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original pos. and variants - RO

Posted By: Daniel Murphy
Date: Monday, 20 February 2012, at 12:07 a.m.

In Response To: original pos. and variants - RO (pontiac)

Money game

5-4 18/13 18/14 is 0.299 better than 18/9, wins 38.10% cubeless

4-3 18/14 18/15 is 0.035 better than 18/11, wins 33.13% cubeless

Why?

(1) 5-4 18/13 18/14 gets missed on 16/36 (44.4%) rolls instead of 12/36 (33.3%) after 5-4 18/9. Difference of 11.1%. 4-3 18/14 18/13 gets missed on 15/36 (41.6%) rolls instead of 12/36 (33.3%) after 18/11. Difference of 8.3%.

(2) 5-4 is 9 pips, 2 pips more than 4-3.

---

ATS

Leading 4a7a 18/11 is 0.045 EMG better than 18/14 18/15

Trailing 7a6a 18/11 is 0.007 EMG worse than 18/14 18/15

Why? I can think of two reason, one minor and one major.

The minor -- 18/14 18/15 gets gammoned more often, and these gammon are slightly more costly when Blues leads 4a7a:

Lose, 4a 5a = 57.74%
Lose, 4a 3a = 42.86%, a difference of 14.88%

Lose, 7a 4a = 30.03%
Lose, 7a 2a = 15.79%, a difference of 14.24%

Multiply the difference of 0.62% by the 11% more gammon losses after 18/14 18/15. It's a small point.

The major -- Blue gains a lot when he can redouble to four. He's more likely to redouble to 4 after 18/14 18/15, the play that wins more often. But Blue is a lot less likely to redouble to 4 leading 4a7a than trailing 7a6a. Immediate cube action after a miss by White is not the same at both scores. Leading 4a7a, no redouble. Trailing 7a6a, redouble after most misses.

Blue leads 4a7a

win 4 0a7a = 100%, win 2 2a7a = 84.21%, redouble gains 15.89%, lose 4 4a3a = 42.86%, lose 2 4a5a = 57.74%, redouble risks 14.88%

or with a live cube, redouble to 4, redouble to 8:

win 4 0a7a = 100%, win 2 2a7a = 84.21%, redouble gains 15.79%, lose 8 4a0a = 0%, lose 2 4a5a = 57.74, redouble risks 57.75%

Blue trails 7a6a

win 4 3a6a = 71.16%, win 2 5a6a = 56.66%, redouble gains 14.50%, lose 4 7a2a = 15.79%, lose 2 7a4a = 30.03%, redouble risks 14.24%

or with a live cube redouble to 4, redouble to 8:

win 8 0a6a = 100%, win 2 5a6a = 56.66%, redouble gains 43.34%, lose 8 7a0a = 0%, lose 2 7a4a = 30.03%, redouble risks 30.03%

We should expect Blue to redouble to 4 more often after 18/14 18/15 at either score, and more often trailing 7a6a after either play. In Gnubg rollouts of White's cube action, that is what happens:

Score	Play	How often does Blue redouble to 4?
Leading 4a7a	18/14 18/15	All 37.19%	Pass 6.40%	Take 30.79%
Trailing 7a6a	18/14 18/15	All 44.36%	Pass 5.32%	Take 39.04%
Leading 4a7a	18/11	All 30.09%	Pass 3.78%	Take 26.31%
Trailing 7a6a	18/11	All 36.88%	Pass 4.94%	Take 31.94%

An example:

Blue trails 0-1/7. Blue on roll. White 83 Blue 63 Position ID: bdsMBgB394CAAA Match ID: UQngABAAAAAE Cube decision Rollout cubeless equity +0.4378 (Money: +0.4384) Cubeful equities: 1. Double, take +0.8543 2. Double, pass +1.0000 +0.1457 3. No double +0.6209 -0.2334 Proper cube action: Redouble, take Rollout details Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.7223 0.0075 0.0000 - 0.2777 0.0133 0.0003 +0.4378 +0.6209 Standard error 0.0008 0.0008 0.0038 - 0.0008 0.0011 0.0001 0.0020 0.0027 Player White owns 4-cube 0.7278 0.0076 0.0001 - 0.2722 0.0137 0.0002 +0.9545 +0.8543 Standard error 0.0007 0.0016 0.0001 - 0.0007 0.0019 0.0000 0.0031 0.0040 Full cubeful rollout with var.redn. 534 games, Mersenne Twister dice gen. with seed 912839339 and quasi-random dice Play: supremo 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class]

Blue leads 3-0/7. Blue on roll. White 83 Blue 63 Position ID: bdsMBgB394CAAA Match ID: UQngAAAAGAAE Alert: wrong double ( -0.4094)! [very bad] Cube decision Rollout cubeless equity +0.4442 (Money: +0.4440) Cubeful equities: 1. No double +0.5845 2. Double, pass +1.0000 +0.4155 3. Double, take +0.1752 -0.4094 Proper cube action: No redouble, take (49.6%) Rollout details Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.7230 0.0101 0.0001 - 0.2770 0.0120 0.0002 +0.4442 +0.5845 Standard error 0.0008 0.0007 0.0002 - 0.0008 0.0009 0.0001 0.0024 0.0029 Player White owns 4-cube 0.7247 0.0115 0.0002 - 0.2753 0.0164 0.0001 +0.9952 +0.1752 Standard error 0.0008 0.0015 0.0000 - 0.0008 0.0025 0.0000 0.0040 0.0047 Full cubeful rollout with var.redn. 442 games, Mersenne Twister dice gen. with seed 912395146 and quasi-random dice Play: supremo 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 16 more moves within equity 0.32 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class]

Messages In This Thread

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    Daniel Murphy -- Friday, 17 February 2012, at 9:04 p.m.
    • BootCamp problem
      christian munk-christensen -- Friday, 17 February 2012, at 9:20 p.m.
      • BootCamp problem
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    • original pos. and variants - RO
      pontiac -- Saturday, 18 February 2012, at 12:44 p.m.
      • original pos. and variants - RO
        Daniel Murphy -- Monday, 20 February 2012, at 12:07 a.m.
        • original pos. and variants - RO
          pontiac -- Tuesday, 21 February 2012, at 6:35 a.m.