29 June 2013

The KID Family Goes the Distance

After writing my previous post on The KID Family, I noticed that the start position (SP) featured in that post (SP599 RQBNKRNB) had another unusual property. It differs from the traditional start position (SP518) in that exactly two pairs of pieces have been switched. The Queen and Queen's Knight have been switched, while the King's Bishop and Rook have also been switched. The other four pieces are all standing on their traditional start squares.

Is this a trivial observation or something significant? I decided to compare all twelve members of the KID family to answer the question. I dragged my chess960 database out of storage -- last seen in the related posts Pieces, Start Squares, and Scores and Of Knights and Start Squares -- and constructed a query based on 'distance'.

I discussed the notion of distance in a couple of old posts: More on the Concept of Distance and A Chess960 Almanac. In brief, it's an attempt to measure the displacement of the pieces in a chess960 SP compared to SP518.

Here's a table showing the distance calculation for the twelve members of the KID family (****KRNB). The column 'zLR' shows the displacement of the 'left' Rook from the a-file, while 'zRR' shows a similar calculation for the 'right' Rook. The distance is the sum of the eight displacements divided by two.

What does this table show? Probably not much. The simplest KID position is SP615, where only the King's Bishop and Rook have been switched. This amounts to a distance of two. One SP has a distance of three, and three SPs (including SP599) have a distance of four. Since the maximum distance is ten, all of the KID positions are well under the max. This means that they don't stray too far from SP518, but we knew that already from the way the family was defined. If I get any other bright ideas from this table, I'll let you know.

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