Re: [Bug-gnubg] Two-Sided Bearoff DB and Cube Analysis

[Christian Anthon]

The art of using cubeless winning chances in cubeful games is a gray
one at the best of times. The reason is that a) the plays may well
depend on the cube position and b) cubeactions leads to premature
ending of the games and c) the plied evaluation of the cube may
contain suboptimal plays because of the way that cubes and moves are
handled by the gnubg engine. So what seems simple is in fact not
because of the internals of the gnubg engine, which works fine in
general, but is quite puzzling to the human mind in positions we feel
we understand well.

Christian.

On Fri, Dec 11, 2009 at 7:14 AM, Neil Robins <address@hidden> wrote:
> In the position below I received a cube which, if taken, is for the match. I
> have on disk the Two-Sided Bearoff DB for up to 11 chequers on 6 points,
> which gives:
>
>              Player       Opponent
> Position         4049          6690
>
> Cubeless equity               : +0.5006
> Owned cube                    : +0.7930
> Centered cube                 : +0.7679
> Opponent owns cube            : +0.4452
>
> It seems to me it is trivially easy to obtain from the Cubeless equity that,
> if the game is played out for the match, my opponent will win the match
> 75.03% of the time and my MWC is 24.97%. The rollout indeed concurs with
> these figures and, for once, 0-ply agrees as well.
> As you increase the number of plys from 1-ply through to 7-ply, not only are
> all the figures wrong, but, there is a straightforward relatiosnhip of every
> ply higher being just as bad or worse than a ply lower. Analysis at 7-ply
> produces the worst result. Surely this is not what should be expected,
> and shouldn't all plys be bringing the correct figure here?
>
>     GNU Backgammon  Position ID: tW0AAKjNAQAAAA
>                     Match ID   : AQFgAAAAAAAA
>     +-1--2--3--4--5--6-------7--8--9-10-11-12-+  O: gnubg (Cube: 2)
>  OO | O  O  O  O     O |   |                  |  0 points
>   O |       O  O     O |   |                  |  On roll
>   O |                O |   |                  |
>   O |                  |   |                  |
>   O |                  |   |                  |
>     |                  |BAR|                  |^ 3 point match
>   X |                  |   |                  |
>   X |                  |   |                  |
>   X |                  |   |                  |
>   X |       X  X  X  X |   |                  |
>   X | X  X  X  X  X  X |   |                  |  0 points
>     +24-23-22-21-20-19------18-17-16-15-14-13-+  X: Neil
>
> Rollout details:
> Player gnubg owns 2-cube:
>   0.744 0.000 0.000 - 0.256 0.000 0.000 CL  62.26% CF  70.82%
>  [0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.00% CF   0.00%]
> Player Neil owns 4-cube:
>   0.750 0.000 0.000 - 0.250 0.000 0.000 CL  75.03% CF  75.03%
>  [0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.00% CF   0.00%]
> Full cubeful rollout with var.redn.
> 25920 games, Mersenne Twister dice gen. with seed 839486310 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]
>
> Cube analysis
> 0-ply cubeless MWC  62.55% (Money:  +0.501)
>   0.750 0.000 0.000 - 0.250 0.000 0.000
> Cubeful equities:
> 1. Double, take         75.03%
> 2. Double, pass         75.08%  (  0.05%)
> 3. No double            72.29%  ( -2.74%)
> Proper cube action: Redouble, take
>
> Cube analysis
> 1-ply cubeless MWC  62.28% (Money:  +0.490)
>   0.745 0.000 0.000 - 0.255 0.000 0.000
> Cubeful equities:
> 1. Double, take         74.48%
> 2. Double, pass         75.08%  (  0.60%)
> 3. No double            71.73%  ( -2.75%)
> Proper cube action: Redouble, take
>
> Cube analysis
> 2-ply cubeless MWC  62.28% (Money:  +0.490)
>   0.745 0.000 0.000 - 0.255 0.000 0.000
> Cubeful equities:
> 1. Double, take         74.48%
> 2. Double, pass         75.08%  (  0.59%)
> 3. No double            70.73%  ( -3.76%)
> Proper cube action: Redouble, take
>
> Cube analysis
> 3-ply cubeless MWC  62.28% (Money:  +0.490)
>   0.745 0.000 0.000 - 0.255 0.000 0.000
> Cubeful equities:
> 1. Double, take         74.48%
> 2. Double, pass         75.08%  (  0.59%)
> 3. No double            70.64%  ( -3.85%)
> Proper cube action: Redouble, take
>
> Cube analysis
> 4-ply cubeless MWC  61.99% (Money:  +0.478)
>   0.739 0.000 0.000 - 0.261 0.000 0.000
> Cubeful equities:
> 1. Double, take         73.92%
> 2. Double, pass         75.08%  (  1.16%)
> 3. No double            70.60%  ( -3.31%)
> Proper cube action: Redouble, take
>
> Cube analysis
> 5-ply cubeless MWC  61.79% (Money:  +0.470)
>   0.735 0.000 0.000 - 0.265 0.000 0.000
> Cubeful equities:
> 1. Double, take         73.51%
> 2. Double, pass         75.08%  (  1.57%)
> 3. No double            70.48%  ( -3.03%)
> Proper cube action: Redouble, take
>
> Cube analysis
> 6-ply cubeless MWC  61.77% (Money:  +0.469)
>   0.735 0.000 0.000 - 0.265 0.000 0.000
> Cubeful equities:
> 1. Double, take         73.46%
> 2. Double, pass         75.08%  (  1.61%)
> 3. No double            70.44%  ( -3.02%)
> Proper cube action: Redouble, take
> Cube analysis
> 7-ply cubeless MWC  61.67% (Money:  +0.465)
>   0.733 0.000 0.000 - 0.267 0.000 0.000
> Cubeful equities:
> 1. Double, take         73.27%
> 2. Double, pass         75.08%  (  1.80%)
> 3. No double            70.34%  ( -2.94%)
> Proper cube action: Redouble, take
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