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Subject: Re: passed pawn evaluation.

Author: Alessandro Damiani

Date: 14:27:46 01/13/04

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>You need to be _very_ careful doing what you describe.  It leads to a
>scoring discontinuity, or a "boundary condition" that can be very bad
>with minimax/alpha-beta search.  If you know what a discontinuous function
>is, you just defined one (IE in Laplace transforms, you see "unit step
>functions" that have this property.)  The problem here is that when you
>are searching positions where you _cross_ the boundary in the search, the
>program gets to pick when and where it crosses, and since you are talking
>about a positional score of +/- 3 pawns or more, what it might do is give
>up two pawns rather than lose the 3 pawn advantage.  Not a good plan,
>usually.  Your evaluation function _really_ should be a continuous function
>that has no such "discontinuities".
>
>IE you might do just fine where you have lots of pieces and use that
>trick, and once there are no pieces, you are also OK.  But around the
>"edge" where you go from "have to have not" the search can do some amazing
>things to use that discontinuity to produce results wildly different from
>what you would normally expect to see.  IE early in Crafty I did that for
>endgames, where material <= N.  And at the transition point, I saw some
>_ugly_ ideas pop out of the search.  Now it is a smooth transition from one
>phase to the next with no sudden large jumps..
>
>I think Hans Berliner wrote a paper about this topic but I can't recall the
>title for the life of me...

SNAC (Smoothness, Non-Linearity, and Application Coefficients). I remember the
content, but I don't remember where I put it. Maybe in one of the boxes that are
in the cellar since I relocated. ;-)

Alessandro



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