Queen vs 3 Minors part 2

I did some more research in the case of a material imbalance of 3 minors vs a queen. In my previous post I determined the imbalance to be worth 0,82 pawns.

Unfortunately this seems to be too simple. The above imbalance figure includes the bonus for the bishop pair which the side with the minors usually enjoys. To remove this effect I repeated the test with positions where the 3 minors did not include the bishop pair.

An additional factor not covered so far is the effect coming from the number of rooks still on the board. In my previous test all starting positions included 2 rook pairs. The theory says that the bonus for the minors should be bigger if the rooks are still on the board. The bonus might be different if some rooks are removed. So I performed several tests to test this hypothesis. 

Here are my results

QRR vs RRBNN

In those positions all rooks were still on the board

Queen side scores 43,0% with equal number of pawns
Queen side scores 23,8% with Minors having an extra pawn

Value of Imbalance for Queen side: -0,37 pawns

QRvsRBNN

In those positions 1 rook for each side was removed

Queen side scores 50,5% with equal number of pawns
Queen side scores 28,9% with Minors having an extra pawn

Value of Imbalance for Queen side: +0,02 pawns

QvsBNN

 In those positions all rooks are removed

Queen side scores 70,8% with equal number of pawns
Queen side scores 44,5% with Minors having an extra pawn

Value of Imbalance for Queen side: +0,79 pawns






It seems the number of rooks has huge impact on the value of the imbalance. Its value changes by more than a pawn. 

 Probably the imbalances of queen and pawns vs a rook and two minors are to hard to be calculated or require a bigger effort. The missing pawns give the side with the minors some development compensation and also half open files, so the value of the imbalance gets polluted with other stuff. So this remains maybe as a future but not immediate exercise.