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Kevin Pacey wrote on Tue, Oct 31, 2017 11:09 PM UTC:

Comparing a wazir and ferz in the context of a chesslike game with pawns promoting to some decisive piece type (such as a queen) is an interesting exercise. For comparing two non-compound piece types previously, namely a bishop and a knight, I noted that they each have 3 advantages (and thus also disadvantages) respectively compared to one another, so that they ought to be close in value (each worth at least 3 pawns, as either often restrains 3 pawns in an ending). Namely a bishop is colour-bound, does not leap and moves in half the directions of a knight, but the disadvantages of a knight are that a bishop reaches more squares on an empty board on average, is both a long and short-range piece and it can influence both sides of the board in widely seperated sectors at times. Perhaps e.g. the diminishing of importance of a knight's leaping power's worth in many open board endgames might give the bishop a microscopic edge on average?!

Looking at wazirs and ferz' in a somewhat similar manner, a ferz is colour-bound but a wazir reaches less valuable (i.e. non-forward) directions more often than the former. That is, if we number forward directions as worth 2 and sideways and backward directions as worth 1, we see that the sum of the value of the wazir's 4 directions equals 2+1+1+1=5 while the the sum of the value of the ferz' directions equals 2+2+1+1=6, or slightly more than the wazir's sum. So, one advantage and disadvantage each so far for these two piece types.

Next, how do they compare in stopping or capturing chess-like pawns? Well, a ferz would normally not be able to capture a pawn in front of it (short of being aided by zugzwang), but note it will naturally stop it in a one on one battle, plus at times restrain the advance of a pawn on a neighbouring file, too (sometimes it will not, if the pawn pair may start as a phalanx). This may even suggest a ferz is worth (1+2)/2=1.5 pawns on average, at least in terms of restraining power. Now, how does a wazir stack up? A wazir can surely destroy a pawn in front of it, in a one on one battle. However it seldom even restrains two connected passed pawns; it may win one of them, but then the surviving neighbour will race ahead and unstoppably promote. So, a wazir is worth less than 2 pawns this suggests, but also that it's worth more than one pawn. Why not suppose it's 1.5 pawns, too? We do already know a wazir and a ferz already each have one advantage going for them over the other, from the last paragraph. Well, such ways of sizing up the values of piece types may seem like virtually guesswork, but at least I was pleasantly surprised to see that Ralph Betza in a CV Piece Article which alluded to his Chess with Different Armies variant gave the wazir and ferz as each having 'ideally' the same value as half a knight (not absolutely sure if this means these pieces should thus be theoretically entirely equal in value). I seem to recall this hasn't been the first time I've finished up weighing piece type attributes and apparently agreed with Mr. Betza's valuations (in this particular case I'm assuming a knight is worth 3 according to him, while I put it at Euwe's 3.5, however), though I've put less thought into such as a rule.

I would note that whether or not we suppose a ferz is worth 1.5 and a wazir the same (or even close), the compound of these two pieces is a guard. My primative way of evaluating a compound piece is to often just add a pawn's value to the sum of their values, so Guard=Ferz+Wazir+Pawn=1.5+1.5+1=4, which is (even if somewhat surprisingly) the fighting value a King was thought to have on chess' 8x8 board by a number of old-school chess greats including World Champion Lasker. If we take a Guard as worth 3.2 instead (as per computer study), and place a wazir at the low value of 1.25, that still doesn't give too much of a bonus for the compound of these two piece types in the form of the Guard, that is the bonus for compounding would be only 0.45, which somewhat surprises me, somehow.

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