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Cubeless games in cubeful rollouts

Posted By: Daniel Murphy
Date: Friday, 2 September 2011, at 3:16 p.m.

Here's a very simple example.

Blue leads 15-12/17 (2-away 5-away). Blue on roll.

White	6
Blue	7
Position ID: IQAAoAAAAAAAAA Match ID: cAkgAsAAeAAE

Blue's cubeless GWC is 66.1694%. Blue has 17/36 (47.22%) immediate winners. If Blue doesn't double, White won't double either at the score, despite having 65.89% GWC on roll, so Blue wins 66.28% of all games (with cube access, Blue avoid losing when he rolls 2-1 twice). If Blue doubles, he will have to pass White's redouble, so Blue wins 47.22% of all games. Should Blue double? Yes he should. Here's the rollout report:

Cube decision
Rollout cubeless equity		+0.3234	(Money: +0.3234)
Cubeful equities:
1.	Double, take	+0.3818
2.	Double, pass	+1.0000	+0.6182
3.	No double	+0.3256	-0.0562
Proper cube action:		Double, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.6617 0.0000 0.0000 - 0.3383 0.0000 0.0000 +0.3234 +0.3256 Standard error 0.0000 0.0000 0.0000 - 0.0000 0.0000 0.0000 0.0000 0.0000 Player White owns 2-cube 0.6617 0.0000 0.0000 - 0.3383 0.0000 0.0000 +1.2584 +0.3818 Standard error 0.0000 0.0000 0.0000 - 0.0000 0.0000 0.0000 0.0000 0.0000
Full cubeful rollout with var.redn.
7776 games, Mersenne Twister dice gen. with seed 927765845 and quasi-random dice
Play: 4-ply cubeful prune
keep the first 0 0-ply moves and up to 12 more moves within equity 0.2
Skip pruning for 1-ply moves.
keep the first 0 2-ply moves and up to 4 more moves within equity 0.1
Skip pruning for 3-ply moves.
Cube: 4-ply cubeful prune

It's been argued that cubeless outcomes and cubeless equities are irrelevant, even worthless, in live cube rollouts. So should the rollout report instead look like this:

Cube decision
Cubeful equities:
1.	Double, take	+0.3818
2.	Double, pass	+1.0000	+0.6182
3.	No double	+0.3256	-0.0562
Proper cube action:		Double, take
Rollout details
Win Win double Win triple Lose Lose double Lose triple Cubeful Centered 1-cube 0.6628 0.0000 0.0000 - 0.3372 0.0000 0.0000 +0.3256 Standard error 0.0000 0.0000 0.0000 - 0.0000 0.0000 0.0000 0.0000 Player White owns 2-cube 0.4722 0.0000 0.0000 - 0.5277 0.0000 0.0000 +0.3818 Standard error 0.0000 0.0000 0.0000 - 0.0000 0.0000 0.0000 0.0000
Full cubeful rollout with var.redn.
7776 games, Mersenne Twister dice gen. with seed 927765845 and quasi-random dice
Play: 4-ply cubeful prune
keep the first 0 0-ply moves and up to 12 more moves within equity 0.2
Skip pruning for 1-ply moves.
keep the first 0 2-ply moves and up to 4 more moves within equity 0.1
Skip pruning for 3-ply moves.
Cube: 4-ply cubeful prune

Note again the position's simplicity: the game is over in one or two rolls, there are no gammons, and no takable redoubles.

Messages In This Thread

• Cubeless games in cubeful rollouts
  Daniel Murphy -- Friday, 2 September 2011, at 3:16 p.m.
  • Cubeless games in cubeful rollouts
    Timothy Chow -- Friday, 2 September 2011, at 4:56 p.m.
  • Cubeless games in cubeful rollouts
    Neil Robins -- Saturday, 3 September 2011, at 4:49 a.m.
    • Cubeless games in cubeful rollouts
      Timothy Chow -- Saturday, 3 September 2011, at 5:28 p.m.
      • Cubeless games in cubeful rollouts
        Daniel Murphy -- Saturday, 3 September 2011, at 7:09 p.m.
        • Cubeless games in cubeful rollouts
          Timothy Chow -- Sunday, 4 September 2011, at 6:37 p.m.
          • Cubeless games in cubeful rollouts
            Neil Robins -- Monday, 5 September 2011, at 7:53 a.m.
            • Cubeless games in cubeful rollouts
              Timothy Chow -- Tuesday, 6 September 2011, at 12:41 a.m.
  • Cubeless games in cubeful rollouts #2
    Daniel Murphy -- Sunday, 4 September 2011, at 1:17 a.m.