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Re: [Bug-gnubg] 0ply doubles early


From: Robert-Jan Veldhuizen
Subject: Re: [Bug-gnubg] 0ply doubles early
Date: Fri, 15 Dec 2006 15:02:09 +0100

Here's a very simple, unspectacular example:

    GNU Backgammon  Position ID: sO3uAACwu3sAAA
                    Match ID   : cAkAAAAAAAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: Kit Woolsey
    |             O  O |   | O  O  O  O       |  0 points
    |             O  O |   | O  O  O  O       | 
    |                  |   |    O  O  O       | 
    |                  |   |                  | 
    |                  |   |                  | 
    |                  |BAR|                  |v (Cube: 1)
    |                  |   |                  | 
    |                  |   |       X          | 
    |                X |   | X  X  X          | 
    |             X  X |   | X  X  X          |  On roll
    |             X  X |   | X  X  X          |  0 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: GOL Readers

Rollouts indicate it's not quite a double yet, with 71.21% GWC.

2-ply and 4-ply cube see 71.18 and 71.32% GWC and also say not quite a double.

0-ply cube sees LESS winning chances, only 70.74%, yet it doubles (0.0243 difference even).

So 0-ply doubles because it overestimates volatility, whereas it actually underestimates GWC here.

Could it be that some parameters used for 0-ply cube decisions need a bit more fine-tuning? This is a very simple long race position where you'd expect volatility to be fairly predictable just by the pipcounts.

Here's the GNUBG output, note that I use a 1-sided DB to the ninepoint so your output may differ slightly, but it seems irrelevant for this issue.

Cube analysis
0-ply cubeless equity  +0.4149
   70.74%   0.00%   0.00% -  29.26%   0.00%   0.00%
Cubeful equities:
1. Double, take         +0.6290
2. Double, pass         +1.0000  ( +0.3710)
3. No double            +0.6047  ( - 0.0243)
Proper cube action: Double, take

Cube analysis
2-ply cubeless equity  +0.4235
   71.18%   0.00%   0.00% -  28.82%   0.00%   0.00%
Cubeful equities:
1. No double            +0.6528
2. Double, pass         +1.0000  ( +0.3472)
3. Double, take         +0.6520  ( -0.0008)
Proper cube action: No double, take (0.2%)

Cube analysis
4-ply cubeless equity  +0.4265
   71.32%   0.00%   0.00% -  28.68%   0.00%   0.00%
Cubeful equities:
1. No double            +0.6654
2. Double, pass         +1.0000  ( +0.3346)
3. Double, take         +0.6637  ( -0.0017)
Proper cube action: No double, take (0.5%)
=======================================
Cube analysis
Rollout cubeless equity  +0.4251

Cubeful equities:
1. No double            +0.6660
2. Double, pass         +1.0000  ( +0.3340)
3. Double, take         +0.6573  ( -0.0087)
Proper cube action: No double, take ( 2.5%)
Rollout details:
Centered 1-cube:
   71.26%   0.00%   0.00% -  28.74%   0.00%   0.00% CL  +0.4251 CF  +0.6660
 [  0.01%   0.00%   0.00% -   0.01%   0.00%   0.00% CL   0.0003 CF   0.0031]
Player Kit Woolsey owns 2-cube:
   71.21%   0.00%   0.00% -  28.79%   0.00%   0.00% CL  +0.8484 CF  +0.6573
 [  0.01%   0.00%   0.00% -   0.01%   0.00%   0.00% CL   0.0006 CF   0.0031]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 1017692672 and quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]

Cube analysis
Rollout cubeless equity  +0.4252

Cubeful equities:
1. No double            +0.6685
2. Double, pass         +1.0000  ( +0.3315)
3. Double, take         +0.6527  ( -0.0158)
Proper cube action: No double, take (4.6%)
Rollout details:
Centered 1-cube:
   71.26%   0.00%   0.00% -  28.74%   0.00%   0.00% CL  +0.4252 CF  +0.6685
 [  0.01%    0.00%   0.00% -   0.01%   0.00%   0.00% CL   0.0003 CF   0.0031]
Player Kit Woolsey owns 2-cube:
   71.21%   0.00%   0.00% -  28.79%   0.00%   0.00% CL  +0.8485 CF  +0.6527
 [  0.01%   0.00%   0.00% -   0.01%   0.00%   0.00% CL   0.0006 CF   0.0034]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 1017692672 and quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 2-ply cubeful prune [world class]
 
--
Robert-Jan Veldhuizen
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