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H.G.Muller wrote on 2008-04-28 UTC
The Commoners did make a strong come-back in my GG vs NN end-game test, and
finally won a 133-game match by 55.3%. This shows that indeed they do
perform vbetter in the end-game than in the opening, compared to Knights.

Normally I would say that the 5.3% excess score corresponds to 40cP, so
that each Commoner is 20cP than a Knight, i.e. 320. (In stead of their
opening value 265.)

Here that would be really premature, as I have not determined the end-game
value of a Pawn. (My intuition tells me it must score better than the 62%
for Pawn odds in the opening, as the best you could hope for in the latter
case is to preserve the advantage to the ending through game stages that
are still full of tactical surprises, which could easily erase the
advantage. Unlike a Piece advantage, a Pawn advantage in general does not
automatically grows during the progress of the game. You can only start
building out a Pawn advantage when the board gets empty enough that it can
be converted to a passer that can be safely pushed through enemy territory.
So an end-game Pawn might give an excess score larger than 12%, and hence
the 5.3% would correspond to less than 40cP.)

But no matter what the end-game Pawn value is, it is clear that the G-N
difference changes sign. This could be due to a drop in value of the
Knight as well, and is not necessarily proof that the Commoner rises in
value. According to Larry Kaufman's analysis of 8x8 games, a Bishop or
Rook rise in value compared to other pieces (including the Knight) as
well. He expresses this as a function of the number of Pawns present, and
the B-N swing can be 50cP in going from positions with all Pawns to
positions without Pawns. This is similar to what we observe for the G-N
value. It would take far more end-game test matches, involving all piece
types, to determine this. (In particular Q vs 3 minors would be useful.)

Whatever the case, the relative Commoner increase is a comparatively small
effect. It never ever even gets close to the commonly encountered estimate
of 400.

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