Every cache square for every player in the initial state has some piece of
that player.

A player moves by moving some piece of that player from some cache square for
that player to some empty board square.

A player wins when every square in some row has some piece of that player.
A player wins when every square in some column has some piece of that player.
A player wins when every square in some diagonal has some piece of that
player.

A player draws when no player wins and that player has no move.