[Bug-gnubg] Cubeless equity in cubeful rollouts

[stiebler]

I have a question concerning the cubeless equity derived from cubeful rollouts



Date: Dezember 14, 2008
Move number 3: X to play 32

    GNU Backgammon  Position ID: mGdrBgDLzInBAA
                    Match ID   : cImpACAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: somebody
    |          O     O |   | X  O  O  O  O  X |  2 points
    |          O     O |   | X  O  O     O  X | 
    |                O |   |                  | 
    |                O |   |                  | 
    |                  |   |                  | 
    |                  |BAR|                  |v 5 point match (Cube: 1)
    |                  |   |                  | 
    |                  |   |                  | 
    |                  |   |    X             | 
    | X        X     X |   |    X           O |  Rolled 32
    | X  X     X     X |   |    X     X     O |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: You
Pip counts: O 124, X 120

* You moves 18/15*/13


This is a cubeless rollout result:

    1. Rollout          8/6 8/5                      Eq.:  -0,008
       0,498 0,015 0,000 - 0,502 0,014 0,001 CL  -0,008
      [0,001 0,001 0,000 - 0,001 0,001 0,000 CL   0,003]
        Full cubeless rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 812588963 and quasi-random dice
        Play: 0-ply cubeful prune
        Cube: 0-ply cubeful prune
    2. Rollout          18/15*/13                    Eq.:  -0,134 ( -0,127)
       0,464 0,174 0,005 - 0,536 0,174 0,009 CL  -0,134
      [0,002 0,002 0,001 - 0,002 0,002 0,001 CL   0,006]
        Full cubeless rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 812588963 and quasi-random dice
        Play: 0-ply cubeful prune
        Cube: 0-ply cubeful prune


And this is a cubeful rollout result:

    1. Rollout          18/15*/13                    Eq.:  +0,031
       0,465 0,176 0,006 - 0,535 0,176 0,015 CL  -0,025 CF  +0,031
      [0,002 0,002 0,001 - 0,002 0,002 0,002 CL   0,006 CF   0,012]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 812585055 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]
    2. Rollout          8/6 8/5                      Eq.:  -0,009 ( -0,040)
       0,500 0,017 0,000 - 0,500 0,014 0,001 CL  -0,001 CF  -0,009
      [0,001 0,001 0,000 - 0,001 0,001 0,000 CL   0,003 CF   0,006]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 812585055 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]



I know why we should not expect the w/g/bg breakdowns to be the same (with the cubeful rollout being truncated in case of a double/pass), but anyway in this case they are close. What I don't understand at all is why the cubeless equity of 18/15*/13 differs so much in the cubeful and in the cubeless rollout.