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Comment Re:2x2 board (Score 2) 117

This 8 move game disproves your claim:

      . .
      . .
A2
      X .
      . .
B1
      X .
      . O
A1
      X .
      X O
B2
      . O
      . O
A1
      . O
      X O
A2
      O O
      . O
A1
      . .
      X .
B2
      . O
      X .
A2
      X O
      X .
pass
pass

Btw, we're counting all games, not just games without mistakes.

Comment Re: 2x2 board (Score 1) 117

That's NOT how it's used in chess.
Even though the notion of chess position might include some game state information
  like side to move, castling rights, and en-passent capturability,
I've NEVER seen it include the set of all previous board states, as would be necessary
for applying the 3-fold repetition rule in the game's future.

Comment Re: 2x2 board (Score 4, Insightful) 117

The 386356909593 games do account for superko.
That is exactly the number of simple (meaning not visiting the same point twice) paths starting
from the empty node in the graph in Figure 4 on page 5 of our paper http://tromp.github.io/go/gost...

Without superko, the number of 2x2 games would simply be infinite...

Comment Re:2x2 board (Score 5, Interesting) 117

Author here.

A single 2x2 game can visit as many as 48 of the 57 legal 2x2 positions, with many dozens of passes in between moves, and obviously many captures.

This page

http://tromp.github.io/java/go...

on solving 2x2 go with various search methods may be helpful. I've lost track of my original 2x2 game counting code but suspect it was a close relative of this code.

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