The game of noughts and crosses is played, on a three by three square
grid, by two players; one of whom marks the grid with circles (noughts), the
other with crosses. They alternate, taking turns to put a mark in a vacant cell
of the grid; the winner is the first to complete a line of three. Naturally,
this game is entirely deterministic. Half-way sensible play proceeds as
follows:
O
O
X
O
X
O
allowing X to play centre and force a draw, if careful.
O
X
O
which yields a draw provided X is careful.
O
X
O
yielding a draw unless someone is foolish.
O
X
O
yielding a draw provided X is careful.
O
O
X
O
X
O
X
allowing O to play the centre and win.
O
O
X
O
O
X
X
allowing O to play the centre and win.
O
X
O
O
X
O
X
allowing O to play top right and win.
O
X
O
O
X
O
O
X
X
forcing O to play centre and win.
O
O
X
O
X
O
X
allowing O to play centre and win.
O
O
X
O
X
O
X
allowing O to play centre and win.
O
X
O
X
forcing O to play centre and win.
O
O
X
X
leading inexorably to a draw.
O
O
X
X
O
O
O
X
X
forcing X to play top right and win.
O
O
O
X
X
leading inexorably to a draw.
O
O
O
X
X
leading inexorably to a draw.
O
O
X
X
O
allowing X to play top right and win
O
O
X
X
O
forcing a draw.
O
O
X
X
O
O
X
X
O
forcing X to play centre and win.
O
O
X
X
O
O
X
O
X
allowing X to play top right and win.
O
O
X
leading inexorably to a draw.
O
O
X
allowing X to play bottom right and, if careful, force a draw.
O
X
O
allowing X to play top middle or centre and force a draw.