[Bug-gnubg] I don't understand this bearoff rollout

[Øystein Johansen]

Hi all!

    GNU Backgammon  Position ID: NwAAwDMAAAAAAA
                    Match ID   : UQkAAAAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: GNU Backgammon
 OO | O  O             |   |                  |  0 points
 OO | O  O             |   |                  |
 OO | O                |   |                  |
 OO |                  |   |                  |
 OO |                  |   |                  |
    |                  |BAR|                  |v
  X |                  |   |                  |
 XX | X                |   |                  |
 XX | X                |   |                  |
 XX | X     X          |   |                  |  On roll
 XX | X     X          |   |                  |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: Oystein (Cube: 2)

In a money game at the club I reached this position as X. Knowing that I play
against a weak player, who might think this is a three roll position and don't
see that he can recube after any 2, and therby drop, I decide to redouble
this.

Then I go back to my GNU Backgammon and put the position and evaluate the
position with the two-sided bearoff database.

Evaluator:      BEAROFF2

             Player       Opponent
Position          473           216

Cubeless equity               : +0,2345
Owned cube                    : +0,3913
Centered cube                 : +0,2734
Opponent owns cube            : +0,1137

             Player       Opponent
Position          473           216

Bearing off                             Bearing at least one chequer off
Rolls   Player  Opponent        Player  Opponent
    0     0,000   0,000         100,000 100,000
    1     0,000   0,000           0,000   0,000
    2    20,911  30,556           0,000   0,000
    3    58,770  69,444           0,000   0,000
    4    20,319   0,000           0,000   0,000

Average rolls
Bearing off                             Saving gammon
        Player  Opponent        Player  Opponent
Mean      2,994   2,694           0,000   0,000
Std dev   0,642   0,461           0,000   0,000

        Win     W(g)    W(bg)   L(g)    L(bg)   Equity  (cubeful)
static: 0,617   0,000   0,000   0,000   0,000   (+0,234  (+0,391))
 1 ply: 0,617   0,000   0,000   0,000   0,000   (+0,234  (+0,391))
 2 ply: 0,617   0,000   0,000   0,000   0,000   (+0,234  (+0,391))


No redouble         : +0,391
Redouble, pass      : +1,000   (+0,609)
Redouble, take      : +0,227   (-0,164)

Correct cube action: No redouble, take

This looks al right!

Then I roll the position out. I use expert on chequerplay and 2-ply on cube
decisions. The cubeful equity of a 4-cube at the other side changes.


Cube analysis
Rollout cubeless equity  +0,234

1. No double            +0,391
2. Double, pass         +1,000  ( +0,609)
3. Double, take         +0,356  ( -0,035)
Proper cube action: No redouble, take (5,5%)
Rollout details:
Player Oystein owns 2-cube:
  0,617 0,000 0,000 - 0,383 0,000 0,000 CL  +0,234 CF  +0,391
 [0,000 0,000 0,000 - 0,000 0,000 0,000 CL   0,000 CF  +0,000]
Player GNU Backgammon owns 4-cube:
  0,617 0,000 0,000 - 0,383 0,000 0,000 CL  +0,469 CF  +0,356
 [0,000 0,000 0,000 - 0,000 0,000 0,000 CL   0,000 CF  +0,006]
Full cubeful rollout with var.redn.
1296 games, seed 1154560512 using quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 2-ply cubeful 100% speed [world class]

Why does the cubeful equity change? Which cubeful equity is right?

0.227 to 0.356 that's quite a lot!


-Øystein