Single Comment

I was mainly going by parts of the commentary on your Eurasian Chess page, Fergus, i.e. about the relative values of the various pieces (given at one point in decreasing order of value, though excluding any numerical values) . This was based on the various listed bare means of delivering basic Eurasian Chess checkmates. Correctly or not, I tried to take these listed bare means heavily into account myself when putting a N as slightly ahead a B (in numerical terms, in my case).

By way of comparison purposes, for my own 10x10 Sac Chess variant, I estimated a B at 3.5 and the N at 3, i.e. the reverse of what I've estimated their worth at in Eurasian Chess, which is in line with the premise your question (greater B mobility on a 10x10 board should favour it on average) as far as that game goes. However, Sac Chess is played with Ks that are like chess Ks (unlike in Eurasian Chess), so even for an average case Sac Chess endgame, I'd suppose the relative values of B and N would not be in any way affected. It may seem I'm going into contorsions a little to justify these values, but fwiw it seems to me one often has to use somewhat convoluted thinking to come up with estimates of the relative values of fairy chess pieces, unless one trusts fully in computer studies (in my case, I'd prefer to at least have a program used for a study that has a strong chess rating, if nothing else).

Note that even for Eurasian Chess I thought a B should be worth at least 3 pawns, but neither it nor a N should be worth 4 pawns. I wasn't going to have a Cannon worth 4.5 pawns (I think it was valued this in a Chinese Chess book I've seen, for what that's worth, though that book put R=9 to give context).

Note that a drawback of having V=2 is that three Vs=6 (greater than a R) yet any colour combination of these would never suffice to mate a lone K, not even by a helpmate.

I must point out that there's a slight discrepency between my Sac Chess value Q=10 and my Eurasian Chess value Q=9.5 (with the formula Q=R+B+P used for both games), given that the Eurasian Chess value for the Q really ought to be ten pawns too, in my view, but since in general reality cannot be perfect in every way, I wasn't going to quibble over 1/2 a P in value for such a high value piece as a Q (noting, though, that 2Rs=Q+P is a material equivalency formula that perhaps ought to still be valid in practice on average, in the event that that material balance happens in either game).

P.S.: Partly to avoid the slight discrepancy mentioned in the previous paragraph, here's my latest (possibly more accurate) set of relative values for the Eurasian Chess pieces, albeit with more (and uglier) fractional values included: P=1; V=1.75; B=3.5; N=3.75; C=3.75 (but just 2.75 in an endgame); R=5.5; Q=10 and K has fighting value=5. This set of values has the added point that 3Vs are now worth less than a R, though at the moment I'm feeling slightly uncomfortable with having such a relatively low value for a V, since for one thing it's possible 2V+K, or perhaps even V+K, can routinely hold a draw against B+P+K with ease (e.g. perhaps just by parking a V, if of the opposite colour of the B, on a square on its own side of the board in front of the P, and then only moving the defending K from then on). Also, is a N really worth more than 2V on average? Granted, this piece plus a V mate a lone K, unlike 3V...