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501 Essential BG Problems #23 Rollouts + Variants

Posted By: Igor
Date: Friday, 16 August 2013, at 12:07 a.m.

In Response To: 501 Essential Backgammon Problems #23 (Igor)

Robertie observes that given the fact that blue had already made his 4pt, the standard 24/21(2) 13/10(2) move should be reevaluated. He does not doubt for a second that 24/21(2) is still correct no matter what, but instead of 13/10(2), he suggests that blue should play 8/5(2).

This analysis somewhat puzzled me, as the only crystal clear part of the move is 8/5(2) -- the 4-5-6 structure is so powerful that ones needs very serious reasons to forgo it, of which I can find none in the OP.

With white's stacked and inflexible position she is likely to leave a shot next roll. If we have a four point board then a hit allows us to spin the cube and most likely cash the game right away. I completely agree with Casper regarding this observation. So, it should be clear that the best play is a "next."





White is Player 2

score: 0
pip: 156
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-a--B-D-B---fE---c-e----B-:0:0:1:33:0:0:1:0:10
Blue to play 33

1.Rollout18/5(2) 6/3(2)eq: +0.495
Player:
Opponent:
59.91% (G:24.19% B:0.56%)
40.09% (G:7.64% B:0.36%)
Conf.: ± 0.009 (+0.486...+0.503) - [100.0%]
Duration: 20 minutes 00 second
2.Rollout124/21(2) 8/5(2)eq: +0.436 (-0.058)
Player:
Opponent:
59.31% (G:18.11% B:0.31%)
40.69% (G:4.85% B:0.19%)
Conf.: ± 0.006 (+0.430...+0.443) - [0.0%]
Duration: 23 minutes 58 seconds
3.Rollout224/21 13/10 8/5(2)eq: +0.409 (-0.086)
Player:
Opponent:
57.87% (G:22.09% B:0.51%)
42.13% (G:8.00% B:0.38%)
Conf.: ± 0.010 (+0.399...+0.419) - [0.0%]
Duration: 11 minutes 53 seconds
4.Rollout213/10(2) 8/5(2)eq: +0.408 (-0.087)
Player:
Opponent:
57.98% (G:22.00% B:0.56%)
42.02% (G:8.87% B:0.41%)
Conf.: ± 0.010 (+0.398...+0.418) - [0.0%]
Duration: 12 minutes 00 second
5.Rollout324/21(2) 13/10(2)eq: +0.388 (-0.107)
Player:
Opponent:
58.84% (G:16.78% B:0.45%)
41.16% (G:6.62% B:0.27%)
Conf.: ± 0.013 (+0.375...+0.401) - [0.0%]
Duration: 7 minutes 25 seconds
6.Rollout324/18(2)eq: +0.369 (-0.125)
Player:
Opponent:
58.46% (G:14.62% B:0.31%)
41.54% (G:6.39% B:0.26%)
Conf.: ± 0.013 (+0.357...+0.382) - [0.0%]
Duration: 8 minutes 37 seconds
7.Rollout324/21(2) 6/3(2)eq: +0.367 (-0.127)
Player:
Opponent:
58.22% (G:16.19% B:0.39%)
41.78% (G:5.42% B:0.23%)
Conf.: ± 0.013 (+0.354...+0.380) - [0.0%]
Duration: 7 minutes 15 seconds
8.Rollout313/7(2)eq: +0.356 (-0.139)
Player:
Opponent:
57.65% (G:19.52% B:0.63%)
42.35% (G:9.49% B:0.45%)
Conf.: ± 0.013 (+0.343...+0.369) - [0.0%]
Duration: 6 minutes 49 seconds
9.Rollout313/10(2) 6/3(2)eq: +0.337 (-0.158)
Player:
Opponent:
57.34% (G:19.86% B:0.57%)
42.66% (G:9.60% B:0.45%)
Conf.: ± 0.014 (+0.323...+0.350) - [0.0%]
Duration: 6 minutes 32 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 90333169
Moves: 3-ply, cube decisions: XG Roller

2 2592 Games rolled with Variance Reduction.
Dice Seed: 90333169
Moves: 3-ply, cube decisions: XG Roller

3 1296 Games rolled with Variance Reduction.
Dice Seed: 90333169
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Next comes the bonus question that I forgot to ask in the original post. What kind of improvement in white's position would it take to make advancing back checkers come out on top of making the fourth home board point?

Let's do it one step at a time.





White is Player 2

score: 0
pip: 152
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-a--B-D-B---dEb--c-e----B-:0:0:1:33:0:0:1:0:10
Blue to play 33

1.Rollout18/5(2) 6/3(2)eq: +0.265
Player:
Opponent:
55.10% (G:19.71% B:0.53%)
44.90% (G:9.15% B:0.44%)
Conf.: ± 0.005 (+0.260...+0.270) - [100.0%]
Duration: 45 minutes 09 seconds
2.Rollout124/21(2) 8/5(2)eq: +0.252 (-0.013)
Player:
Opponent:
54.76% (G:15.11% B:0.30%)
45.24% (G:5.47% B:0.21%)
Conf.: ± 0.005 (+0.247...+0.257) - [0.0%]
Duration: 54 minutes 09 seconds
1 10368 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

The two plays are now very close, but not quite enough improvement for white to make blue start moving back checkers.





