King+Pawn+Tropism

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an endgame evaluation feature concerning the distance of a king to pawns, with the motivation to either defend or support own ones, or to attack or block opponent ones - in both cases, the closer the better.
 * King Pawn Tropism**,

=Implementation= A common way to implement tropism is to calculate the average Manhattan-distance of the king square to all pawn squares, weighted by some factor to consider passed and weak pawns (i.e. 6:3:2 for passers, backward and remaining pawns as applied in Bobby and also Kraas' and Schrüfer's didactic Basic program Demoschach, described in //Das große Computerschachbuch// ). Two accumulators are used to aggregate all the Manhattan-distances times weight, and all the weights as well, to finally divide the weighted sum of distances by the number of pawn weights for an average distance

> math \LARGE{\Delta\Phi} = \normalsize\frac {\displaystyle\sum_{i=1}^{n} {Wi \Delta_i}} {\displaystyle\sum_{i=1}^{n} {Wi}} math

in the 1..14 Manhattan range, somehow interpreted as penalty for the king side.

=See also=
 * King Centralization
 * Pawn Endgame
 * Réti Endgame Study
 * Rule of the Square
 * King Piece Tropism
 * Unstoppable Passer

=External Links=
 * [|tropism - Wiktionary]
 * [|Tropism from Wikipedia]

=References= =What links here?= include page="King Pawn Tropism" component="backlinks" limit="40"
 * Up one Level**