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Rollout and analysis

Posted By: Timothy Chow
Date: Sunday, 27 July 2014, at 6:47 p.m.

In Response To: Avoid gammonish positions at 2a3a? (Timothy Chow)

It's fairly clear that 24/14 is the DMP play and that the motivation for 8/2* 6/2 is to play for a juicy undoubled gammon. Which plan is correct?

Bob and Dmitriy correctly pointed out that it's insufficient to think about which play wins more cubeless gammons; you have to think about the cube as well. At any score when your opponent has the potential to send you a gammicidal cube, you need to judge how likely that is. In general, the more contact there is, the longer the game will tend to last, and the greater the chances of a random fluctuation that will send that gammicidal cube flying your way at some point, even if you win the game in the end. Conversely, the stronger a grip you have on the position, the more likely you'll be able to stave off the cube and win a meaningful gammon.

In the Donkey Corner position, I mentioned that a GNU rollout confirmed that Blue would win a significant percentage of undoubled gammons, and not very many gammons with the cube already turned. In this position, though, my 1296-trial GNU rollout indicates (via "View Statistics") that after 8/2* 6/2, Blue wins an undoubled gammon only about 12% of the time. Contrast that with the cubeless estimate of 25% gammons in the XG rollout below. A high proportion of those gammons are won with the cube turned, when they don't matter any more.

I rolled this position out both ATS and for money. Although one has to be cautious about comparing EMG equities across different scores, it seems fair to say that 8/2* 6/2 is a bigger error ATS than for money. This might seem puzzling if you focus only on the fact that the 2a player's gammon value is elevated, but I would explain it by saying that for money, the opponent's cube isn't gammicidal.

Since winfox raised the question of reversing the score, I also did a short rollout with Blue trailing 3a2a. According to XGR++, it is then a borderline double before the roll, so I put the cube on White's side of the board. Now 8/2* 6/2 does come out ahead, though by a relatively small margin. Blue now doesn't have to worry about getting gammoned but his own gammon value is normal, and according to the rollout, 8/2* 6/2 just barely manages to overcome the usual 2-to-1 tradeoff between extra gammons won and extra games lost.





White is Player 2

score: 4
pip: 158
7 point match
pip: 145
score: 5

Blue is Player 1
XGID=-aa--BE-B---dE--ab-db---A-:0:0:1:64:5:4:0:7:10
Blue to play 64

1.Rollout124/14eq: +0.348
Player:
Opponent:
61.93% (G:16.33% B:1.78%)
38.07% (G:9.04% B:0.71%)
Conf.: 0.014 (+0.334...+0.362) - [100.0%]
Duration: 27 minutes 00 second
2.Rollout18/2* 6/2eq: +0.251 (-0.097)
Player:
Opponent:
57.93% (G:24.90% B:4.92%)
42.07% (G:10.58% B:1.01%)
Conf.: 0.017 (+0.235...+0.268) - [0.0%]
Duration: 25 minutes 43 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2


For money:





White is Player 2

score: 0
pip: 158
Unlimited Game
pip: 145
score: 0

Blue is Player 1
XGID=-aa--BE-B---dE--ab-db---A-:0:0:1:64:0:0:0:0:10
Blue to play 64

1.Rollout124/14eq: +0.452
Player:
Opponent:
62.10% (G:12.30% B:0.51%)
37.90% (G:8.25% B:0.29%)
Conf.: 0.006 (+0.445...+0.458) - [100.0%]
Duration: 1 hour 45 minutes
2.Rollout18/2* 6/2eq: +0.428 (-0.024)
Player:
Opponent:
58.15% (G:22.82% B:1.24%)
41.85% (G:10.46% B:0.45%)
Conf.: 0.008 (+0.420...+0.436) - [0.0%]
Duration: 1 hour 19 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10


With the score reversed:





White is Player 2

score: 5
pip: 158
7 point match
pip: 145
score: 4

Blue is Player 1
XGID=-aa--BE-B---dE--ab-db---A-:1:-1:1:64:4:5:0:7:10
Blue to play 64

1.Rollout18/2* 6/2eq: +0.379
Player:
Opponent:
58.04% (G:22.87% B:2.76%)
41.96% (G:10.41% B:0.71%)
Conf.: 0.008 (+0.371...+0.386) - [100.0%]
Duration: 8 minutes 05 seconds
2.Rollout124/14eq: +0.357 (-0.022)
Player:
Opponent:
62.00% (G:12.28% B:1.58%)
38.00% (G:8.33% B:1.19%)
Conf.: 0.006 (+0.350...+0.363) - [0.0%]
Duration: 9 minutes 22 seconds
1 648 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

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