Kevin Pacey wrote on Sun, Dec 20, 2020 08:02 PM UTC:
Estimating fairy piece values is a major topic for chess variant players and theoreticians alike; it would be hard to play a chess variant game well without knowing/guessing what kind of trade(s) are more or less okay to make from a materialistic point of view alone.
Some people have tried to develop formulae to make estimates that would apply well to even a large number of board sizes and/or shapes. Special rules for some chess variants can make estimating piece values even harder than usual. For rectangular/square boards especially, there have also been efforts made to statistically analyse the results of engine vs. engine games with fairy pieces included in one or both armies (if two sides play, as usually the case). Personally I take even such more scientific efforts with a grain of salt, e.g. the composition and/or initial setup of the armies can affect the results somewhat, just maybe. However, I am not a thought-leader on such a statistical approach. :) Here's is a link to one effort to estimate piece values, by someone who made a big contribution to the development of chess variants (this can also be taken with a grain of salt, as formulae are not foolproof):
Incidentally, even the values for chess are not completely agreed upon. Some such as myself use Euwe's values of P=1, N=B=3.5, R=5.5, Q=10 on 8x8; however, 2 Bishops are generally worth a bit more than two Ns (or N and B), and almost all chess Grandmasters still slightly prefer a lone B to a lone N on average - to express that, I personally change N to be something like = 3.49, if I tried to be more exact (but still it's a guess). Once again, computer statistical work has been tried with chess piece values (this time using games of pretty strong human players), and curiously finds N=B exactly (though I don't know what's thought the margin of error).
For what it's worth, here's the wiki on fairy pieces, which among other things mentions classification:
Estimating fairy piece values is a major topic for chess variant players and theoreticians alike; it would be hard to play a chess variant game well without knowing/guessing what kind of trade(s) are more or less okay to make from a materialistic point of view alone.
Some people have tried to develop formulae to make estimates that would apply well to even a large number of board sizes and/or shapes. Special rules for some chess variants can make estimating piece values even harder than usual. For rectangular/square boards especially, there have also been efforts made to statistically analyse the results of engine vs. engine games with fairy pieces included in one or both armies (if two sides play, as usually the case). Personally I take even such more scientific efforts with a grain of salt, e.g. the composition and/or initial setup of the armies can affect the results somewhat, just maybe. However, I am not a thought-leader on such a statistical approach. :) Here's is a link to one effort to estimate piece values, by someone who made a big contribution to the development of chess variants (this can also be taken with a grain of salt, as formulae are not foolproof):
https://www.chessvariants.com/piececlopedia.dir/ideal-and-practical-values.html
Incidentally, even the values for chess are not completely agreed upon. Some such as myself use Euwe's values of P=1, N=B=3.5, R=5.5, Q=10 on 8x8; however, 2 Bishops are generally worth a bit more than two Ns (or N and B), and almost all chess Grandmasters still slightly prefer a lone B to a lone N on average - to express that, I personally change N to be something like = 3.49, if I tried to be more exact (but still it's a guess). Once again, computer statistical work has been tried with chess piece values (this time using games of pretty strong human players), and curiously finds N=B exactly (though I don't know what's thought the margin of error).
For what it's worth, here's the wiki on fairy pieces, which among other things mentions classification:
https://en.wikipedia.org/wiki/Fairy_chess_piece
Classification is a thankless task to attempt, as the list just grows... Here's one (by no means complete) attempt on this website:
https://www.chessvariants.com/piececlopedia.dir/taxonomy.html