I think I used MVV/LVA for ordering captures. We can also use other good heuristic to sort captures within themselves.Interesting. What I had in mind was to make the probabilities proportional to (1+f*victimValue)/pieceValue. This does seem to avoid the problem you mention; QxP captures could be discouraged, while PxQ captures would be strongly enhanced.
Mind you, I am not claiming that you could ever play good Chess with such an algorithm. I am just curious if one could create such a simple strategy that was at least able to exploit a material advantage (making the game unstable, diverging away from equality rather than converging towards it).
Intuitively I would think that paranoia is good, because pieces could be defended and empty squares could be attacked. OTOH, QxQ should probably be strongly encouraged, because the Queen could have been unprotected. So f=2 seems a reasonable value, which would prefer QxQ by a factor 19/9=2.11 over a Pawn push, while PxQ would have relative probability 19, and QxP 3/9=0.33.
What was problematic was captures weights relative to non-captures! If the capture is forced, that move should get all the weight
despite 40 other non-capture moves possible. If it gets equal simulations (1/40 of them), it will fail.
In checkers this is naturally taken care of by the rules of the game, and playing only among the captures converges fast on the best one.
The "standing pat" is a big problem since it requires a SEE or qsearch. There are also other good tactical moves even in non-captures.
Pins , forks and checks are some of them. The best result I got with MC was in endgames but still had problems with those tactical moves...
I think the best strategy is to select among a reduced pool of good moves instead of pinning down the best move statically, as that is less error prone.
IIRC I also tried using hand-written tactic detection for upto 5-piece endgames to predict results of the game and help compression..
It worked to some extent so then I tried SEE and shallow searches but it was too slow and I couldn't finish compressing some of the big files.
I think that running very fast games with regular search is a much better alternative with less hassle (as Rybka does). We will not be able to produce games as fast as a MC engine does, but then we will have a much better quality of games.