18 September 2010

Castling Patterns Visualized

Some time ago, in a post titled Introduction to Chess960 Geometry, I worked out the number of unique castling patterns in chess960. By 'unique', I mean a type of position where the King and two Rooks start on different files. It happens that there are 56 such patterns. Listing them in logical sequence gives the following picture.

RKR***** 18
RK*R**** 18
RK**R*** 18
RK***R** 18
RK****R* 18
RK*****R 18
R*KR**** 18
R*K*R*** 12
R*K**R** 18
R*K***R* 12
***R**KR 18
****RKR* 18
****RK*R 18
****R*KR 18
*****RKR 18

The number in the second column is the count of different chess960 positions that share that unique castling pattern. For example, there are 18 positions that have the 'RKR*****' pattern and 12 that have 'R*K*R***'. In the previous post I worked out why some castling patterns encompass 18 positions (there are 48 such patterns) and others only 12 positions (8 patterns). It has to do with positions where the R, K, & R all start on squares of the same color.

The same type of visual table can be used to show the number of positions where castling is possible on the first move. There are 72 positions where castling O-O-O is immediately possible:-

**RKR*** 18
**RK*R** 18
**RK**R* 18
**RK***R 18

And there are 90 positions where O-O is immediately possible:-

R****KR* 18
*R***KR* 18
**R**KR* 18
***R*KR* 18
****RKR* 18

Some day it might be interesting to examine patterns from real games and determine how many times the players castled O-O-O vs. O-O. For now, though, there are too few recorded games to make this worthwhile.

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