There's no formula. It's all relative.
Does anyone have a good formula to calculate variant chess pieces's strength?
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You can't really create a good formula, because it heavily depends on the variant. You can however try, for example for a given variant, you can see piece imbalances in expert games and you see the relative strength of the pieces, and maybe then compute average strengths of the piece. Also, you can try asking @wolyn, because he knows variant engine stuff and maybe he can do something for some variants
Rounded off of number of squares it can move to in an 8*8 grid *400/1024 and this whole thing by 64/number of squares it coued theoretically visit.
E.G: bishops can move at most 13 squares, 13*400/1024=5.08. this by two gives a number close to 3
eg: Knight can move 8, 8*400/1024= 3.125
it realy depends on the user
Oct 20, 2025
0
#6
How much a piece is worth varies - a long-ranged piece is worth more on larger boards, which is common with variants and 4PC, and which is why bishops are worth 5 in variants. Grasshoppers can be nearly useless on some boards, and it's much more useful in variants such as mini forest. @Oliver_Brimley, a piece's worth doesn't really depend on the user. I know that what you're probably trying to say is that people have preferences to pieces, but it doesn't really change the piece's value.
CzarnyResorak567 wrote:
You can't really create a good formula, because it heavily depends on the variant. You can however try, for example for a given variant, you can see piece imbalances in expert games and you see the relative strength of the pieces, and maybe then compute average strengths of the piece. Also, you can try asking @wolyn, because he knows variant engine stuff and maybe he can do something for some variants
^
Oct 21, 2025
0
#8
asthebird wrote:
CzarnyResorak567 wrote:
You can't really create a good formula, because it heavily depends on the variant. You can however try, for example for a given variant, you can see piece imbalances in expert games and you see the relative strength of the pieces, and maybe then compute average strengths of the piece. Also, you can try asking @wolyn, because he knows variant engine stuff and maybe he can do something for some variants
^
^
Oct 21, 2025
0
#9
Maybe just calculate how many squares it can move to in a position, for example, e4.
Oct 21, 2025
0
#10
Fet wrote:
I need one, because I asked ChatGPT, of course, it couldn't create anything worthy of looking. I got a formula from somewhere in the forums, but it's not so accurate:
Formula to compute the value of a non-royal piece:
f(Amount of squares it controls * g(amount of squares it can potentially visit))
g(x) = + 33333
f(x) = *log base of x + 02605x
For example,
P =
N =
B =
R =
Q =
Adjusted so a pawn equals 1(multiplying by ),
P = 1
N =
B =
R =
Q =
Finding a value of a old queen(ferz):
f(4 * g(32)) = f(4* ⅔) = f(8/3) =
F =
Adjusted in pawns:
F =
For an alfili:
f(4 * g(16)) = f(4*1/2) = f(2) =
A =
Adjusted in pawns:
A = 1
For an Amazon(Z):
f(35 * g(64)) = f(35) =
Z =
Adjusted in pawns,
Z =
Does anyone have a better formula? Because this formula does not contain these two factors:
1. The distance the piece can reach.
2. If the piece can jump over pieces or not.
Please use white for all us dark mode folks
CzarnyResorak567 wrote:
You can't really create a good formula, because it heavily depends on the variant. You can however try, for example for a given variant, you can see piece imbalances in expert games and you see the relative strength of the pieces, and maybe then compute average strengths of the piece. Also, you can try asking @wolyn, because he knows variant engine stuff and maybe he can do something for some variants
Agreed. There can be no standard formula that applies to every variant. A queen on an 8x8 board is worth many more (relative) points than a queen on the XXL (14x14) board. However, if you impose some restrictions, this question is quite an interesting one (and led me to comment on this post).
If you consider a piece on an 8x8 chessboard, in the Chess Variants forum, @HGMuller has written quite extensively on this topic, such as here. It may be of your interest.
To paraphrase him, in general, for leapers with maximum number of available moves N, the function f(N) = 0.7N² + 33N approximates its value (in centipawns, where 1 pawn is worth 100 centipawns) somewhat decently. For example, the knight (N = 8) would be worth 3.08 centipawns, or roughly 3 points.
Oct 27, 2025
0
#12
cp≈45M+35F−60C+50L+25K+B
Where M is the average number of squares the piece can go to when placed in the center of a 8x8 board
F is the average number of forks a piece can make in a move
C is 1 if the piece is colourblind
L is 1 if it’s a rider, 0.5 if it’s hopper(leaper), 0 if not a leaper
K is 1 if piece can mate king by it self
B is a tweak that depends on the piece
I need one, because I asked ChatGPT, of course, it couldn't create anything worthy of looking. I got a formula from somewhere in the forums, but it's not so accurate:
Formula to compute the value of a non-royal piece:
f(Amount of squares it controls * g(amount of squares it can potentially visit))
g(x) = 0.0104167x + 0.333333
f(x) = 0.285322*log base 1.84 of x + 0.302605x
For example,
P = 0.93
N = 3.394
B = 3.634
R = 5.471
Q = 9.713
Adjusted so a pawn equals 1(multiplying by 1.0752688172),
P = 1
N = 3.64946236558
B = 3.9075268817
R = 5.8827956989
Q = 10.4440860215
Finding a value of a old queen(ferz):
f(4 * g(32)) = f(4* ⅔) = f(8/3) = 1.266
F = 1.266
Adjusted in pawns:
F = 1.36129032258
For an alfili:
f(4 * g(16)) = f(4*1/2) = f(2) = 0.93
A = 0.93
Adjusted in pawns:
A = 1
For an Amazon(Z):
f(35 * g(64)) = f(35) = 12.25
Z = 12.25
Adjusted in pawns,
Z = 13.1720430107
Does anyone have a better formula? Because this formula does not contain these two factors:
1. The distance the piece can reach.
2. If the piece can jump over pieces or not.