##
Summary of Part 1

I didn't solve the problem, did I?
On the other hand, I did introduce a
method of calculating piece
values that is a great advance beyond what has gone before:
to take the average mobility on all squares, *taking into account
the fact that the board is never empty*.

I also introduced a lot of ideas, including and especially
Forwardness,
about factors that affect the absolute values of
pieces.

I described a way of testing values empirically, which gives very
precise results of dubious meaning.

The Average-With-Probability method seems to generate interesting
results for the single-step pieces, and seems to be able to give an
approximation of the results of "Rider" pieces ( Rook, Bishop,
Queen, KnightRider ) relative to one another.

Either on its own, or combined with an ad-hoc calculation of
*Forwardness*, this calculation has a lot of predictive
value; but it is still too rough and too approximate to be useful
for designing games of Chess where the two sides have different
armies.

Although this method is known to be incomplete, it is worthwhile to
pretend for a moment that it is correct; using the values we have at
hand, it is possible to create a new Chess army composed of
completely different pieces than the original, but having almost the
same values.

To test the validity of this method, one need only play a
game where one side uses the standard chess pieces, but the
other uses:

EQUIVALENT NEW PIECE
========== =========
Knight Wazir plus Dabbaba; 5.25 colorbound
Bishop Alfil plus Wazir; 5.75
Rook KnightRider; ???
Queen KnightRider plus Alfil plus Wazir
King Dabbaba plus Wazir 5.625

The values are close enough, but I gave explained above why it is
that they are too low; this army is
slightly too weak to play against the normal Chess army.
Still, if you try playing this game you'll find it to be surprising
how close these two different armies are; a sign that we're on the
right track.

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