[Bug-gnubg] 0-ply (expert) Cube Decision Rollouts

[Eberlein, Robert (REBERLEI)]

I have found a bug in the 0-ply (expert) cube decision evaluation.  Whenever
the 0-ply evaluation for an initial cube should be Double-Take, the result
is coming back either No Double - Take, or Optional Double - Take, with the
equity for No Double always exactly matching (to the reported number of
decimals) the equity for Double - Take.  As a result, when a 0-ply cube
decision rollout is performed, no double from a centered cube is ever taken,
and the rollout statistics show only drops in the centered cube case, with
"cube efficiencies" (actually take rates) always 0.  Because of this massive
market loss, the equity for the No Double case that the 0-ply rollout
reports is very much too low.

        I tested a series of positions starting with:   54:     24-20, 13-8
31:     8-5*, 6-5.
                                                        66:       -     P1
21:     13-11, 6-5
                                                        66:       -     P2
51:     13-8, 24-23
                                                        66:       -     P3
61:     13-7, 8-7
                                                        66:       -     P4
21:     6-4, 5-4
                                                        66:       -     P5
?

I then analyzed the cube decision for each of the 5 positions after the
dancing has begun.

Position                0 Eval  1 Eval  2 Eval  0 Rollout - 324 games,
variance reduction
P1 ND           0.4850  0.5310  0.4870  0.3411
P1 DT           0.4640  0.5110  0.4290  0.4627
P2 ND           0.6820  0.7030  0.6530  0.4796
P2 DT           0.6820  0.7250  0.6470  0.6167
P3 ND           0.8840  0.8890  0.8240  0.5349
P3 DT           0.8840  0.9400  0.8850  0.7773
P4 ND           1.0000  1.0360  0.9600  0.7223
P4 DT           1.2660  1.3540  1.2430  1.2123
P5 ND           1.0800  1.1340  1.0810  0.8553
P5 DT           1.5970  1.7780  1.5830  1.5608

The version of gnubg I used was the Windows version 0.13-devel 030425
NoFreetype (Clog 1.1061) (build Apr 27 2003)
I had the Jacoby rule off, but I don't think this matters.

I have seen this problem for a long time in rollouts, but my insight came
only after I mistakenly analyzed a match with 0-ply cube evaluations and
noticed a bunch of "No double, take" and "Optional double, take" evaluations
that were the same for both doubling and not doubling.