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Related positions (B vs D)

Posted By: Igor
Date: Friday, 4 September 2015, at 4:29 p.m.

In Response To: Related positions (B vs D) (Nack Ballard)

Thank you, Nack. Very instructive, as always.

Here is a rollout for 31P-64R-33:





White is Player 2

score: 0
pip: 157
Unlimited Game
Jacoby Beaver
pip: 163
score: 0

Blue is Player 1
XGID=-a---BD-B--aeE---c-e----B-:0:0:1:33:0:0:3:0:10
Blue to play 33

1.Rollout124/21(2) 13/10(2)eq: +0.448
Player:
Opponent:		59.94% (G:17.11% B:0.44%)
40.06% (G:6.08% B:0.23%)		Conf.: ± 0.003 (+0.445...+0.451) - [57.6%]
Duration: 11 hours 30 minutes
2.Rollout113/7(2)eq: +0.448 (0.000)
Player:
Opponent:		60.00% (G:20.43% B:0.67%)
40.00% (G:9.58% B:0.45%)		Conf.: ± 0.003 (+0.445...+0.451) - [42.4%]
Duration: 10 hours 31 minutes
3.Rollout224/21(2) 6/3(2)eq: +0.434 (-0.014)
Player:
Opponent:		59.66% (G:16.85% B:0.45%)
40.34% (G:5.89% B:0.23%)		Conf.: ± 0.005 (+0.429...+0.439) - [0.0%]
Duration: 4 hours 32 minutes
1 31104 Games rolled with Variance Reduction.
Dice Seed: 40211140
Moves: 3-ply, cube decisions: XG Roller

2 10368 Games rolled with Variance Reduction.
Dice Seed: 40211140
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

I believe I have a reasonable explanation why 13/7(2) does better in this position compared to 31P-65R-33. When I was studying 2nd rolls, I was trying to understand the set of positions 62R-11, 63R-11, 64R-11 where N (8/7(2) 6/5(2)) goes up in equity relative to E (24/22 6/5(2)) from being second best for 62R-11 to essentially tied (but still second) for 63R-11 and to best for 64R-11. David Rockwell explained to me that the purpose of playing N with 11 in the opening is often to block opponent's sixes for the rear checker.

So, I believe with the structure arising after 31P-64R, making the bar point prevents white from connecting the rear checkers via 64, and this is what makes the difference compared to 31P-65R-33.

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