Single Comment

To Derek:

I am aware that the empirical Rook value I get is suspiciously low. OTOH,
it is an OPENING value, and Rooks get their value in the game only late.
Furthermore, this only is the BASE VALUE of the Rook; most pieces have a
value that depends on the position on the board where it actually is, or
where you can quickly get it (in an opening situation, where the opponent
is not yet able to interdict your moves, because his pieces are in
inactive places as well). But Rooks only increase their value on open
files, and initially no open files are to be seen. In a practical game, by
the time you get to trade a Rook for 2 Queens, there usually are open
files. So by that time, the value of the Q vs 2R trade will have gone up
by two times the open-file bonus. You hardly have the possibility of
trading it before there are open files. So it stands to reason that you
might as well use the higher value during the entire game.

In 8x8 Chess, the Larry Kaufman piece values include the rule that a Rook
should be devaluated by 1/8 Pawn for each Pawn on the board there is over
five. In the case of 8 Pawns that is a really large penalty of 37.5cP for
having no open files. If I add that to my opening value, the late
middle-game / end-game value of the Rook gets to 512, which sounds a lot
more reasonable.

There are two different issues here:
1) The winning chances of a Q vs 2R material imbalance game
2) How to interpret that result as a piece value

All I say above has no bearing on (1): if we both play a Q-2R match from
the opening, it is a serious problem if we don't get the same result. But
you have played only 2 games. Statistically, 2 games mean NOTHING. I don't
even look at results before I have at least 100 games, because before they
are about as likely to be the reverse from what they will eventually be,
as not. The standard deviation of the result of a single Gothic Chess game
is ~0.45 (it would be 0.5 point if there were no draws possible, and in
Gothic Chess the draw percentge is low). This error goes down as the
square root of the number of games. In the case of 2 games this is
45%/sqrt(2) = 32%. The Pawn-odds advantage is only 12%. So this standard
error corresponds to 2.66 Pawns. That is 1.33 Pawns per Rook. So with this
test you could not possibly see if my value is off by 25, 50 or 75. If you
find a discrepancy, it is enormously more likely that the result of your
2-game match is off from to true win probability.

Play 100 games, and the error in the observed score is reasonable certain
(68% of the cases) to be below 4.5% ~1/3 Pawn, so 16 cP per Rook. Only thn
you can see with reasonable confidence if your observations differ from
mine.