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H. G. Muller wrote on Fri, Sep 30, 2011 08:51 AM UTC:
IIRC my tests with Fairy-Max (allowing promotion only to the strongest piece of your own army) found the Clobberers to have a small edge over FIDE, and the Nutters a much larger edge, of nearly a full Pawn. (i.e. against FIDE I had to give them Pawn odds to approximately equalize).

I did experiment only once with the effect of promotion on Pawn value, in the context of Spartan Chess. The result was (surprisingly) that there seemed to be none. In particular, in an attempt to weaken the Spartan army, I changed the single allowed promotion in Fairy-Max of their Hoplite Pawns from 'Warlord' (BN, value ~8.75 on the Kaufman scale, where Q=9.5 and N=3.25) to 'Captain' (WD, value ~3). This did not seem to have any effect on the score.

My interpretation / explanation of this was that in practice unhindered promotion only occurs when a game is already decided, and normally the pawn will be captured directly after promotion, or even before, when promotion is unavoidable. So typically a promotion means the opponent loses a minor piece by sacrificing it, no matter to what you promote. But loss of even a minor piece is usually decisive.

Only in variants like Shatranj, where you can only promote to a completely worthless piece, this reasoning does not apply,and Pawn value gets depressed. (Note that the WD still has mating potential, however. Perhaps limiting promotion to a piece without mating potential would have some impact.)

Note that the Clobberers are not really disadvantaged that much, as the value difference between Q and BN is less than a Pawn. So even promotion races where both sides promote don't lead to a large disturbance of the balance of power. In fact the Nutters suffer more, because their 'Colonel', although much closer in value to a Queen, has almost no backward moves. Thus even when the Nutters do promote first in a promotion race, they have no way to stop the other side from promoting as well 2 or 3 moves later, and thus miss the win. But despite that disadvantage, the Nutters seem to havethe strongest army anyway, so perhaps this is a good thing.

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