There are 189,174,688,641 distinct games on a 5x5 sized board. Half of these games end with one of the 8 scores from 11:14 to 18:7, all of these scores resulting for 10.3 to 14.75 billion games. There are a lot more games that player 1 wins than games that player 2 wins.
My histograms have a maximum bin content of 2 billion events (32 bit integer), so I can't plot this without making some changes first.
The shortest games end after nine disks are played with scores of 13:0 (8 times), 12:1 (once), followed by games ending in 14:0 (once) and 6:8 (4 times).
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3 comments:
Keep up the excellent work!
I believe to have independely verified your results for the 4x4 board and am currently looking into some optimization techniques before looking at larger boards.
Any idea when some 6x6 results will be posted?
I can verify that 1.89E+11 distinct games exist from each of the following equivalent positions:
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--x--
--xx-
--xo-
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...or...
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-xxx-
--xo-
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(o to move; x represents black, and o represents white)
These boards, however, are not equivalent to:
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--ox-
--xx-
---x-
...or...
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--ox-
--xxx
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Which (assuming my code is correct) each have a total of 44,473,349,511 games. Therefore, taking the euqivalent boards into account, 233,648,038,152 distinct games exist from the starting position:
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--ox-
--xo-
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