Trading penalty with imbalances

[Lyudmil Tsvetkov]

Btw., in the case of Q vs 3 pieces imbalance, a sensible thing would be to assign additional 10cps bonus for the side with the 3 pieces for any piece after the 3rd. Thus, with 4 pieces, you will have, 10cps bonus, with 5 20cps, etc. This would be much more precise.

Again, that is basically the same as increasing all piece values (except Pawns) by 10cP. You don't need bonuses for that, just tune the piece values differently. Unless you mean to only do that against a Queen. But then it is equivalent elephantiasis: subtract 10 cP from Q for each piece the opponent has. (Except that 10 cP seems too little.)

The incremental bonus would be valid only in the case of imbalances with unequal number of pieces: Q vs 3 pieces, as well as when one of the sides has a single piece more, but not in the case of imbalances with equal number of pieces. If you have tuned values for imbalances with equal number of pieces, then they will be detuned for imbalances with unequal number of pieces, and vice versa. If you tune them to fit both categories, then they will be equally tuned and detuned for both. But the categories perform differently. You need to specify for each particular case, i.e. piece values in the case with imbalances with equal number of pieces, piece values in the case with imbalances with unequal number of pieces, etc.

[hgm]

The incremental bonus would be valid only in the case of imbalances with unequal number of pieces:

But if you increase all piece values by the same amount, such as 10 cP, this will never affect imbalances with equal pieces. the bonuses for each side just cancel. Only when one side has more pieces than the other he will see 10 cP per extra piece remain.

[Lyudmil Tsvetkov]

The incremental bonus would be valid only in the case of imbalances with unequal number of pieces:

But if you increase all piece values by the same amount, such as 10 cP, this will never affect imbalances with equal pieces. the bonuses for each side just cancel. Only when one side has more pieces than the other he will see 10 cP per extra piece remain.

The trick is that the bonus should be incremental, as the 7th piece is worth more than the 6th, the 6th more than the 5th, etc.

But you should still make a distinction, because for example, an equal 10cps bonus for each piece will fail in the case of one of sides having 2 pieces more, i.e. Q vs 3 pieces imbalance.

As I see it currently, in order to be correct, one must split imbalance evluation into at least 3 main imbalance categories:

- imbalances with equal number of pieces, where piece types and repetitions/redundancies would determine which side is better
- imbalances with one of the sides having a piece more, where you can apply both piece types, repetitions, but also incremental bonus for any piece after the first
- imbalances with one of the sides having 2 pieces more, i.e. Q vs 3 pieces, where already you use a special formula + the same incremental bonus