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


From: Neil Robins
Subject: [Bug-gnubg] Two-Sided Bearoff DB and Cube Analysis
Date: Fri, 11 Dec 2009 06:14:52 -0000

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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