Author: Ernst A. Heinz
Date: 01:00:43 10/15/98
Go up one level in this thread
On October 14, 1998 at 21:13:07, Roberto Waldteufel wrote:
>
> [...], but surely for KBNK you need two evaluations, depending on the bishop
>you have, since the king needs to be forced into the right corner.
You can account for this in one single formula. Let me quote from my article
"Efficient Interior-Node Recognition" as published in the ICCA Journal 21(3)
and available electronically from the WWW page of "DarkThought" at URL
<http://wwwipd.ira.uka.de/Tichy/DarkThought/>:
*******************************************************************************
Recognizer scores
[...]
In order to illustrate how scoring functions for interior-node
recognition work, we develop such functions for the well-known classes
KBBK (with differently coloured Bishops) and KBNK of elementary
endgames. The winning strategy for KBBK with is to drive the lone King
into any corner and mate it there by a concerted effort of all three
pieces. The strong King must approach the scene, too, because two minor
pieces cannot mate on their own. The same winning strategy applies to
KBNK with the notable exception that the lone King has to be driven into
a corner controlled by the Bishop of the strong side. Therefore, the
distance between the lone King and the nearest target corner as well as
the distance between the lone and the strong King are important traits
of the respective positions. Beside these explicitly obvious relations
of the two Kings the recognizer scores should also reflect the different
degrees of difficulty involved in winning KBBK (with a maximal
distance-to-mate of 19 moves) in contrast to winning the much harder
KBNK (with a maximal distance-to-mate of 33 moves).
The below two scoring functions KBBK(p) and KBNK(p) implement the
above guidelines for given positions p with minor pieces valued at
3.25 Pawns and k_corner_dist(), kb_corner_dist(), as well as
kk_dist() suitably defined. Both scoring functions are efficient to
compute and easy to implement. They let the search make progress in all
recognized positions and channel it into greatly preferring KBBK over
KBNK but not over positions where the winning side is up a Queen or more.
KBBK(p) = material_balance(p) + winning_bonus(p)
= 6.5 + 2.5 - 0.25*k_corner_dist(p) - 0.125*kk_dist(p)
= 9 - 0.25*k_corner_dist(p) - 0.125*kk_dist(p)
KBNK(p) = material_balance(p) + winning_bonus(p)
= 6.5 - 0.5 - 0.25*kb_corner_dist(p) - 0.125*kk_dist(p)
= 6 - 0.25*kb_corner_dist(p) - 0.125*kk_dist(p)
*******************************************************************************
Using solely the above two scoring functions, "DarkThought" is able to mate
the lone King easily in the according endgames.
=Ernst=
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