Single Comment

OK, after fixing some bugs, and some testing mistakes, I have the first
valid results. To begin with, I made one change in the engine: the factor
two discount on a Pawnless (but otherwise unsuspect) lead is not applied
when the opponent has a bare King. When you have mating potential (mating
minor, more than a minor ahead and no 'defective pair' or a color-bound
piece, or 3 pieces) there is no reason to shy away from the end-game.
Mating potential is mating potential... This solves problems in KRPKB, here
the advantage can be very high if the Pawn is on 7th rank (and counts for
~2.5, so you are at +4.5), where the Bishop covers the promotion square, so
you cannot make progress other than forcing the BxP trade, to convert to
KRK. But with a 'Pawnless penalty' that would only be +2.5, so the engine
refuses to do it unless the KRK mate is already within the horizon. (Which
it usually isn't at the fast games I do, so this easily won game ends in a
50-move draw...)

With this change Pair-o-Max beat the old Fairy-Max by 53.67% in 409 games
(here the statistical error is 2%), so I don't have to worry that it has
lost strength because the implemented changes slow it down too much (>90%
confidence). The more accurate scoring of the Bishop pair and recognition
of drawishness more than make up for it. The 3.67% excess score corresponds
to a superiority of 25 Elo.

With this version of Pair-o-Max I ran a Commoners vs Knights match,
replacing 2 Knights by 2 Commoners for one side in the FIDE setup. In half
the games I then swapped B and C of the Commoner side, to provide more game
variety. The Commoners player alternately had black and white, to elimiate
the white advantage, and in half the games black was given the first move,
also to drive up game variety.

After 393 games the Commoners are leading by 52.3%. This is just a bit
larger than the standard deviation, so barely significant. But, hen taken
at face value, the 2.3% excess corresponds to 16 centi-Pawn. And because
that is for a pair, it implies the Commoner is 8cP (+/- 7cP) stronger than
a Knight. This is consistent with the value of 333 I programmed for C
(where N=325). In an earlier run I had programmed C at 300, i.e. below N,
but when this run also had the Commoners winning (even more!), I changed
the value to mae it consistent, and redid the run. As usual, this did not
have a dramatic effect on the average score.

The test now runs on to increase the precision. I will start a second test
in parallel (now new-vs-old version is decided), for Commoners vs Bishops.