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Re: computer-go: 5 x 5 perfect play



I just love dismal calculations:

25! is about 1.5 x 10^25 (which is somewhere around 2^80) Assuming we can play through 10^9 of these per second (one Giga-game per second), we're still looking at 10^16 seconds which is a bit over 475 million years. Since computing speeds double every two years, though... oh, never mind.

I believe the number of possible board configurations would be 3^25 which is about 8.4 x 10^11. One has to subtract a passel of illegal board configurations, which will slightly reduce this number. Thus, given a one Giga-Board-Analysis per second computer, we can enumerate the legal board positions in a matter of minutes.

Apologies if I hit the wrong keys on my calculator for the above,

Best regards,

Erik



On Tuesday, October 15, 2002, at 03:29 PM, Mitchell Timin wrote:

Jeffrey Rainy wrote:
<snip>
Also, 2^25 is not the actual number of possible 5x5 board positions. On one hand,
the capture rule lowers this number a lot. On the other hand, the ko rule raises this
number somehow. But that is just nitpicking ;-)

Jeff.
Of what value is the number 2^25?  That doesn't seem relevant to me.  A
first estimate of the number of different games is 25!, which is a much
bigger number than 2^25.  (Symettry will reduce it, but the capture of
large groups will increase it.)

2^25 is the number of different full boards, with no empty
intersections, from all black stones to all white stones.

z

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