[computer-go] UCT finds the right answer, but...

[Peter Drake]

Consider this position:

...wBw...
.w.wBwwww
...wBBBBB
wwwwB....
BBBBBBBBB
wwwwBwwww
w..wBw...
w..wBw.w.
w.wwBw...

This is black to play, no komi.

As I read it (correct me if I'm wrong!), the white groups at upper  
left and lower right can't be killed (assuming white defends them).  
Black can kill either of the other groups, and white can respond by  
saving the remaining one. Since killing the upper right white group  
is not big enough, black's only winning move is to kill the lower  
left group by playing at b2.

Orego (now using UCT) quickly finds the correct answer, but the  
estimates of the probability of winning are strange. Here's a graph:


The probability of winning by starting at b2 is greater than the  
probability starting elsewhere, but shouldn't it approach 1.0, since  
b2 is a winning move? Do others get this same behavior? Does anyone  
have an explanation?

For what it's worth, here are the probabilities and <black wins> /  
<total runs> through each move:

B1 (0.262654 = 1510/5749):
G1 (0.269305 = 2504/9298):
H1 (0.276537 = 5200/18804):
J1 (0.263229 = 1567/5953):
*B2 (0.290454 = 134822/464177):
C2 (0.288902 = 69762/241473):
G2 (0.274577 = 4156/15136):
J2 (0.276275 = 5034/18221):
B3 (0.261835 = 1427/5450):
C3 (0.269523 = 2554/9476):
G3 (0.269982 = 2655/9834):
H3 (0.27404 = 3927/14330):
J3 (0.273359 = 3660/13389):
F6 (0.25266 = 831/3289):
G6 (0.268461 = 2334/8694):
H6 (0.273485 = 3706/13551):
J6 (0.247165 = 632/2557):
A7 (0.269866 = 2632/9753):
B7 (0.274571 = 4157/15140):
C7 (0.268814 = 2404/8943):
A8 (0.275441 = 4577/16617):
C8 (0.277177 = 5617/20265):
A9 (0.259601 = 1237/4765):
B9 (0.27903 = 7180/25732):
C9 (0.268422 = 2324/8658):
G9 (0.257561 = 1090/4232):
H9 (0.277021 = 5513/19901):
J9 (0.262094 = 1452/5540):
PASS (0.221808 = 238/1073):

Peter Drake
Assistant Professor of Computer Science
Lewis & Clark College
http://www.lclark.edu/~drake/




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