(;
SZ[2]
C[What is optimal play on a 2x2 board?

The following game tree shows that
Black has a 1 point win.

The analysis assumes Chinese area
scoring using Super Ko in which no
move may recreate a previous board
position with the same player to
move next.

Source:
    Myron Souris];
B[bb]
C[All the other Black moves are
the same under symmetry.];
W[aa];
B[ba]
C[Black cannot play conservatively.
If Black passes instead, White can
pass, and the game ends in a tie.]
(;
W[ab];
B[ba]
C[The only winning Black move.

If Black had played in the lower
right corner, White would capture
the lone Black stone and Black
could not recapture the 3 White
stones without repeating node 1.
White would win by 4 points.]
(;
W[]
C[White passes.];
B[bb]
(;
W[aa]
C[This board position appeared
earlier in this line at node 3.
But here Black is to move
instead of White, so White's
move is legal.]
(;
B[]
C[After Black passes here, White
cannot capture without repeating
node 4.

So Black wins by 1 point.]
)
    (;
    B[ab]
    C[Black's pass in the main line
already gives Black at least a 1
point win.  But can Black win by
more?];
    W[aa];
    B[bb];
    W[ab]
    C[And Black cannot capture the two
White stones without repeating
node 7.

In this variation, White wins
by at least 1.  So Black's
attempt to win by more than 1
has failed.]
    )
)
    (;
    W[ab]C[The only other White possibility.];
    B[]
    C[But after Black passes, White
cannot capture without
repeating node 4.

So Black wins by 1 in this
variation also.]
    )
)
    (;
    W[bb];
    B[ba];
    W[ab];
    B[bb]
    C[And White cannot capture
without repeating node 4.

Black wins by 1.

Note that the game tree has
already shown that other earlier
White lines of play can hold
Black to a 1 point win.  So
this line only needs to show
that Black can do no worse
than a 1 point win.]
    )
)
    (;
    W[]
    C[If White passes here, Black
simply passes to ensure a win
by 1 point.]
    )
)
