I consider m-by-n dots go under territory scoring. By symmetry, I restrict to m ≤ n .
To make things a little shorter, by "move", I mean board play .
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1x3 dots go
1x4 dots go
For all non-negative integers n, on the 0-by-n board, the only legal game is pass-pass, after which the score is 0. The same applies to the 1x1 board.
Black-to-move passes to win by 4 points. reduces Black's winning margin by 1 point. Black's other move reduces Black's winning margin by _at least_ 1 point, and will reduce it by another point unless Black gets a point of territory from an empty ko intersection because White has no legal move immediately after Black takes that ko. ()
is a two-stone suicide, and White otherwise has no legal moves.