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Kevin Pacey wrote on 2016-08-17 UTC

IMO in Circular Chess a Q ought to be worth more than 8 pawns, as in chess, where a Q is often considered worth 9 pawns. I'd (tentatively) put a Q at this value in Circular Chess, too. Note Q=R+B+P in value in chess, thus here meaning R+B=8, and I'll assume that applies to Circular Chess, too (a Q is often set equal to 3 minor pieces [B or N] in chess, too, but let's ignore that for now). In Circular Chess a lone R can't normally mate a lone K (but 2 Rs, or a Q, can) IMO, nor can two minor pieces mate (though N + 2Bs can) IMO, but a R and minor piece can mate IMO, so let's say for now it takes a minimum of 8 points worth of material to mate a lone Circular Chess K (not counting pawns).

If a R were supposed worth 6 (how often is it worth six pawns in an endgame? - in chess, 4 pawns often beat a rook in such), and a B or N were thus supposed worth just 2, this does not quite compute, if it is realized 3 minor pieces perhaps ought to be worth more than a R (which can't normally mate like the 3 minors may). Plus, how often is a R worth minor piece + 4Ps? Or 2Rs worth Q + minor piece + P? If a R were supposed worth 5.5 (and a minor piece thus 2.5, or still less than 3) then it is realized that 3 minor pieces would be worth less than 8, so that doesn't compute with the end of my previous paragraph. A rook could be set to a value of up to only 5.33, as one way to avoid this problem, however (another way is to suppose that, say, 7.5 points minimum are required to mate, and I prefer that, as we'll see later). IMO, a R should be worth at least 5, since a B seems generally no stronger in Circular Chess than it is in chess. Next, note IMO a N is at least as strong as a B in Circular Chess, except note that IMO 2Ns + B may at the least have more difficulty mating a lone K than 2Bs + N, so IMO a B seems to be at least as strong as a N after taking this into consideration, thus making the pieces worth equal value.

The question I've been beating around is, is a minor piece worth less than 3 pawns in Circular Chess? Under at least some circumstances IMHO in an endgame either minor piece can deal with or at least restrain 3 enemy passed pawns, if the pawns are all going in the same direction on the round board. It's similar if 2 minor pieces faced 6 passed pawns, with exactly 3 going in either direction. This is perhaps analogous to uncommon scenarios faced in chess endgames, i.e. with passed pawns on either wing, though in all cases a lot may depend on the positions of the kings. Thus I could hazard to put a minor piece (i.e. B or N) as worth 3 pawns (it's likely more than 2, anyway), and thus a R as worth 5, in Circular Chess (I'd note one of the quirks of chess is that 3 minor pieces are often somewhat better than 2 rooks, but in Circular Chess it seems IMHO the other way around). This matches the values many accept for chess pieces. That's in spite of being contrary to the wisdom of, say, wikipedia's entry for Circular Chess (which points out K + P vs. K is almost always a win, unlike chess, which IMHO makes up a little for other drawn basic endgames that would be basic mates in chess). For those who really dislike setting a minor piece equal to 3, I can suggest they try Q=R+B+P=9, say with R=5.5 and B(or N)=2.5, which is my favourite guess (without getting into uglier fractions) for what applies in an 'average' position, but perhaps this undervalues a Q. In any case, IMHO 2 minor pieces can be worth at least a R in an endgame, if all the R side's pawns are going just one direction, and the minors side's pawns going the opposite direction, unless either of the minors is unsafe, e.g. perhaps if they are widely seperated. Also note 2Rs vs. 3 safe minor pieces + 2 pawns going in the same direction may be hard for the Rs in an endgame. On the whole the wealth of considerations based on the terrain of Circular Chess makes it understandable that there is no consensus yet on the relative values of a R, the minor pieces or a Q, as wikipedia alludes to:

As in standard chess, IMO in Circular Chess a King (K) has a fighting value of 4, even though it cannot be exchanged.

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