##
Getting More Data

One way to assign reasonable values to the above factors is to start
with well-established values for a wide range of pieces that
illustrate differences in forwardness and distance, and then try to
discern patterns in those values.
In order to determine the values of some of these pieces, I have
recorded the results of a series of computer chess games in which
the computer played both sides, and in which all the normal pieces
except one were used.

For example, in one series of games Black had all the normal pieces, but
White had a piece that moved like Wazir or Alfil instead of the
Knights; this new piece ( shall we call it the *Waffle*? )
has a mobility of 5.75 ( 3.5 from the Wazir, 2.25 from the Alfil ),
but seems to be weaker than the Knight; after 5256 games, White's
winning rate was 0.457002 ( for reference, White's winning rate in
standard chess was 0.49227 after 13842 games ).

The large number of games played gives the results a degree of
certainty; a result of 0.46 after 4000 games is different from one
of 0.47, standard deviations, t-tests, and all.

The large number of games played was achieved by networking. One
machine can crank out 36 games in four hours.

The number of games is always a multiple of 6 because the opening
position is permuted 6 ways: that is, one game has Ra1, Nb1, Bc1,
the next has Ra1, Bb1, Nc1, and so on. This is important, but the
reason for it is several chapters ahead.

The results are reproducible, but their meaning is unclear. For
example, King versus Knight has a win rate of 0.37: this seemed fine
to me, it seemed like the results I got when I tried it by hand,
with me playing both sides. Then I discovered a better strategy for
the side with the King, and found that the real win rate should be
over 50%!

I'm certain that you don't want to
see more details
about the methodolgy and the results.

The meaning is unclear, but sometimes it works. For example, it was
the computer results that made the game of
Different Augmented Knights become a reality. The game has been
played by masters, and the computer results turned out to be
correct.

##
And In Closing, May I Say

Sometimes it works, but it doesn't help with the problem of finding
a general solution to calculating the values of pieces.

Because I can't succeed at finding a way to calculate piece values,
well, naturally, now I want to prove that it's impossible!

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