Author Topic: How to Compute the Value of Chess Pieces on Boards of any size  (Read 143 times)

GothicChessInventor

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I have become extremely skeptical of any method that tries to calculate the value of pieces ab initio, i.e. using nothing but their move pattern. Because even though these usually work for the orthodox Chess pieces, (they are of course constructed that way, and never see the light of day when they fail there), they often give completely wrong values (like 1-2 Pawns off) for unorthodox pieces.

Remember it was the mathematical framework of Taylor in 1876 that gave us the initial piece weights using something other than a subjective method. Recall going from "0" to "1" is a rate of change of "infinity," but going from "1" to "2" is merely a doubling, "2" to "3" even less, etc. So Taylor gave us something to work with, while previously we had nothing!

Once the basis was established, refinements via human tuning happen much more efficiently.

Using this method, I get an amazingly high value for the Archbishop, much higher than anyone ever suspected.

Capablanca was the first source I encountered (in Edward Lasker's "The Adventure of Chess") that thought the Archbishop was as powerful as a Queen, but he held the same view of the Chancellor. I likewise believe the Archbishop is extremely undervalued and the Chancellor over-valued. The Chancellor is effectively a Rook for most of the game and must be used as sparingly. At best it is first functionally useful in the late middlegame, although it can be initially deployed in the early middlegame to make a veiled threat or two or add an extra layer of protection to an attack against its own king. However, there is some inflection point where the Chancellor transitions from Rook-ish to deadly, especially if the opponent has no Chancellor of his own and his King is in flight. The Archbishop is agile and nimble, able to dart in and out, and in the endgame it can inflict the deadly solo-checkmate.

I believe the solo-checkmate feature of the Archbishop is what gives it the mysterious extra value that is so hard to categorize. Even with it's high rate of exchange, there is no piece worth "Mate in X" if that X is the result of a forcing combination that cannot be avoided!
« Last Edit: January 23, 2018, 03:45:19 pm by GothicChessInventor »

HGMuller

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Indeed, when watching Gothic Chess bullet games between computers, it is striking how active the Archbishop is. It flashes back and forth, doing damage gere, and then there. It seems especially good at destroying Pawn chains.

I really think this piece should have been called 'Dancer'. Its movement patterns are like no other piece I have ever seen.