Computing the value of fairy pieces beyond one move?

What you are saying is basically that piece values are meaningless, because they would differ for every player. Well, I guess when you get into the realms of negative Elo, that could be true; if a player has no idea at all that a Queen is allowed to move and capture, that Queen would be pretty useless for him. Nevertheless, he would probably still profit enormously from trading his Rook for the opponent Queen (assuming he does know how a Rook moves), because otherwise he would lose many pieces to 'surprise captures' by that opponent Queen, which he did not see coming at all.

But if we get into the realm of reasonable play (say Elo > 1500), piece values tend to converge. They follow from the win/draw/loss statistics of the set of reasonable, quiet positions with a given combination of material on the board. Those statistics are not very sensitive to the quality of play, because error that turn theoretically won positions into a draw are compensated by errors that turn theoretically drawn positions into a loss. Less accurate play just gives more of both.

Anyway, the Dragon Bishop is hugely more powerful than a Rook. If I replace one of the Rooks in the FIDE startposition by a Dragon Bishop, the player with the latter scores about 80% (measured in 250 games). Pawn odds typically results in 65-68% scores, so the difference is far more than Pawn. If R=5, it seems Dragon Bishop is close to 7.

And yes, I have an engine that can play Dragonanga. Not that playing real Dragonanga will tell you much: both players start with the same pieces there. And because all the other Dragonanga pieces hardly exceed Pawn quality, it will not really be possible to set up a meaningful imbalance where a Dragon Bishop has to battle a set of other pieces at near equality. (The second-most-valuable piece is the non-royal King, which is similar to an orthodox Knight in strength.) Which leaves the value of the Dragon Bishop undetermined, other than that it must be large compared to any combination of other pieces you are likely to encounter in a game.

Which engine are you using

I used Fairy-Max for testing the value of the Dragon Bishop. Fairy-Max has always given me good piece values for 8x8 or 10x8 boards. For playing actual Dragonanga I used a Fairy-Max derivative, which promotes on 5th rank instead of 8th rank, and not only the first piece type but the first two piece types.

i'll have to check it out.

Join the Dragonanga club on chess.com https://www.chess.com/join/dragonanga

there's a forum post in the club with step by step instructions on how to set up the variant using chess.com (website--not available on the app).

Once you click the link it will take you to the club and the forums can be found by scrolling to the bottom of the page.

I would say any serious evaluation function should consider the ability to create mate threats. As obviously for example checkmating a knight would be different than checkmating a king.

HOWEVER, one thing that inevitably happens is the tradeoff between concentrated mobility and long range mobility. I feel like to some extent, just thinking about the pieces' ability to attack in general limits the value of mate threat credibility analyses except in very non-chesslike variants.

Also for very simple situations like a couple pieces vs royal piece on an empty board, I feel like you can either find a mate or you can't. If the engine didn't know how to make with some combination of pieces, it would probably not figure it out unless the opponent blundered. If it did, then it can just go M13 or whatever rather than a piecewise evaluation. And optimizing toward a mate you can't see will have to be positional, not piecewise, evaluation.

So in some ways I think you're gonna run into the issue that the mating value of pieces in anything but a sterile endgame is gonna behave a lot like its capture mobility value. It only diverges if the game is extremely simplified. Or I suppose with some extremely strong pieces (Amazon or even stronger), or very unique board positions (i.e. a 5,2-leaper in starting positin of the kingside Knight, which has M1).

There seems to be confusion here between evaluating pieces and evaluating positions.

I'm not evaluating the immediate term value of a piece here. A wazir or alfil or pawn can have incredibly strong effects on a position that are handled by calculation and careful consideration of aspects of the position itself rather than the pieces involved.

When I'm talking about piece values, I mean "what will keeping this piece give me over the course of the game?" Not "does this thing do anything useful right now?" The answer to that question produces ridiculously varies values based on the position. For example, queens and kings defend 5 squares, knights defend 1 square and have 2 squares to move that are empty. Pawns attack 2 squares but have 2 squares they can move too. Rooks defend two squares.

So if we make the approximation that defense is equal to mobility and peaceful or capture-only moves are half that, we get:

pawn: 1.5-2.0

bishop, rook: 2.0

knight: 3.0

King, Queen: 5.0.

In mobility terms.

These are pure nonsense values because they only account for the current state of the game and not what it could evolve into. This is not what I mean by piece values. The value of a piece is about potential of that piece to do something important an indeterminate number of moves later. When you won't know:

•What is left on the board.

•Where most of that stuff is, except for very slow or colorbound pieces where you might have a general idea.

•Who will have the advantage in material or position.

•Whether that piece is still on the board or not in the endgame.

This means that worrying too much about the value of a piece in specific positions is only important if it is uncharacteristically bad at getting somewhere else important over the course of the game. Like how bishops are "very not good" at changing colors or pawns have very limited success at crossing the board.