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Cube action? Rollout

Posted By: Daniel Murphy
Date: Sunday, 27 January 2008, at 2:46 a.m.

In Response To: Cube action? (Daniel Murphy)

Here is the original position. Blue, on the bar, had to play 1-1:

The score (after 0 games) is: White 0, Blue 0 (match to 7 points)

Move number 3: Blue to play 11

White125


' ' '2X2X3X1X3X ' '2X2O

2O2O2O2O '2O2X2O ' ' ' '

Blue99

Position ID: 2K5jwADbZgYDQA Match ID: cInkAAAAAAAA

Below is a rollout of Blue's 1-1 play (Gnubg 2-ply, world class, 1296 trials) when White does not double immediately:

W WG WBG L LG LBG Cubeless Cubeful Behind by
b/22 6/5 0.346 0.126 0.002 - 0.654 0.169 0.007 -0.359 -0.598
b/22 4/3 0.334 0.089 0.002 - 0.666 0.169 0.006 -0.421 -0.635 0.037
b/22 3/2 0.331 0.100 0.001 - 0.669 0.177 0.006 -0.424 -0.651 0.053
b/23 13/12(2) 0.330 0.068 0.001 - 0.670 0.098 0.003 -0.375 -0.657 0.059
b/22 2/1 0.333 0.091 0.002 - 0.667 0.166 0.007 -0.420 -0.659 0.061
b/24 13/12(2) 6/5 0.311 0.075 0.001 - 0.689 0.112 0.003 -0.421 -0.702 0.104
bar/23 6/5(2) 0.324 0.074 0.001 - 0.676 0.128 0.004 -0.412 -0.738 0.140

For White, Gnubg 2-ply does not double after any of these plays. However, 1296-trial 2-ply rollouts of White's cube decision change all seven No Doubles to Double/Takes.

After bar/22 6/5, ND is a 0.046 error. After bar/23 13/12(2), the cube decision is an insignificant toss-up: 0.662 for No Double and 0.674 for Double/Take with SDs = 0.006 and 0.009, and JSD is less than 1. However, I think, but have not verified, that the ND equity is inflated by bad takes later, for instance after White makes a five prime (but this may also be true after the other plays).

Below are the results of seven rollouts of Blue's 1-1 play (Gnubg 2-ply, world class, 1296 trials) when White does double immediately:

W WG WBG L LG LBG Cubeless Cubeful Behind by
b/22 6/5 0.325 0.132 0.002 - 0.675 0.178 0.007 -0.831 -0.650
b/23 13/12(2) 0.305 0.068 0.002 - 0.695 0.096 0.002 -0.861 -0.674 0.024
b/22 2/1 0.310 0.097 0.002 - 0.690 0.170 0.006 -0.952 -0.751 0.101
b/22 4/3 0.311 0.094 0.003 - 0.689 0.172 0.005 -0.957 -0.766 0.116
b/23 6/5(2) 0.303 0.072 0.005 - 0.697 0.132 0.005 -0.946 -0.771 0.121
b/22 3/2 0.309 0.106 0.003 - 0.691 0.184 0.006 -0.962 -0.775 0.125
b/24 13/12(2) 6/5 0.291 0.071 0.002 - 0.709 0.113 0.004 -0.950 -0.782 0.132

Bar/22 6/5 appears to be best and slightly better than bar/23 13/12(2). 2% more wins, 8.2% more gammon losses, but also 6.4% more gammon wins. Note the danger of blotting in the outfield, and that like bar/23 the other 13/12(2) play also loses fewer gammons.

Plays 4/3, 3/2 and 2/1 (which the rollouts don't separate significantly) appear to seriously compromise Blue's ability to remake a board and avoid leaving more blots in some scenarios and contain White in others. I think this explains why 6/5 wins so many more gammons.

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