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Rollout

Posted By: Daniel Murphy
Date: Wednesday, 11 July 2007, at 3:27 a.m.

In Response To: Rollout (Misja)

Is this just some kind of freak event because the sample size of the rollout was not big enough?

No, I doubt very much that with more trials Gnubg would reverse the order of wins after ND and DT. But that doesn't mean that the "cubeless" numbers are correct.

That still does not make me understand why blue wins more games in the game breakdowns after he redoubles than when he chooses to hold the cube (forever).

I believe the correct explanation is that Blue doesn't actually win more games holding the cube forever and the "cubeless" equity is not the equity Blue would get by never doubling; the "cubeless" equity isn't truly cubeless. Rather, after ND and a subsequent double/pass, for the cubeful equity, Gnubg scores that result as 1.000 for Blue, and for the "cubeless" equity, Gnubg doubles and passes and estimates Blue's winning chances. And it's underestimating those chances, perhaps by a lot, as in this example, where the underestimate is about 4%:

The score (after 0 games) is: White 0, Blue 0

Move number 7: Blue on roll, cube decision?

White	94
Blue	66
Position ID: Wt8VACD2dkcAAA Match ID: UQkAAAAAAAAA

• Blue doubles

Alert: wrong double ( -0.0038)!

Cube decision
Rollout cubeless equity		+0.9212
Cubeful equities:
1.	No double	+1.0038
2.	Double, take	+1.7976	+0.7938
3.	Double, pass	+1.0000	-0.0038
Proper cube action:		Too good to redouble, pass (0.5%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.9372 0.0461 0.0007 - 0.0628 0.0000 0.0000 +0.9213 +1.0038 Standard error 0.0023 0.0051 0.0001 - 0.0023 0.0013 0.0000 0.0046 0.0044 Player White owns 4-cube 0.9435 0.0325 0.0006 - 0.0565 0.0000 0.0000 +1.8407 +1.7976 Standard error 0.0027 0.0052 0.0003 - 0.0027 0.0016 0.0000 0.0107 0.0133
Full cubeful rollout with var.redn.
129 games, Mersenne Twister dice gen. with seed 1069443956 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]

Annotation

Cube analysis
2-ply cubeless equity +0.9037
0.9042 0.0992 0.0029 - 0.0958 0.0066 0.0001
Cubeful equities:
1. Double, pass +1.0000
2. Double, take +1.7423 ( +0.7423)
3. No double +0.9959 ( -0.0041)
Proper cube action: Redouble, pass

Messages In This Thread

• Michigan Doubles Final Recube for Match?
  Stick -- Monday, 9 July 2007, at 5:25 a.m.
  • Michigan Doubles Final Recube for Match?
    garyo -- Monday, 9 July 2007, at 6:33 a.m.
  • Michigan Doubles Final Recube for Match?
    Misja -- Monday, 9 July 2007, at 8:15 a.m.
  • Michigan Doubles Final Recube for Match?
    Mislav Radica -- Monday, 9 July 2007, at 10:56 a.m.
  • Michigan Doubles Final Recube for Match?
    bob koca -- Monday, 9 July 2007, at 12:18 p.m.
  • Michigan Doubles Final Recube for Match?
    Matt Cohn-Geier -- Monday, 9 July 2007, at 3:37 p.m.
  • Michigan Doubles Final Recube for Match?
    Chuck Bower -- Monday, 9 July 2007, at 6:36 p.m.
    • Michigan Doubles Final Recube for Match?
      Stick -- Monday, 9 July 2007, at 6:43 p.m.
      • Michigan Doubles Final Recube for Match?
        neilkaz -- Monday, 9 July 2007, at 7:05 p.m.
      • Michigan Doubles Final Recube for Match?
        Chuck Bower -- Monday, 9 July 2007, at 7:34 p.m.
  • Rollout
    Stick -- Tuesday, 10 July 2007, at 11:27 a.m.
    • Rollout
      Misja -- Tuesday, 10 July 2007, at 1:07 p.m.
      • Rollout
        Daniel Murphy -- Tuesday, 10 July 2007, at 3:03 p.m.
        • Rollout
          Misja -- Tuesday, 10 July 2007, at 6:48 p.m.
          • Rollout
            Daniel Murphy -- Wednesday, 11 July 2007, at 3:27 a.m.