Simplify KBPKB endgame with opposite bishops
When we reach a position with only two opposite colored bishops and
one pawn on the board, current master would give it a scale factor
of 9/64=0.14 in about one position out of 7200, and a scale factor
of 0.0 in the 7199 others. The patch gives a scale factor of 0.0 in
100% of the cases.
STC:
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 55845 W: 11467 L: 11410 D: 32968
http://tests.stockfishchess.org/tests/view/5abc585f0ebc5902926cf15e
LTC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 11915 W: 1852 L: 1719 D: 8344
http://tests.stockfishchess.org/tests/view/5abc7f750ebc5902926cf18c
We also have exhaustive coverage analysis of this patch effect by
Alain Savard, comparing the perfect evaluation given by the Syzygy
tablebase with the heuristic play after this patch for the set of
all legal positions of the KBPKP endgame with opposite bishops, in
the comments thread for this pull request:
https://github.com/official-stockfish/Stockfish/pull/1520
Alain's conclusion:
> According to this definition and the data, I consider this PR is
> identical to master to "solve for draw" and slightly better than
> master to solve earlier for "wins".
Note: this patch is a side effect of an ongoing effort to improve
the evaluation of positions involving a pair of opposite bishops.
See the GitHub diff of this LTC test which almost passed at sprt[0..5]
for a discussion:
http://tests.stockfishchess.org/tests/view/5ab9030b0ebc5902932cbf93
No functional change (at small bench depths)