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Some further observations about David Presser's position

Posted By: Timothy Chow
Date: Sunday, 31 August 2014, at 7:30 p.m.

Recently David Presser posted 64S-22E-44 and asked for comment. I looked at this a bit and have a few additional comments to offer.

I believe that my previous comments were basically on the right track. That is, after 13/9 18/14, Pottling with the remaining two 4's has all the usual advantages: If Blue isn't immediately hit, then he can probably convert to a favorable holding game, and that is a big gain.

Of course, 22 shots from a stacked midpoint is not to be sneezed at. The following variants help us get a quantitative feeling for the tradeoffs involved.


Variant 1





White is Player 2

score: 0
pip: 157
Unlimited Game
pip: 157
score: 0

Blue is Player 1
XGID=---b--E-CA--eD---cAc--b-A-:0:0:1:44:0:0:0:0:10
Blue to play 44

1.Rollout118/10 13/9(2)eq: +0.223
Player:
Opponent:
56.08% (G:12.20% B:0.51%)
43.92% (G:11.03% B:0.40%)
Conf.: 0.007 (+0.216...+0.230) - [100.0%]
Duration: 1 hour 46 minutes
2.Rollout124/16 18/14 13/9eq: +0.203 (-0.020)
Player:
Opponent:
56.73% (G:8.25% B:0.36%)
43.27% (G:11.96% B:0.34%)
Conf.: 0.007 (+0.196...+0.210) - [0.0%]
Duration: 1 hour 57 minutes
3.Rollout124/20 18/10 13/9eq: +0.201 (-0.022)
Player:
Opponent:
56.02% (G:10.74% B:0.47%)
43.98% (G:11.86% B:0.37%)
Conf.: 0.010 (+0.191...+0.211) - [0.0%]
Duration: 1 hour 49 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

In this variant, White owns her 3pt instead of her 4pt. Now 18/10 13/9(2) comes out on top of the rollout. I'm not too concerned with whether it would retain its #1 ranking with different rollout settings. The main thing is that 18/10 13/9(2) has gained in equity relative to 24/16 18/14 13/9. Why is this? You might think that since the 4pt gives White a stronger board, Blue should be even more leery of leaving those outfield blots when White owns her 4pt compared to when White owns her 5pt. However, the computer seems to be saying that it's the other way around.

Examining the temperature map reveals what's going on. When White owns the 4pt, it's not just that her hits are stronger because of her better board. Her non-hitting rolls (if Blue stays on the 24pt) are much better when she owns the 4pt, because of the superior priming potential. Therefore Pottling to avoid getting primed is more urgent when White owns her 4pt, despite the increased pain from getting hit. We can conclude that if Pottling looks very wrong to you in David Presser's original position, then you are probably underestimating the danger of your straggler getting trapped relative to the danger of getting hit.


Variant 2





White is Player 2

score: 0
pip: 159
Unlimited Game
pip: 151
score: 0

Blue is Player 1
XGID=---b--E-CB--eC--Ac-c-b--A-:0:0:1:45:0:0:0:0:10
Blue to play 45

1.Rollout124/20 16/11eq: +0.141
Player:
Opponent:
54.49% (G:10.29% B:0.43%)
45.51% (G:12.32% B:0.37%)
Conf.: 0.008 (+0.134...+0.149) - [100.0%]
Duration: 1 hour 59 minutes
2.Rollout116/11 13/9eq: +0.103 (-0.039)
Player:
Opponent:
53.16% (G:10.79% B:0.45%)
46.84% (G:12.00% B:0.39%)
Conf.: 0.007 (+0.095...+0.110) - [0.0%]
Duration: 1 hour 49 minutes
3.Rollout124/15eq: +0.056 (-0.085)
Player:
Opponent:
53.10% (G:8.14% B:0.35%)
46.90% (G:13.37% B:0.45%)
Conf.: 0.007 (+0.049...+0.063) - [0.0%]
Duration: 1 hour 55 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

(To see why this is a variant of David Presser's position, note that if we change the roll from 54 to 64, then Blue's three main options yield the same terminal positions as after his three main options in 64S-22E-44.)

Here, Pottling is apparently very wrong, even though superficially, Variant 2 presents us with a choice similar to the one in 64S-22E-44. Examining the temperature map again, I believe that there is a simple explanation: The number of shots matters. In Variant 2, after 24/15, White has 23 shots instead of 22, and double 4's hits twice. This causes the equity of Pottling to drop noticeably. The equity of the play that stays back on the 24pt, if anything, rises slightly because of the fewer fly shots from the anchor.

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