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

Neoliminal 02/18/2006 15 comments

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

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 11

')">

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

This article is worthy of a second look to test it against chess and chess variants in a variety of positions. This method could prove valuable in correspondence play where there is plenty of time for analysis.

It's not clear how well it would work against dark or benedict-type variants.

Very interesting. As I understand it, this only applies to new (fairy) pieces with novel moves, all other chess rules as normal, and gives them a value. Is there scope for calculating piece values in variants with different rules. I have often wondered what the piece value is in Alice for example. It was also very interesting that the values worked out so well for standard pieces - does this work as well for other positions?

Answering Harold's Questions:

I haven't tried the method on any other variants. I would expect that in Alice Chess piece values would be nearly half since they can only attack half the board at any one time... however that's speculation on my part.

As for testing with other positions, I have not. But I suspect that as long as all the pieces are still on the board (no captures) and you are in a relatively good middle game (something experts/masters would play) that you would end up with similar results. I choose this position by scanning opening databases for a long opening sequence with no captures and both kings castled.

2 rooks represent piece, dark squares moves, pawns captures(if different from moves), knight squares to jump, white rook opposing piece, white knight
How about the wall?
(takes up 2 squares, moves and captures 2 squares forward/backward, 1 side to side)
8/8/3??3/3??3/2?rr?2/3??3/3??3/8

I'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.

Nice interesting idea, but unfortunately it doesn't work. A Bishop is normally accepted to be a bit more than a knight (especially on larger boards) here seems the opposite. The Pao is less than a knight. Actually in XiangQi a Pao is a bit more than a Ma (Horse) but the board is bigger there, plus the Ma is not like our knight: it can't jump over pieces. In few words: the Pao value is around 2.5, half of a Rook not more. So the order Bishop>knight>Pao which the common sense suggest here has been reverted. And of course an Archbishop is notably less than a Marshall, which is almost equal to a Queen, so again those values doesn't compare properly one to another. An Archbishop in Gothic Chess is valued 6.5, so it's more like a pair of Bishops, not 9 like a Queen...