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Hey, Sam. The FIDE attack density is 4.0, check your numbers. ;-)

This balances the attack density of FIDE with Capa. So what accounts for
the extra strength of Capa, compared to FIDE? There are a number of factors
that might enter into this. Compression, for example, the ratio of width to
depth. For FIDE, 8/8 = 1.0, for Capa, 10/8 = 1.25. The opposing pieces are
relatively squeezed together. And that's why Grand Chess, 10/10 = 1, feels
so open compared to Capa. At least it does for me. Even though the extra
squares are 'behind' the starting arrays. Elongation is a good name for
this, and it has its own effects. Gary Gifford used them in his ShortRange
Project games. The Capa - Grand Chess pair is a very good example of
elongation.

But that's just one part of the [very complex, non-linear] equation. With
FIDE, Capa [and Grand, all] having the same attack density, why is Capa
'stronger' than FIDE? Consider the long range pieces. FIDE has 5/8th of
its pieces long range, 62.5%; Capa has 7/10th, 70%. With the individual
rook or bishop types, FIDE is 3/8, 37.5%, to Capa's 4/10, 40%. This
doesn't quite seem to be enough to explain all the difference between the
2 games. ;-)

Okay, here I'll admit that FIDE has one grade A power piece, of 8, 12.5%.
Capa has 3 of 10, 30%. This does explain why the games feel different, but
it doesn't give a lot of insight into the exact how. Just how are they
different? Can we put numbers to this, that have predictive value for other
games, with less-familiar pieces? So we should keep looking around.

The mean free path is another concept that keeps popping up as relevant.
How far can a piece move before it bumps into another piece? This area has
a lot of wrinkles to it. Enough so they might wait for the next post.