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Spoilers

Posted By: Bob Koca
Date: Wednesday, 7 July 2010, at 8:59 p.m.

In Response To: Spoilers (Nack Ballard)

Well done Matt and Nack. Here is my solution:

The score (after 0 games) is: red 0, black 0 (match to 2 points)

Move number 2: black on roll, cube decision?

red68


4X2X2X2X2X2X ' ' ' ' ' '

1X2O3O3O3O3O ' ' ' ' ' '

black83

Position ID: dncHAEBv2wYAIA Match ID: MAFAAAAAAAAA

The best sequence for black is anyroll - 44 which gives a very clear cash:

The score (after 0 games) is: red 0, black 0 (match to 2 points)

Move number 3: black on roll, cube decision?

red52


6X4X2X2X ' ' ' ' ' ' ' '

1X2O3O3O3O3O ' ' ' ' ' '

black83

Position ID: v7cBACB2dwcAQA Match ID: cAlAAAAAAAAA

• black doubles

Cube decision
Rollout cubeless MWC 59.90%(Money: +0.513)
Cubeful equities:
1.Double, pass 68.15%
2.Double, take 74.74% 6.60%
3.No double 61.96% -6.18%
Proper cube action:Double, pass
Rollout details
WinW gW bg LoseL gL bgCubelessCubeful
Centered 1-cube0.7370.0530.001-0.2630.0150.000 59.90% 61.96%
Standard error0.0010.0010.001-0.0010.0020.000 0.05% 0.08%
Player red owns 2-cube0.7470.0770.001-0.2530.0270.000 74.74% 74.74%
Standard error0.0010.0070.000-0.0010.0050.000 0.10% 0.10%
Full cubeful rollout with var.redn.
453 games, Mersenne Twister dice gen. with seed 891260719 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

After black's worst roll of any roll red has a clear double:

The score (after 0 games) is: red 0, black 0 (match to 2 points)

Move number 4: red on roll, cube decision?

red68


4X2X2X2X2X2X ' ' ' ' ' '

1X2O3O3O3O3O ' ' ' ' ' '

black83

Position ID: dncHAEBv2wYAIA Match ID: MAFAAAAAAAAA

• red doubles

Cube decision
Rollout cubeless MWC 51.62%(Money: +0.060)
Cubeful equities:
1.Double, take 54.08%
2.Double, pass 68.15% 14.07%
3.No double 46.95% -7.13%
Proper cube action:Double, take
Rollout details
WinW gW bg LoseL gL bgCubelessCubeful
Centered 1-cube0.5390.0310.000-0.4610.0500.001 51.62% 46.95%
Standard error0.0020.0050.000-0.0020.0060.000 0.07% 0.15%
Player black owns 2-cube0.5410.0460.000-0.4590.0510.001 54.08% 54.08%
Standard error0.0020.0080.000-0.0020.0070.000 0.18% 0.18%
Full cubeful rollout with var.redn.
464 games, Mersenne Twister dice gen. with seed 891260719 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

So black has a market losing sequence but the cube will always be turned on red's turn anyways. Thus, the double by black is optional.

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