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Rollout: How strong is a 5-prime?

Posted By: Timothy Chow
Date: Monday, 12 April 2010, at 1:01 a.m.

In Response To: How strong is a 5-prime? (Timothy Chow)

I was playing Blue here. Not so long ago, I would have considered passing as White, being spooked by the 5-prime. Here I was confident that White had a take, but I also thought Blue had a strong double. The rollout, however, says that the double is essentially optional. Blue has a strong position but is not likely to roll a crusher, and can afford to wait a turn to see if things go south. And things can go south, as the subsequent play illustrates.

I rolled 6-4 and ran 21/11; White rolled a lucky 4-4 and pointed on me with 13/9(2) 8/4*(2); I danced. I know some people who would double as White in the resulting position, figuring that any 6 would be a market loser and that Blue was in big trouble with a checker on the bar against a 5-point board. But in fact, it's a huge beaver. White is not in a position to close the board, and hitting loose risks getting another checker sent behind the 5-prime.

White did not double, and escaped a checker with 6-5. I danced again, reaching Position 2, in which White redoubled. I passed, but the rollout indicates that Blue can take. White's dead checker is important here, significantly reducing White's attacking power. And again, the 5-prime means that any return hit puts Blue right back into the game.

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Rollout of Position 1 (Blue on roll):

White	116
Blue	134
Position ID: OzaDAQzYboMBBg Match ID: cAkAACAAAAAA

Cube decision
Rollout cubeless equity		+0.511
Cubeful equities:
1.	No double	+0.842
2.	Double, pass	+1.000	+0.158
3.	Double, take	+0.836	-0.006
Proper cube action:		No double, take (3.5%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.703 0.156 0.005 - 0.297 0.056 0.001 +0.511 +0.842 Standard error 0.001 0.001 0.000 - 0.001 0.001 0.000 0.002 0.006 Player White owns 2-cube 0.706 0.162 0.006 - 0.294 0.055 0.001 +1.050 +0.836 Standard error 0.001 0.002 0.000 - 0.001 0.001 0.000 0.005 0.007
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 848894668 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]

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Rollout of Position 2 (White on roll):

White	89
Blue	128
Position ID: 2G4jA0A725gACA Match ID: AQEAACAAAAAA

Cube decision
Rollout cubeless equity		+0.592
Cubeful equities:
1.	Double, take	+0.916
2.	Double, pass	+1.000	+0.084
3.	No double	+0.737	-0.179
Proper cube action:		Redouble, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player White owns 2-cube 0.657 0.319 0.001 - 0.343 0.041 0.001 +0.592 +0.737 Standard error 0.001 0.002 0.000 - 0.001 0.001 0.000 0.002 0.005 Player Blue owns 4-cube 0.661 0.324 0.001 - 0.339 0.040 0.001 +1.211 +0.916 Standard error 0.001 0.002 0.000 - 0.001 0.001 0.000 0.005 0.007
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 849007741 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

• How strong is a 5-prime?
  Timothy Chow -- Sunday, 11 April 2010, at 2:12 a.m.
  • Rollout: How strong is a 5-prime?
    Timothy Chow -- Monday, 12 April 2010, at 1:01 a.m.
    • Rollout: How strong is a 5-prime?
      Daniel Murphy -- Monday, 12 April 2010, at 1:16 a.m.
  • Another 5-prime cube decision
    Timothy Chow -- Thursday, 15 April 2010, at 1:29 a.m.