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H.G.Muller wrote on 2008-04-27 UTC
OK, final report of the pilot tests (~100 games in a Chess context).

The re-run of M vs HP with HP set at 650 did not make the HP mre valuable
compared to when the engines thought they were equal. On the contrary, the
result was 45.4% (51+ 64- 26=) for the Ministers, against 42% earlier. The
4.6% excess score for the High Priestesses corresponds to about 35 cP, or
17 cP a piece. That confirms the value 650 (against 633 for the Minister).
Perhaps the first time the High Priestesses were partly lucky. Note that
the standard error is 31 cP.

Then I tried the 'Elephant' (F+A, or Elepherz, really) and 'Dababbah'
(W+D, Wazibabbah), in pairs against a pair of Knights (so that the
opponent actually had 4 Knights in the array RNNBQKBNNR against RNEBQKBENR
or RYNBQKBNYR). Note that I started the Wazibabbahs at b1 and i1, because
the on c1 and h1 there was a terrible development conflict with the
Knights.

EE vs NN was practically equal (I had already anticipated that, and
programmed the value at 290 against the Knight's 300, for a slight
discouragement of trading the imbalance away for no reason): 49.5% (39+
40- 21=). So a _pair_ of E is worth 600. But, being color-bound pieces, I
have no doubt that part of this is for the pair bonus, and that an
unpaired E is worth less than half of it due to the inability to access
the other color. Fairy-Max is not really a good system to test this, as it
has no pair bonusses in its evaluation. As the piece itself is less
valuable than the Bishop, (a pair of those isworth 750 on 10x8), my
educated guess would be that the pair bonus is also smaller, about 30.
That would make the E base value 285.

YY vs NN gave a clear win for the Knights: 45.5% (37+, 46-, 18=). The 4.5%
excess score translates to only 30cP for the YY pair, though. Thus each
Wazibabbah comes out at 285. It seems an isolated F+A and D+B are equal in
value, and that the F+A achieves its higher value only through the pair
bonus.

Finally the Commoner, which I already tested before once on 8x8. Again I
tested a pair of them against two Knights. As expected, also on 10x8 a
very clear win for the Knights: 40% (35+ 46- 14=). That corresponds to
70cP, or 35cP per Commoner, which thus comes out at 265 (very close to the
preset of 260 I gave it, so no need for a second iteration).

Note that this low Commoner value falsifies about every speculation that
has been made about it (usually presented as 'King end-game value'),
which all put it above the Bishop, around 400. It is not an effect of the
bigger board, as I found nearly the same value on 8x8. This is opening
value, though, and Betza has mentioned that the opening value of the
Commoner is indeed very low, but that it gets very strong in the end-game.
So I am testing that now, By setting up varies Pawn chains of 7 or 8 Pawns
on 2nd and 7th rank (making sure each side plays each Pawn setup equally
often in both directions), plus Kings on i1/i8, and then giving one side
Knights on b1 and f1, and the other Commoners on b8 and f8. No other
pieces are on the board, and I would say this definitely qualifies as
end-game. 13 games is a bit early, but the Commoners are not doing very
well here either (61.5% for the Knights, so far).

So the preliminary conclusion of the piece values in a Chess context is:
HP=650
M=630
N=300
E=285 (pair bonus=30)
Y=285
G=265
P=85

It seems that all pieces with 8 targets cluster around 290, and those with
16 targets around 640, with very litle spread. (I measured an F+D earlier,
and it came out at 580 for a pair, also fitting this pattern). For the
Commoner this is a surprise (although it is not completely clear why
others over-estimated it so much, as it is simply another piece with 8
targets, like the Knight, and much slower at that...).

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