of the game is the player with the most stones at the end of \(n^2\) rounds.   Lichtenstein and Sipser (1980) demonstrated the \(\textbf{PSPACE}\)-completeness of the following problem: