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David Paulowich wrote on 2011-04-18 UTC

Ralph Betza wrote: 'The Chancellor is roughly equivalent to the Queen even though the ideal value of N is presumably less than Bishop: the Bishop is colorbound and its practical value is ever so slightly more than a Knight, combining it with R removes the colorboundness, and therefore is a classical case of 'combining pieces to mask their weaknesses and thus allow their practical values to be fully expressed'; and therefore one might expect the Q to be worth notably more than the Chancellor.'

'One hypothesis about why the Chancellor does so well is that the R has a weakness that is masked when N is added to form Chancellor. This weakness would be its relative slowness and difficulty of development, and perhaps its lack of forwardness (it has only one forwards direction).'

P=100, N=300, B=300, R=500, C=850, Q=900 are my preferred values on 8x8 boards. Sometimes I like to say that the value of a Bishop is 5/8 times that of a Rook on any square board, which would bump the Bishop up to 312.5 points here (an insignificant change, which does not affect my strategy when playing FIDE chess). Back in the 1990s I used to debate the relative values of Queen and Chancellor with Betza. Years later I came up with a way to compare these two pieces indirectly, by introducing some new pieces. The 'Elephant' moves like a Ferz or an Alfil, and is worth 50 points less than a Bishop (I believe Joe Joyce agrees with me on that). The 'Grand Rook' moves like a Rook or an Elephant, and is worth 50 points less than a Queen (I am casting my solitary vote for that value). The Grand Rook and the Chancellor are similar enough in design that I would expect them to have the same value on any square board.

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