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A position. - RO

Posted By: Daniel Murphy
Date: Thursday, 16 February 2012, at 11:42 p.m.

In Response To: A position. Backgammon may be solved ... (Daniel Murphy)

The score (after 2 games) is: White 1, Blue 4 (match to 11 points)

Move number 39: Blue on roll, cube decision?

White	48
Blue	136
Position ID: 990AQABsc6NAAQ Match ID: UQlgARAAIAAE

Cube decision
Rollout cubeless equity		+0.5112	(Money: +0.5211)
Cubeful equities:
1.	Double, take	+0.9840
2.	Double, pass	+1.0000	+0.0160
3.	No double	+0.8305	-0.1536
Proper cube action:		Redouble, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.8051 0.0000 0.0000 - 0.1949 0.0886 0.0005 +0.5112 +0.8305 Standard error 0.0007 0.0000 0.0000 - 0.0007 0.0007 0.0001 0.0017 0.0039 Player White owns 4-cube 0.8331 0.0000 0.0000 - 0.1669 0.0731 0.0005 +1.1415 +0.9840 Standard error 0.0009 0.0000 0.0000 - 0.0009 0.0008 0.0001 0.0053 0.0057
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 908023327 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]

Annotation

Cube analysis
2-ply cubeless equity +0.3830 (Money: +0.3961)
0.7570 0.0000 0.0000 - 0.2430 0.1171 0.0008
Cubeful equities:
1. No double +0.6406
2. Double, pass +1.0000 ( +0.3594)
3. Double, take +0.4570 ( -0.1836)
Proper cube action: No redouble, take (33.8%)

Cube analysis
4-ply cubeless equity +0.4891 (Money: +0.5003)
0.8007 0.0000 0.0000 - 0.1993 0.1003 0.0008
Cubeful equities:
1. No double +0.7546
2. Double, pass +1.0000 ( +0.2454)
3. Double, take +0.7314 ( -0.0233)
Proper cube action: No redouble, take (8.7%)

---

Double/Take at the score.

Pass -> White trails 10a5a -> 23.3% ME
Take and win single (no redouble) -> White leads 6a7a -> 56.3% ME
Take and lose -> White trails 10a3a -> 12.9% ME

R/(R+G) = 10.4/43.4 = 23.9% cubeless gammonless take point.

Pass -> White trails 10a5a -> 23.3% ME
Take and win single (no redouble) -> White leads 6a7a -> 56.3% ME * 56% = 31.53%
Take and win gammon (no redouble) -> White leads 2a7a -> 84.2% ME * 44% = 37.0%
Take and lose -> White trails 10a3a -> 12.9% ME

R/(R+G) = 10.4/55.6 = 18.7% cubeless gammon-adjusted take point.

---

At DMP, Blue wins about 83.3%% (rollout not shown here).

---

Recube to 8 ATS after double/take ... Blue 43:13/9 12/9?

Yes, and easy take. Pass is a -0.359 = 7.8% ME error (rollout, not shown). White wins about 53% with about 24.5% gammons, and loses about 47%. I think Blue hits about 42% on Blue's next roll.

Pass -> Blue leads 7a6a -> 43.7% ME
Take and win the match
Take and lose -> Blue trails 7a2a -> 15.8% ME, or loses the match on a gammon -> average ME = 8.6%

R/(R+G) = 27.9/84.2 = 33% gammonless take point.

R/(R+G) = 35.1/91.4 = 38.4% gammon-adjusted take point.

---

Money game pass:

MG. Blue on roll.

White	48
Blue	136
Position ID: 990AQABsc6NAAQ Match ID: UQkAABAAAAAE

Cube decision
Rollout cubeless equity		+0.5101
Cubeful equities:
1.	Double, pass	+1.0000
2.	Double, take	+1.1310	+0.1310
3.	No double	+0.8239	-0.1761
Proper cube action:		Redouble, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player 11s owns 2-cube 0.8006 0.0000 0.0000 - 0.1994 0.0904 0.0007 +0.5101 +0.8239 Standard error 0.0011 0.0000 0.0000 - 0.0011 0.0012 0.0001 0.0025 0.0048 Player gnubg owns 4-cube 0.8319 0.0000 0.0000 - 0.1681 0.0715 0.0006 +1.1833 +1.1310 Standard error 0.0015 0.0000 0.0000 - 0.0015 0.0015 0.0002 0.0071 0.0090
Full cubeful rollout with var.redn.
809 games, Mersenne Twister dice gen. with seed 907377453 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]

Annotation

Cube analysis
2-ply cubeless equity +0.3961
0.7570 0.0000 0.0000 - 0.2430 0.1171 0.0008
Cubeful equities:
1. No double +0.7055
2. Double, pass +1.0000 ( +0.2945)
3. Double, take +0.6339 ( -0.0715)
Proper cube action: No redouble, take (19.5%)

Cube analysis
4-ply cubeless equity +0.5004
0.8007 0.0000 0.0000 - 0.1993 0.1002 0.0008
Cubeful equities:
1. Double, take +0.8938
2. Double, pass +1.0000 ( +0.1062)
3. No double +0.7705 ( -0.1233)
Proper cube action: Redouble, take

White actually won 18.3% of games after double/take in this MG rollout.

Messages In This Thread

• A position. Backgammon may be solved ...
  Daniel Murphy -- Tuesday, 14 February 2012, at 4:08 p.m.
  • Rerecube to 8 After a Miss?
    Paul Weaver -- Tuesday, 14 February 2012, at 4:52 p.m.
    • Rerecube to 8 After a Miss?
      Daniel Murphy -- Tuesday, 14 February 2012, at 5:11 p.m.
  • A position. Backgammon may be solved ...
    Turz -- Tuesday, 14 February 2012, at 5:15 p.m.
  • A position. - RO
    Daniel Murphy -- Thursday, 16 February 2012, at 11:42 p.m.