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
(0.0243difference 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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