White is Player 2

score: 0
pip: 150
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-a--B-D-B---dE-b-c-e----B-:0:0:1:33:0:0:1:0:10
Blue to play 33

1.Rollout18/5(2) 6/3(2)eq: +0.210
Player:
Opponent:
54.17% (G:18.08% B:0.53%)
45.83% (G:9.64% B:0.46%)
Conf.: ± 0.012 (+0.197...+0.222) - [100.0%]
Duration: 5 minutes 46 seconds
2.Rollout124/21(2) 8/5(2)eq: +0.105 (-0.105)
Player:
Opponent:
50.73% (G:14.39% B:0.28%)
49.27% (G:5.63% B:0.20%)
Conf.: ± 0.015 (+0.090...+0.120) - [0.0%]
Duration: 7 minutes 01 second
1 1296 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Naturally, you are less interested in making an anchor that is perfectly blocked by white 10pt precisely 6 pips away.





White is Player 2

score: 0
pip: 148
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-a--B-D-B---dE--bc-e----B-:0:0:1:33:0:0:1:0:10
Blue to play 33

1.Rollout18/5(2) 6/3(2)eq: +0.117
Player:
Opponent:
51.86% (G:16.75% B:0.45%)
48.14% (G:10.29% B:0.51%)
Conf.: ± 0.006 (+0.111...+0.124) - [100.0%]
Duration: 23 minutes 33 seconds
2.Rollout124/21(2) 8/5(2)eq: +0.094 (-0.024)
Player:
Opponent:
50.58% (G:13.43% B:0.24%)
49.42% (G:5.84% B:0.23%)
Conf.: ± 0.007 (+0.087...+0.100) - [0.0%]
Duration: 27 minutes 01 second
3.Rollout224/21(2) 13/10(2)eq: +0.064 (-0.054)
Player:
Opponent:
50.65% (G:12.79% B:0.31%)
49.35% (G:7.26% B:0.29%)
Conf.: ± 0.013 (+0.051...+0.077) - [0.0%]
Duration: 7 minutes 30 seconds
4.Rollout224/21(2) 6/3(2)eq: +0.035 (-0.082)
Player:
Opponent:
49.97% (G:11.63% B:0.29%)
50.03% (G:6.48% B:0.26%)
Conf.: ± 0.013 (+0.022...+0.049) - [0.0%]
Duration: 7 minutes 30 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Still not good enough. To be honest, I was surprised to see the rollout results for this position. I expected 24/21(2) to finally come out on top.





White is Player 2

score: 0
pip: 144
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-a--B-D-B---dE---cbe----B-:0:0:1:33:0:0:1:0:10
Blue to play 33

1.Rollout124/21(2) 8/5(2)eq: +0.064
Player:
Opponent:
49.91% (G:12.29% B:0.24%)
50.09% (G:5.45% B:0.21%)
Conf.: ± 0.004 (+0.060...+0.069) - [100.0%]
Duration: 48 minutes 59 seconds
2.Rollout124/21(2) 13/10(2)eq: +0.050 (-0.015)
Player:
Opponent:
50.27% (G:11.60% B:0.29%)
49.73% (G:7.27% B:0.28%)
Conf.: ± 0.005 (+0.045...+0.054) - [0.0%]
Duration: 53 minutes 31 seconds
3.Rollout28/5(2) 6/3(2)eq: +0.015 (-0.049)
Player:
Opponent:
49.33% (G:15.90% B:0.43%)
50.67% (G:10.79% B:0.49%)
Conf.: ± 0.014 (+0.001...+0.029) - [0.0%]
Duration: 5 minutes 24 seconds
4.Rollout224/21(2) 6/3(2)eq: +0.014 (-0.050)
Player:
Opponent:
49.58% (G:10.53% B:0.27%)
50.42% (G:6.27% B:0.24%)
Conf.: ± 0.011 (+0.002...+0.025) - [0.0%]
Duration: 7 minutes 04 seconds
1 10368 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Now both 8/5(2) and 24/21(2) should be pretty clear to anybody. Blue does need to start fighting against white's starter prime and hence moving the back anchor is a must. Another surprise for me -- 13/10(2) is somewhat a contender for 8/5(2).





White is Player 2

score: 0
pip: 140
Unlimited Game
Jacoby
pip: 161
score: 0

Blue is Player 1
XGID=-a--B-D-B---dE---c-eb---B-:0:0:1:33:0:0:1:0:10
Blue to play 33

1.Rollout124/21(2) 8/5(2)eq: -0.058
Player:
Opponent:
46.88% (G:10.70% B:0.22%)
53.12% (G:6.35% B:0.21%)
Conf.: ± 0.007 (-0.065...-0.051) - [76.1%]
Duration: 23 minutes 09 seconds
2.Rollout124/21(2) 13/10(2)eq: -0.061 (-0.003)
Player:
Opponent:
47.39% (G:10.07% B:0.23%)
52.61% (G:7.89% B:0.28%)
Conf.: ± 0.006 (-0.068...-0.055) - [23.8%]
Duration: 24 minutes 58 seconds
3.Rollout28/5(2) 6/3(2)eq: -0.081 (-0.023)
Player:
Opponent:
47.63% (G:13.89% B:0.43%)
52.37% (G:12.90% B:0.79%)
Conf.: ± 0.013 (-0.094...-0.068) - [0.0%]
Duration: 5 minutes 01 second
1 5184 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 94782038
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Now blue is actually worse off, so flexibility becomes ever so improtant. It is a tossup between making the 5pt and unstacking the midpoint.

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