Equation for Handicap

Question

Are there any sort of equations for how much of a handicap one should receive to make a game between two players with differing Elo ratings as balanced as possible?

There might be a time equation to determine how much more time one player should receive in relation to the other. Or, an equation to determine how many more points one player should be up in relation to the other at the start of the game. Or, an equation that factors in both a time and point handicap. (When I refer to points, I am not referring to Elo. Rather, I am referring to point difference given from an engine analysis.)

If there's some way to translate point difference towards probability of winning then making a point handicap equation should be fairly easy, since one can figure out the probability of winning given the Elos of the players.

(I realize there are questions similar to this question. I have seen those questions, and they were not asking for the specifics that I am asking for.)

Answer 1

Are there any sort of equations for how much of a handicap one should receive to make a game between two players with differing Elo ratings as balanced as possible?

The short answer is "No", there is no scientific equation, but it doesn't stop people from trying.

For instance, our club runs an annual handicap tournament in which it tries to produce a practical answer to this question. The rules for the tournament are here.

Players are first put into numbered bands according to their grading with the highest graded players in band 1 and lower graded players in bands 2 and upwards. Then the handicap when two players meet is determined from the following table according to the difference between the players’ bands.

0 – no handicap, first named player in the draw has white
1 – colour, player in the higher band number has white
2 – 2 moves, player in the higher band number has white and makes two moves instead of one to start the game
3 – f pawn and move, player in the higher band number has white, remove f7 pawn
4 – f pawn and 2 moves, remove f7 pawn, player in the higher band number has white and makes two moves instead of one to start the game
5 – knight, remove b1 knight, player in the lower band number has white
6 – rook, remove a1 rook, player in the lower band number has white
7 – queen, remove d1 queen, player in the lower band number has white
8 – queen and knight, remove b1 knight, remove d1 queen, player in the lower band number has white
9 – queen and rook, remove a1 rook, remove d1 queen, player in the lower band number has white

Basically if the rating difference is less than 100 then the players are in the same band, a band difference of 1 equates to a 100 to 199 rating point difference, 2 band = 200 - 299 difference, 3 band = 300 - 399 difference, etc.

In recent years the winner's rating has varied between about 1500 and 2000 so it doesn't seem to favour any particular level although from experience I would say with large handicaps there is a definite skill for each player in adjusting how they play in terms of risk-taking.