Experiment to find the relative value of variant pieces

So I did something similar with the Femme Fatale (FF). Depth 6 100 random positions similar like this one:

Outcome was in this experiment, that the Femme Fatale is pretty close to a Rook in value, but slightly less than that.

Actually I did do a rather precise determination of the Femme-Fatale value, for the purpose of preparing me for the Dutch Superchess championship that I won. From materially imbalanced self-play by a specially adapted version of Fairy-Max it turned out to be halfway between R and Q, so 7-7.25 Pawns. I remember we even played against each other in that championship, and I traded my FF for your Princess (worth 8.75), and still had a pretty hard time winning that afterwards. It was my toughest game in that tourney.

In my test from #21 the Rook was the strongest piece at all in the position. I'll see what happens in a position where the Femme Fatale meets the Queen.

Perhaps the presence or absence of stronger traditional pieces have an influence on this kind of measurements.

That is an interesting thought. I only measured it in FIDE context, either replacing Q or one R of one of the players by FF, and observing the resulting score. But since the FF affects the behavior of other pieces, its value could conceivably depend on the opponent material that is present. Just like the Joker's value is.

I am now generating and analysing (with depth 7) positions like this:

Extra white FF againts extra black Rook. Both have a Queen.
The outcome after more than 110 positions is still that it thinks, that FF is a bit weaker than a Rook.

I also remember the OTB tournament and intuitively think that FF should be stronger than a Rook. Interesting ...

Well, with the FF-for-R replacement the FF side won very convincingly (like >75%). Pawn odds under the same conditions typically produces a 65% result.

It could be that you exposed a weakness of your method here, that you average over positions that are too much randomized. This ignores that during most of a game both armies are well separated, making the local density of pieces of a given color much higher than when they are scattered over the board. And that people tend to place their pieces on good squares, rather than poor squares, so that the poor squares do not nearly suppress the average as much as simple arithmetic would suggest.

For the Femme Fatale a good square is where it 'pacifies' as many opponent pieces as possible; the optimal use is to jump into the opponent's camp as early as possible, using the adjacent pacified pieces as shields against distant slider attacs, and simply jump away to another safe square when the opponent finally manages to threaten the FF.

Till now I thought that Fairy Max supports fairy pieces but not (yet) with side effects and special abilities. But from your comment I conclude that you also implemented the Femme Fatale now. Is that indeed the case?

Not really. For the purpose of preparing myself for the Superchess championship I made a special derivative of Fairy-Max that had a hard-coded test on all adjacent squares of a piece that it wanted to generate moves for, in order to test if there was an FF there. This gave it a significant slowdown, which I would not want in the regular version. I did not officially release that version, I think.