A method for calculating the relative value of fairy pieces in chess variants

Neoliminal

In this article Neoliminal takes a standard chess position, and uses a novel and interesting technique to calculate the relative value of fairy pieces.

02/18/2006

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 ABCDEFGH

This is a bit involved so let me say from the outset that my goal is to allow for a relatively objective value of a piece when there is no reasonable method to determine it's value.

I started with the assumption that I wanted to use a fairly standard game of chess as the basis for the analysis. I choose ECO C97 up to the 9th move:

r1bq1rk1/2p1bppp/p2p1n2/np2p3/4P3/1BP2N1P/PP1P1PP1/RNBQR1K1 b - - 0 1

I choose this position because there were no captures and both kings had castled. This resulted in 32 open spaces. I assumed the new piece was Black and placed it in each of the 32 open spaces. The following rules were applied:

A. For each piece that could be either guarded or captured by the piece, it scored points equal to that pieces normal value.

Example: A Queen on d5 could guard Pawns on b5, d6, f7, and e5 each valued at 1 point for a total of 4 points and the Rook at a8 for 5 points. It could also attack the two Pawns e4 and d2, for 2 more points and a Bishop at b3 for 3 points. In total the d5 square was worth 14 points.

B. If the piece was in danger by a piece it could not capture, it scored zero points.

Example: A Knight on d5 could be attacked by the Bishop at B3, but could not capture that piece itself. Even though the Knight could theoretically protect a Pawn, Bishop, and a Knight, it gained no points for these because it could be captured by a piece it would not capture.

C. The King was valued at 20 points.

Example: A rook on h1 would gain 20 points points for the King and 1 point for the Pawn on h3.

D. Promoted Pawns on the last rank were given half the value of a Queen.

Example: A pawn on h1 would be worth half the value of a Queen because it could promote. A Queen on h1 is worth 22, so for a pawn it was worth 11.

All the squares were then added together as divided by 37 and rounded to their nearest whole number. The results were exact matched to the standard values normally given these pieces.

Q = 9 (9.3) 344
R = 5 (4.84) 179
B = 3 (3.05) 113
N = 3 (3.27) 121
P = 1 (1.14) 42

This system takes into account a number of variables that previous systems have not been able to capture. It allows for any particular fairy piece to be given a value.

Example:

Archbishop (Combination Bishop and Knight):
A = 9 (9) 333

Pao (Moves like Rook, must jump a piece to capture it):
Pa= 4 (4.14) 153

Marshall (Combination Knight and Rook):
M = 8 (7.76) 287

Ferz (Move and Capture one space diagonally):
F = 2 (1.59) 59

Lance (May only Move and Capture foward):
L = 1 (.49) 18

Comments

AuthorComment
dogod07/15/2006 13:56It should be, but I used it and it is not.
neoliminal09/29/2007 20:22I've discovered a flaw in the system that needs to be refined. It involves the miscalculation of movement. The rest of the system seems to be working correctly... but I will need to do some more calculations to find a way to add a movement component to the test.
pallab12/08/2008 07:08Marshall if costlier than archbishop. At least that is what I have learnt after playing many variatns game.
GoranPrpic
02/15/2012 04:41
Determining the "value" of an entity is by no means a straight forward task. Being inspired to look into this subject is inspirational. Thanks for bringing it up!

 
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