@Kevin & @HG

I hope you 2 guys are not bothered by me inserting myself into your little talk. For Kevin, I'd like to help answer the last question about the sample size of 1000%. One problem, as always in statistics is if the sample is representative (in principle I think that is your main concern), if so HG has a neat formula for the error taken from physics I guess. The point to be taken for there was that the error decreases by the square root of 2 function meaning you have to quadruple sample size in order to half the error. Still there is the concern of representative sample. At first glance, and it could be sufficient ,the distribution of reasonable situations is rather constant. Even if situations are not constant through the course of games (meaning in average you exchange rooks rather later than minor pieces in an very orthodox like variant) , they are probably very alike in between games. There are probably effects of what Ralph Betza calls sociability (an example would be Fergus's observation about his own Gross Chess that knights cooperate better with vaos) meaning so me pieces have better relationships with each other. Unless very weird cases these effects are likely to be small! Point of whole of this is not to make an truthfully scientific enquirement because that is very difficult but rather to argue that such samples are mostly representative. If they are not you are basically screwed.

I think there is some small friction between the two of you, and maybe I'll post myself somewhere in between, although probably a bit close to HG's take :)! I see HG experimental method more as a tool rather than the answer and I'm confident you do, too HG, as you enquirement about short range leapers on and 8x8 board ended up in a formula :)! On the other hand the mathematician in me does feel the need for explanations of the empiric data. There principles like the ones postulated by Ralph Betza in his essays on piece values (I'm sure you know what I'm talking about so I won't insist) come into play. In my knight vs zebra context on increasingly larger boards the knight has better mobility (due to less of the board jumps), and the zebra has better speed (due to longer jumps). When thinking about a basic formula I don't think it should be that difficult to come up with. It probably is enough to count how many moves a knight and respectively a zebra needs to get from A to B on boards of various sizes starting with 8x8 and ending with say 20x20. That it is not hard to do, maybe tomorrow I'll get the courage. I certainly hope so. But in real variants there is more to take into account than simple triangulation like relations with pawns, checkmating power with another specific minor piece . Here is where HG's statistical method comes into play. But even so for each variant, interpretations may be given.

PS Actually practical questions are allways more difficult the ZvsN theorethical one is not that hard eventually. But the practical problem on what to use in a computer program (hopefully not in a long time I'll go back to Greg's chessV) for the value of the joker in each of the 2 apothecary games is a pretty nasty one :)! Cheers everybody, I hope I have not bored you :(!