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 2/24/2018  Study, M.G. Klaitzkin
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For my chess variant Economy Chess (download) I am trying to work out a formula that gives the weaker player an advantage when playing against a stronger player. (also see an earlier thread on this) I've derived a formula that may work well, and I hope some of you will fill in some values to see if it seems correct to you.
In normal standard chess odds are given by taking away a piece (or tempo). The disadvantage of this system is that you can't give a precise advantage. I.e.: it's impossible to give someone "3/4 knight odds", because you cant take away 3/4 of a knight.
In Economy Chess this is possible because a piece has price. A knight costs 75 coins, so if you want to give "3/4 knight odds" the player gets (3/4*75=) 56 coins to start with.
So in Economy Chess players get odds by giving them startingmoney that can be spend on piece to their own good.
The formula
The goal of the formula is that players can input their own rating and the rating of their opponent. The output is a number of coins that the weaker player gets at the start.
x1 = strong player rating
x2 = weak player rating
Formula: (x1x2)/(40 + 1.0025^x2)*25 = # of coins
Example:
Me (1200) vs computer HARD (2200)
(20001200)/(40+1.0025^1200)*25 = 333 coins
Value of the pieces in Economy Chess:
Default prices (coins):
Pawn: 25
Knight: 75
Bisshop: 78
Rook: 125
Queen: 225
Some more examples:
player A (900) vs player B (1100)
(1100900)/(40+1.0025^900)*25 = 101 coins
player A (1100) vs player B (1400)
(14001100)/(40+1.0025^1100)*25 = 134 coins
player A (1400) vs player B (1800)
(18001400)/(40+1.0025^1400)*25 = 137 coins
player A (1800) vs player B (2400)
(24001800)/(40+1.0025^1800)*25 = 115 coins
Me (1200) vs Carlsen (2835)
(28351200)/(40+1.0025^1200)*25 = 681 coins
So, if you feel like it: input your rating and that of an opponent and see if the result seems right to you. (if you dont know how to do it I can do it for you)