[Bug-gnubg] Strange cube decision

[Jim Segrave]

Someone at dailygammon queried this gnubg analysis and I have to say
that I find the results a bit odd. 

First, the position:

Move number 2: X doubles to 2

    GNU Backgammon  Position ID: DAAAbNu2gAAEAA
                    Match ID   : cBFgAZAAKAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: gnubg
OOO | X     O          | O |             X    |  9 points
 OO |       O          | O |                  |  Cube offered at 2
 OO |                  |   |                  |  
 OO |                  |   |                  |  
 OO |                  |   |                  |  
    |                  |BAR|                  |v 
    |                  |   |                  |  
    |                  |   |                  |  
    |                  |   |                  |  
    | X  X  X  X  X  X |   |                  |  
    | X  X  X  X  X  X |   | X                |  5 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: jim_segrave
Pip counts: O 56, X 87

With a double, the cube is clearly dead. 
The problems noted:

1) gnubg makes very poor estimates of the winning chances here with
   very high even/odd ply variations. This is a well known phenomenem,
   and not really the point of this query.

2) the double/no double decisions seem strange, given that gnubg shows
   the doubling window (Snowie Met) opening at 60.4%, with the take at 21.1%

I rolled the position out, and then did it again with a random roll at
dmp, so I could be sure the rollout results were not being biased by
an assumption of a later double. There was little to choose between
double/no double in the rollouts:

First the rollout of the double, using the Snowie MET:

Alert: wrong take ( -0.07208)!Alert: wrong double ( -0.07030)!
Cube analysis
Rollout cubeless equity  +0.60976 (Money:  +0.60976 +0.60976)

Cubeful equities:
1. Double, pass         +1.00000
2. Double, take         +1.07208  ( +0.00178)
3. No double            +1.07030  ( +0.00000)
Proper cube action: Double, pass
Rollout details:
Centered 1-cube:
  0.80488 0.00000 0.00000 - 0.19512 0.00000 0.00000 CL  +0.60976 CF  +1.07030
 [0.00115 0.00000 0.00000 - 0.00115 0.00003 0.00002 CL   0.00230 CF   0.00494]
Player gnubg owns 2-cube:
  0.80542 0.00000 0.00000 - 0.19458 0.00000 0.00000 CL  +1.07208 CF  +1.07208
 [0.00116 0.00000 0.00000 - 0.00116 0.00006 0.00001 CL   0.00498 CF   0.00498]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 1597743276 and quasi-random 
dice
Stop when best play is enough JSDs ahead: limit 2 (min. 648 games)
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Then as a check, rolling out a random dice throw at DMP

Rolled 51:*    1. Rollout          24/23 14/9                   Eq.:  +0.60388
       0.80194 0.00000 0.00000 - 0.19806 0.00000 0.00000 CL  +0.60388 CF  
+0.60388
      [0.00110 0.00000 0.00000 - 0.00110 0.00036 0.00007 CL   0.00219 CF   
0.00219]

So it seems safe to assume that X wins about 80% of the time and that
gammon losses for X are negligible.

Now the analysis at different plies:

0ply:

Alert: wrong double ( -0.00925)!
Cube analysis
0-ply cubeless equity  +0.34814 (Money:  +0.34826 +0.34814)
  0.67550 0.00000 0.00000 - 0.32450 0.00205 0.00069
Cubeful equities:
  0-ply cubeful [expert]
1. No double            +0.52166
2. Double, pass         +1.00000  ( +0.47834)
3. Double, take         +0.51240  ( -0.00925)
Proper cube action: No double, take (1.9%)

Ignoring the very low winning estimate, the winning percentage is
about 67.5% and the doubling window opens at 60%, why is this not a
clear double/take?

1 ply analysis:

Alert: wrong take ( -0.06727)! [bad]
Cube analysis
1-ply cubeless equity  +0.60614 (Money:  +0.60647 +0.60614)
  0.80431 0.00000 0.00000 - 0.19569 0.00177 0.00037
Cubeful equities:
  1-ply cubeful
1. Double, pass         +1.00000
2. Double, take         +1.06727  ( +0.06727)
3. No double            +0.87311  ( -0.12689)
Proper cube action: Double, pass

Here we get a very good estimate of the winning chances and it's a
clear double/pass

2 ply analysis:

Cube analysis
2-ply cubeless equity  +0.44200 (Money:  +0.44242 +0.44200)
  0.72224 0.00000 0.00000 - 0.27776 0.00178 0.00029
Cubeful equities:
  2-ply cubeful prune [world class]
1. No double            +0.71376
2. Double, pass         +1.00000  ( +0.28624)
3. Double, take         +0.71376  ( +0.00000)
Proper cube action: Optional double, take

The winning chances are low again, but way over the opening window. On
these estimates, the take is clear, so I can't see why this is an
optional double.

3 ply analysis:

Alert: wrong take ( -0.02229)! [doubtful]
Cube analysis
3-ply cubeless equity  +0.58568 (Money:  +0.58600 +0.58568)
  0.79386 0.00000 0.00000 - 0.20614 0.00146 0.00026
Cubeful equities:
  3-ply cubeful prune [grandmaster]
1. Double, pass         +1.00000
2. Double, take         +1.02229  ( +0.02229)
3. No double            +0.99652  ( -0.00348)
Proper cube action: Double, pass

Again, reasonably accurate estimates of the winning chances and, with
these estimates, it's a bare pass

4 ply analysis:

Alert: wrong double ( -0.00012)!
Cube analysis
4-ply cubeless equity  +0.50517 (Money:  +0.50571 +0.50517)
  0.75374 0.00000 0.00000 - 0.24626 0.00165 0.00012
Cubeful equities:
  4-ply cubeful prune
1. No double            +0.84956
2. Double, pass         +1.00000  ( +0.15044)
3. Double, take         +0.84944  ( -0.00012)
Proper cube action: No double, take (0.1%)

-- 
Jim Segrave           address@hidden