Single Comment

As to the Amazon value: I guess you are right worrying about undefended
Pawns when designing a variant that is more fun to play. For the
determination of piece values, however, this is hardly important. In the
first place, I have to delete pieces from the nominal opening setup to
create a difference, sometimes multiple pieces (such as Q+N to balance the
Amazon), and this usually this leaves some undefended Pawns anyway. It is
more important to shuffle the pieces, to create as many different initial
positions as possible. That some of them have extra weaknesses is not so
important, as both sides have that same weakness, and I play it twice with
different sides starting.

I was never able to see a clear effect of the opening array anyway. Not
even when starting one side with Knights or Bishops in the corner, against
a normal setup. I guess this would only show up by really making opening
theory for the specific position. It is just too difficult to find ways to
exploit such weaknesses 'behind the board' at any reasonable time
control.

BTW, I terminitad the initial experiment with the Amazon after 441 games.
The Amazon was leading 52.6% over Queen + Knight, while the standard error
is about 2%, and Pawn-odds advantage 12%. This suggests Amazon to be about
20 cP stronger than Queen + Knight. But it is very possible that on this
slow laptop at this TC the Knight is underestimated by 10 cP.

Anyway, there seems to be very little to no synergy between the Queen and
Knight moves. I guess most synergy in compound pieces results from
crossing a certain threshold, needed for qualifying as 'super-piece'.
Rooks, Knights and Bishops on an empty board can all go to a given target
square along two paths (if it is reachable at all). A Queen can do that in
general in 12 ways (if the board is large enough). This huge jump in
manoeuvrability is what makes the super-pieces so much more valuable. A
superpiece can attack a Pawn chain in several places at once from several
positions, so that normal pieces cannot defend all attacked Pawns, and in
stead have to worry about their own survival. So a super-piece is much
more than just a stronger piece. It is used in in an essentially different
way. E.g. in the early end-game, chasing the King with checks while having
enough freedom to at the same time manoeuvre to get a clear shot at some
other undefended piece.