I did a tiny experiment: I used EXchess_v6.50b_win32 by Dan Homan (thanks Dan! ) because it runs fast into depth. The ideal approach will be the following: play lots of games at certain time controls. But I do not have much time and big CPU resources, so fixed depth is fast enough for me. I choosed depths 5, 6, 7, 8 and 9. Here is my summary of results:
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Engine: EXchess_v6.50b_win32 by Dan Homan.
PC: Intel Pentium D930 (3 GHz) of year 2006.
Test: 2500 games without opening books for each fixed depth.
W(d=5) ~ 0.4139; D(d=5) ~ 0.2858; B(d=5) ~ 0.3002; µ(d=5) ~ 0.5568
W(d=6) = 0.3956; D(d=6) = 0.3612; B(d=6) = 0.2432; µ(d=6) = 0.5762
W(d=7) = 0.4388; D(d=7) = 0.3220; B(d=7) = 0.2392; µ(d=7) = 0.5998
W(d=8) = 0.3396; D(d=8) = 0.3968; B(d=8) = 0.2636; µ(d=8) = 0.5380
W(d=9) = 0.3708; D(d=9) = 0.3812; B(d=9) = 0.2480; µ(d=9) = 0.5614
I encourage everybody to do this sort of test (with fixed depths and/or different time controls). Everybody can expect an increasing draw ratio with higher depths and longer time controls but I can say nothing about the score for white.
I have uploaded the PGN files of the experiment, which was made with cutechess-cli 0.5.1; the command line and engines.json file are also included:
Influence_of_colours_at_fixed_depth.rar (5.35 MB)
Here is the command line that I used:
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cutechess-cli -engine conf="Depth_9a" depth=9 -engine conf="Depth_9b" depth=9 -each tc=inf -concurrency 2 -draw 100 50 -resign 5 900 -games 2 -rounds 1250 -ratinginterval 1 -repeat -wait 5 -pgnout Depth_9.pgn
Ajedrecista.