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Rollout, plus a followup quiz!

Posted By: Timothy Chow
Date: Wednesday, 2 September 2009, at 1:40 a.m.

In Response To: Blitz cube action (Timothy Chow)

According to gnubg, the answer to Problem 1 is double/take (easy take) and the answer to Problem 2 is double/pass (close pass). Scroll down past the rollouts for a followup question.

Problem 1: Money Game
Blue on roll. Cube action?

Chow	164
Motif	143
Position Id: 4HPMAVAa18QBIg Match Id: cAkAAAAAAAAA

Cube decision
Rollout cubeless equity		+0.473
Cubeful equities:
1.	Double, take	+0.715
2.	Double, pass	+1.000	+0.285
3.	No double	+0.654	-0.061
Proper cube action:		Double, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.625 0.304 0.014 - 0.375 0.090 0.004 +0.473 +0.654 Standard error 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.011 Player gnubg owns 2-cube 0.631 0.327 0.014 - 0.369 0.090 0.005 +1.016 +0.715 Standard error 0.002 0.003 0.003 - 0.002 0.001 0.000 0.016 0.021
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 868209228 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]

Problem 2: Money Game
Blue on roll. Cube action?

Chow	146
Motif	136
Position Id: wufgA0CD28EJIA Match Id: cAkAAAAAAAAA

Cube decision
Rollout cubeless equity		+0.619
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.035	+0.035
3.	No double	+0.848	-0.152
Proper cube action:		Double, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.688 0.302 0.006 - 0.312 0.063 0.002 +0.619 +0.848 Standard error 0.001 0.002 0.000 - 0.001 0.001 0.000 0.003 0.009 Player gnubg owns 2-cube 0.687 0.337 0.005 - 0.313 0.068 0.003 +1.291 +1.035 Standard error 0.002 0.003 0.000 - 0.002 0.001 0.000 0.008 0.012
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 867477660 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]

When I first rolled out the above two positions, I was surprised that the equity difference was so large (+0.715 versus +1.000). So I varied the positions to see what the most significant difference between them was. Below are three different modifications of the position of Problem 1. QUESTION: Which modification makes the most difference to the equity of the position?

This might seem to be an unusual question, but according to gnubg the answer is very clear.

Modification 1: Clean up Blue's blots

Money Game
Blue on roll. Cube action?

Chow	164
Motif	146
Position Id: 4HPMAVCM28EBIg Match Id: cAkAAAAAAAAA

Modification 2: Eliminate White's outfield point

Money Game
Blue on roll. Cube action?

Chow	168
Motif	143
Position Id: 4HPwAVAa18QBIg Match Id: cAkAAAAAAAAA

Modification 3: Eliminate White's ability to anchor

Money Game
Blue on roll. Cube action?

Chow	142
Motif	143
Position Id: wueYA0Aa18QBIg Match Id: cAkAAAAAAAAA

Messages In This Thread

• Blitz cube action
  Timothy Chow -- Monday, 31 August 2009, at 5:18 p.m.
  • Blitz cube action
    Neil Robins -- Monday, 31 August 2009, at 6:32 p.m.
  • Blitz cube action
    John O'Hagan -- Tuesday, 1 September 2009, at 4:34 a.m.
  • Blitz cube action
    Keene -- Tuesday, 1 September 2009, at 2:15 p.m.
  • Blitz cube action
    neilkaz -- Tuesday, 1 September 2009, at 10:07 p.m.
  • Rollout, plus a followup quiz!
    Timothy Chow -- Wednesday, 2 September 2009, at 1:40 a.m.
    • Rollout, plus a followup quiz!
      Matt Cohn-Geier -- Wednesday, 2 September 2009, at 4:04 a.m.
    • Answer to followup quiz (rollout)
      Timothy Chow -- Thursday, 3 September 2009, at 10:13 p.m.