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Rollout

Posted By: Timothy Chow
Date: Thursday, 18 February 2010, at 10:54 p.m.

In Response To: Double shot plus 4.5-prime vs. 3-pt anchor: cube action? (Timothy Chow)

Anyone who knows a few 3-point-anchor cube reference positions can see quickly that this is an easy take. But in practice there will be some who will drop, so then we are faced with the interesting practical question of whether this is a practical double. I'll come back to that question in a moment.

First let's consider whether the position is a technical double. The GNU rollout below says that it is a clear ND. Can we trust the rollout? I spot-checked a few variations. For example, consider the sequence ND, 21L (i.e., 22/20* 9/8), dance. GNU 2-ply says that the cube action in the resulting position is double, easy take. A short rollout suggests that the take is closer than GNU 2-ply thinks, but it is still a take. On the other hand, after hit-and-cover (e.g., 22/20* 13/9) and dance, GNU 2-ply drops. To me, this suggests that GNU 2-ply is handling the cube correctly in the most critical variations, so the ND verdict is probably reliable.

What does this mean about doubling in practice? As Nack points out, one has to consider not just the probability of a bad drop this turn, but the probability of future bad drops. However, if we believe GNU's absolute equity numbers, an incorrect drop loses a lot of equity here, so I think doubling is a reasonable practical decision here. If I roll well, then it is true that the chances of an incorrect drop next turn are higher, but at the same time the equity lost by that drop will be lower.

OTB, I doubled here and my opponent took. At the time I knew it was a take but I thought the double was technically correct. I incorrectly thought that sequences like 21L-dance were market losers.

gnubg	162
tchow	151
Position ID: 0HPwAQyw28IBFA Match ID: cAkAAAAAAAAA

Alert: wrong double ( -0.078)! [doubtful]

Cube decision
Rollout cubeless equity		+0.467
Cubeful equities:
1.	No double	+0.737
2.	Double, pass	+1.000	+0.263
3.	Double, take	+0.659	-0.078
Proper cube action:		No double, take (22.9%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.670 0.188 0.009 - 0.330 0.066 0.002 +0.467 +0.737 Standard error 0.002 0.003 0.003 - 0.002 0.001 0.000 0.007 0.017 Player gnubg owns 2-cube 0.672 0.183 0.007 - 0.328 0.065 0.002 +0.932 +0.659 Standard error 0.002 0.003 0.002 - 0.002 0.001 0.000 0.013 0.017
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 844685553 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

• Double shot plus 4.5-prime vs. 3-pt anchor: cube action?
  Timothy Chow -- Wednesday, 17 February 2010, at 9:58 p.m.
  • Double shot plus 4.5-prime vs. 3-pt anchor: cube action?
    neilkaz -- Thursday, 18 February 2010, at 2:44 a.m.
    • XG 3 ply play, 4 ply cube RO in progress
      neilkaz -- Thursday, 18 February 2010, at 7:39 p.m.
  • Double shot plus 4.5-prime vs. 3-pt anchor: cube action?
    Martin -- Thursday, 18 February 2010, at 4:02 p.m.
  • Double shot plus 4.5-prime vs. 3-pt anchor: cube action?
    Nack Ballard -- Thursday, 18 February 2010, at 6:11 p.m.
  • Rollout
    Timothy Chow -- Thursday, 18 February 2010, at 10:54 p.m.
    • XG Rollout
      neilkaz -- Friday, 19 February 2010, at 12:08 a.m.
      • XG Rollout
        Stick -- Friday, 19 February 2010, at 12:25 a.m.
        • XG Rollout
          neilkaz -- Friday, 19 February 2010, at 12:31 a.m.