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501 Essential Backgammon Problems #42 -- Rollout + Variants

Posted By: Igor
Date: Wednesday, 28 August 2013, at 4:25 p.m.

In Response To: 501 Essential Backgammon Problems #42 (Igor)

Hitting with 6/4* unstacks the 6pt and fights for initiative; blue can afford to do so due to the blot on the white 5pt. For the three Robertie recommends 13/10 as it unstacks the midpoint, provides another cover for the blot on our 4pt (and let's not forget duplication of 3's and 4's). This is a very natural logical choice. The downside is that blue leaves four blots; not the best idea when you are outboarded. According to the rollouts 16/13 is a viable option. Shorter 5K and 13K rollouts posted previously suggest that 16/13 is better than 13/10, but as I already mentioned, the longer you keep it going, the closer the two plays become.





White is Player 2

score: 0
pip: 170
Unlimited Game
Jacoby
pip: 159
score: 0

Blue is Player 1
XGID=-b--a-E-C---dE--Ac-bab--A-:0:0:1:32:0:0:1:0:10
Blue to play 32

1.Rollout116/13 6/4* eq: -0.102
Player:
Opponent:
47.90% (G:13.35% B:0.87%)
52.10% (G:15.93% B:0.69%)
Conf.: 0.003 (-0.105...-0.099) - [79.0%]
Duration: 5 hours 57 minutes
2.Rollout113/10 6/4* eq: -0.104 (-0.002)
Player:
Opponent:
47.85% (G:14.83% B:1.17%)
52.15% (G:17.74% B:1.33%)
Conf.: 0.003 (-0.107...-0.101) - [21.0%]
Duration: 5 hours 27 minutes
3.Rollout224/22 16/13eq: -0.153 (-0.051)
Player:
Opponent:
47.28% (G:11.76% B:0.72%)
52.72% (G:18.31% B:0.55%)
Conf.: 0.013 (-0.166...-0.140) - [0.0%]
Duration: 18 minutes 25 seconds
4.Rollout216/11eq: -0.156 (-0.054)
Player:
Opponent:
46.57% (G:12.66% B:0.78%)
53.43% (G:16.08% B:0.63%)
Conf.: 0.011 (-0.168...-0.145) - [0.0%]
Duration: 18 minutes 58 seconds
1 46656 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

2 2592 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

13/10 wins more gammons and loses more gammons, so if this is an AtS decision, it could easily be swayed one way or another. Let's bring one more white checker in the zone:





White is Player 2

score: 0
pip: 163
Unlimited Game
Jacoby
pip: 159
score: 0

Blue is Player 1
XGID=-b--a-E-C---cE--Ac-cab--A-:0:0:1:32:0:0:1:0:10
Blue to play 32

1.Rollout116/13 6/4* eq: -0.266
Player:
Opponent:
44.83% (G:11.66% B:0.73%)
55.17% (G:19.09% B:0.84%)
Conf.: 0.003 (-0.269...-0.263) - [90.6%]
Duration: 5 hours 00 minute
2.Rollout113/10 6/4* eq: -0.269 (-0.003)
Player:
Opponent:
44.72% (G:12.68% B:0.88%)
55.28% (G:21.39% B:1.69%)
Conf.: 0.003 (-0.272...-0.266) - [9.4%]
Duration: 4 hours 34 minutes
3.Rollout216/11eq: -0.282 (-0.016)
Player:
Opponent:
44.39% (G:10.62% B:0.57%)
55.61% (G:19.53% B:0.67%)
Conf.: 0.008 (-0.290...-0.274) - [0.0%]
Duration: 31 minutes 59 seconds
4.Rollout324/22 16/13eq: -0.343 (-0.077)
Player:
Opponent:
43.82% (G:9.53% B:0.54%)
56.18% (G:21.71% B:0.61%)
Conf.: 0.011 (-0.354...-0.332) - [0.0%]
Duration: 14 minutes 19 seconds
1 46656 Games rolled with Variance Reduction.
Dice Seed: 28412616
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Dice Seed: 28412616
Moves: 3-ply, cube decisions: XG Roller

3 2592 Games rolled with Variance Reduction.
Dice Seed: 92893372
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

The two hitting plays are still virtually tied, but now the safer 16/11 naturally gained in relative equity. Now, one of the reasons to hit loose on our 4pt is to unload the heavy 6pt, so let's change the distribution of spares:





White is Player 2

score: 0
pip: 170
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-b--a-D-D---dE--Ac-bab--A-:0:0:1:32:0:0:1:0:10
Blue to play 32

1.Rollout113/10 6/4* eq: -0.104
Player:
Opponent:
48.12% (G:14.09% B:1.04%)
51.88% (G:17.90% B:1.35%)
Conf.: 0.003 (-0.107...-0.101) - [99.5%]
Duration: 5 hours 39 minutes
2.Rollout116/11eq: -0.110 (-0.005)
Player:
Opponent:
47.72% (G:12.34% B:0.73%)
52.28% (G:15.67% B:0.59%)
Conf.: 0.003 (-0.113...-0.107) - [0.5%]
Duration: 5 hours 45 minutes
3.Rollout216/13 6/4* eq: -0.123 (-0.018)
Player:
Opponent:
47.76% (G:12.63% B:0.81%)
52.24% (G:16.03% B:0.71%)
Conf.: 0.006 (-0.129...-0.116) - [0.0%]
Duration: 1 hour 26 minutes
4.Rollout324/22 16/13eq: -0.129 (-0.024)
Player:
Opponent:
47.95% (G:11.07% B:0.65%)
52.05% (G:17.42% B:0.54%)
Conf.: 0.009 (-0.138...-0.120) - [0.0%]
Duration: 37 minutes 43 seconds
1 46656 Games rolled with Variance Reduction.
Dice Seed: 92893372
Moves: 3-ply, cube decisions: XG Roller

2 10368 Games rolled with Variance Reduction.
Dice Seed: 92893372
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 92893372
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Now 16/11 is almost as good as hitting loose for money and might be a better choice AtS depending on given gammon values.

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