Author: Mike S.
Date: 18:16:37 07/21/02
What is the value of having the advantage of the two bishops? Can it be
expressed in figures, i.e. evaluations, or as an %-impact on the performance
percentage?
The previous experiment:
In an old and quite large experiment I did in 1996, I let play chess programs
against themselves from 8 special starting positions, where only one side had
the bishop pair, each (i.e. without Nb1, Bc8 etc.). To avoid having rating
bonuses still included in the evaluation, I waited until one of the two bishops
had disappeared, so I could read a kind of "real rating gain" which the 2
bishops achieved, as the programs evaluated it.
The average "rating success" so to speak, of the 2 bishops was
+0.46 pawns (1996)
-----------
with white and also with black (IOW, there was no advantage of the first move
visible). These games were not finished.
New approach:
Meanwhile, GUIs were much improved. For a new two bishops experiment, I used the
same old 8 starting positions (EPD see below), but let play more games, and
engines against each other (not against themselves). Also, I decided to use only
final results for the statistics, no evaluations.
5 engines played each of the 8 positions twice (w/b) against each of the 4
opponents, which results in 160 games total.
Results: W /D /L % (from the 2 bishop's viewpoint!)
----------------------------------------
White with the 2 bishops: 38/20/22 60,0%
Black with the 2 bishops: 29/19/32 48,1% -> advantage of first move visible!
----------------------------------------
2 bishops total: 67/39/54 54,1%
Based on the previous experiment (and on other experiments without opening
theory), I thought the advantage of the first move would only matter in computer
chess, when opening books or theory positions are used. Without books no white
advantage was visible to me, so far. This seems to have changed. The results
above indicate an advantage for the first move of ~ +6% compared to a
theoretical 50% result. It can also be expressed by the w/b points ratio which
was 89,5:70,5 = 1,27:1 (or ~56:44)
For comparison: In human games (2400+ elo), White scores ~55,2% according to my
database. Chess programs score similar; I got 54,0% and 55,7% for White, from
two large comp-comp databases which are partially identical (a few comp-human
games are included). The main difference is the number of drawn games btw.,
which is ~51% among strong humans, but only ~24%...25% among computers.
The 2 bishops fought with White and with Black, in 80 games each.
Main result:
Having the 2 Bishops Advantage during the experiment, led to a score plus of
~ +4 %, or 86,5:73,5 points = 1,177:1 (or ~54:46)
------
The figures varied comparing the engines: Hiarcs 7.32 - seemingly* - showed the
strongest impact of the 2 bishops (17:12 points), while Junior 5 scored 11,0
with, and 11,5 without the bishop pair.
*) The results inavoidably are a mixture of (A) having the 2 bishops or not, (B)
having the first move or not, and (C) the strength relation between the
opponents. (A) and (B) were separated, see above. (C) shouldn't be a problem
because full round robins were played. - But more important to consider is: The
2 bishops were the only difference at the start, but probably many games were
decided by other factors. For example, in a few games I watched live, the bishop
pair disappeared soon and/or the adavantage seemd to change several times from
one side to the other.
Addendum:
---------
Start positions, i.e. to use in opening databases for engine matches:
rn1qkbnr/pppppppp/8/8/8/8/PPPPPPPP/R1BQKBNR w KQkq - 0 1
rnbqk1nr/pppppppp/8/8/8/8/PPPPPPPP/R1BQKBNR w KQkq - 0 1
rn1qkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKB1R w KQkq - 0 1
rnbqk1nr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKB1R w KQkq - 0 1
r1bqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RN1QKBNR w KQkq - 0 1
rnbqkb1r/pppppppp/8/8/8/8/PPPPPPPP/RN1QKBNR w KQkq - 0 1
r1bqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQK1NR w KQkq - 0 1
rnbqkb1r/pppppppp/8/8/8/8/PPPPPPPP/RNBQK1NR w KQkq - 0 1
Program's total scores:
1 Chess Tiger 14.0 42.0/64
2 Fritz 7 41.0/64
3 Hiarcs 7.32 29.0/64
4 Shredder 5.32 25.5/64
5 Junior 5.0 22.5/64
Regards,
M.Scheidl
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