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

[Joern Thyssen]

On Sat, Dec 14, 2002 at 09:03:48PM +0100, Øystein Johansen wrote
> 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

These are the correct numbers taken from the two-sided bearoff database.

> 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!

Yes, they are taken from the two-sided bearoff database.

> 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

Note that gnubg will truncate the rollout at the bearoff database, so
you've actually not performed at rollout!

Try with "set rollout bearofftruncation twosided off"

However, there was a bug in the rollout bearoff truncation code that
lead to the wrong result above. I've committed a fix.

Jørn