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

[Neil Robins]

Yes, but I'm only seeking to apply cubeless winning chance to the pure 
cubeless position that arises following D/T, when the winner of the game 
wins the match.

----- Original Message ----- 
From: "Christian Anthon" <address@hidden>
To: "Neil Robins" <address@hidden>
Cc: <address@hidden>
Sent: Saturday, December 12, 2009 1:30 PM
Subject: Re: [Bug-gnubg] Two-Sided Bearoff DB and Cube Analysis


> 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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