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Very interesting. I have not gotten to doing end-game tests yet. I tried
some more opening values:

A+H >~ Q
R+B ~ A

I have noticed that in tests like this Rooks tend to be under-estimated a
bit. Probably the opening value of the Rook in orthodox Chess is really
lower than the classical value 5, because it gets into play only late in
the game. But as it is difficult to trade with other material before it
gets into play, neglecting this effect and always using the value 5 (which
probably includes positional contributions like open-file bonus)is a
workable simplifiction.

For humans the best rule of thumb would be to keep simple integers as much
as possible, and the following system is pretty close to the truth:

Q=9
W=8
G=7
R=5 (5- before developed on (half-)open file)
K=5-
L=3+
B=3+
N=C=3
P=H=1

Bishops require some extra explanation anyway, which orthoChess players are
well aware off: alone it is equal to Knight (i.e. 3), but in a pair it is
worth significantly more. I could be said that because of the color-change
move the Lieutenant makes up its own pair, and thus equals the paired
Bishop in value even when it is alone.

So the easy-to-remember implication is that all light pieces are nearly
equal, but if possible, protect your Bishop pair or Lieutenant. The second
rule is that you don't have to be impressed too much by Rook attacks on
your spare King, as long as the latter is protected, and your other King is
in a safe location.

The thing that still puzzles me is that when you add everything up, it
seems the Spartans have a significant advantage. (Of course the Spartans
need some advantage to compensate the fact that they do not hve first move,
but that should be only 1/6 of a Pawn, and they seem to have more.) This
could be compensated by assuming the Hoplite is worth slightly less than a
Pawn. Your tests of K+8P vs K+8H suggest that, but there is more to it, as
in a more open position the Hoplites seem to regain the advantage. Of
course it shoud not come as a surprise that evaluation of Hoplite
structures involves much more than simply adding piece values, as it is
well known that for FIDE Pawns this is certainly the case. Hoplites turn
into passers much more easily than Pawns.

Anyway, currently I am running a match to calibrate the scale of the other
tests, by deleting a single Hoplite, (and after that I want to delete a
single Pawn) to be able to translate all measured score advantages into a
number of Pawns. My plans are to make a slight refinement of Fairy-Max
after that, so that it really implements the Bishop pair, by making the
last piece of a color-bound type worth 12.5% less than the programmed piece
value, and then run some tests of Bishops against Lieutenants.