Re: [Bug-gnubg] Use of Two-Sided DB in matches

[Neil Robins]

I have another position here that GNU seems to fundamentally get almost 
right and I don't really know why it calculates differently than from in my 
initial position.

GNU Backgammon  Position ID: kQcAgEoDAAAAAA
                Match ID   : UQngABAAIAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+     O: gnubg
|                  |   | O     O        O | OO  1 point
|                  |   | O                | OO
|                  |   | O                | OO
|                  |   | O                | OO
|                  |   |                  | O
v|                  |BAR|                  |     7 point match
|                  |   |                  | X
|                  |   |                  | XX
|                  |   |                  | XX
|                  |   | X                | XX  On roll
|                  |   | X  X     X  X  X | XX  4 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+     X: Neil (Cube: 2)

Two sided DB gives:

            Player       Opponent
Position          641           707

Cubeless equity               : +0.7554
Owned cube                    : +0.9339
Centered cube                 : +0.9303
Opponent owns cube            : +0.7441

> From which it is directly calculable that if the leader redoubles and it is 
taken, then opponent recubes for the match ( the take of which is never in 
the slightest doubt):

Leader's MWC = (1 + 0.7554)/2 x 100 = 87.77%

I think 3-ply and 4-ply really should give the same result for D/T, but they 
are out by only 0.01%.

Cube analysis
0-ply cubeless MWC  85.15% (Money:  +0.755)
 0.878 0.000 0.000 - 0.122 0.000 0.000
Cubeful equities:
1. Double, pass         89.02%
2. Double, take         91.76%  (  2.74%)
3. No double            87.65%  ( -1.37%)
Proper cube action: Redouble, pass

Cube analysis
1-ply cubeless MWC  85.15% (Money:  +0.755)
 0.878 0.000 0.000 - 0.122 0.000 0.000
Cubeful equities:
1. Double, take         87.77%
2. Double, pass         89.02%  (  1.26%)
3. No double            87.28%  ( -0.48%)
Proper cube action: Redouble, take

Cube analysis
2-ply cubeless MWC  85.15% (Money:  +0.755)
 0.878 0.000 0.000 - 0.122 0.000 0.000
Cubeful equities:
1. Double, take         87.77%
2. Double, pass         89.02%  (  1.26%)
3. No double            87.61%  ( -0.16%)
Proper cube action: Redouble, take

Cube analysis
3-ply cubeless MWC  85.15% (Money:  +0.755)
 0.878 0.000 0.000 - 0.122 0.000 0.000
Cubeful equities:
1. Double, take         87.76%
2. Double, pass         89.02%  (  1.26%)
3. No double            87.08%  ( -0.68%)
Proper cube action: Redouble, take

Cube analysis
4-ply cubeless MWC  85.15% (Money:  +0.755)
 0.878 0.000 0.000 - 0.122 0.000 0.000
Cubeful equities:
1. Double, take         87.76%
2. Double, pass         89.02%  (  1.26%)
3. No double            87.17%  ( -0.60%)
Proper cube action: Redouble, take

Rollout details:
Player Neil owns 2-cube:
 0.878 0.000 0.000 - 0.122 0.000 0.000 CL  85.15% CF  86.94%
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.00% CF   0.01%]
Player gnubg owns 4-cube:
 0.878 0.000 0.000 - 0.122 0.000 0.000 CL  92.67% CF  87.77%
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL   0.00% CF   0.00%]
Full cubeful rollout with var.redn.
12960 games, Mersenne Twister dice gen. with seed 864628208 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]