Hi Aris
I've always thought, based on most advanced chess books I can recall, that a single bishop is worth a microscopic amount more than a single knight on average. I still find computer studies that say they are equal hard to swallow, and at least locally, John Upper agrees with me (I also heard something about Magnus Carlsen once holding up two minor pieces during a post-mortem and telling an enquiring spectator: "This is a bishop and this is a knight"). In the past one used to hear about 'Winning the Minor Exchange' when referring to taking a bishop with a knight (or as the late IM Bryon Nickoloff put it, he'd win his opponent's B). In spite of all these anecdotes, there's no real proof I can offer. GM Sambuev once told me after I gave up a B for a N that I shouldn't do so without [what he considered] a good reason, as at least it's harder to guard squares of the colour of the missing B afterwards.
I get into piece value debates/quiries now and then with a Dutch math professor named H.G. Muller on the big chess variants website I regularly go to. He's a big believer in the computer studies that he and others do, as are pretty well everyone else that goes to that website. It's his firm belief that a single B is exactly equal to a single N on 8x8 that keeps me going. . That, and his belief that the Amazon fairy piece type (piece moves like Q or N) is worth only a Q plus a N (at least on 8x8). My spider sense tells me that it must be worth more, say a pawn more (just as Q=R+B+P in most books, Amazon may =Q+N+P is my extrapolation). His case for an Archbishop (moves like B or N) supposedly being surprisingly close in value to a Q or Chancellor (moves as R or N) also seems hard to believe for me, at least on a 10x8 board as in Capablanca Chess, and certainly in the case of 10x10. On the smaller 8x8 I'm less doubtful of this (though I still am). Aside from all that, I kind of doubt the methodology of these computer studies, but my explanation would be lengthy, plus I'm not as well versed in math as opposed to chess knowledge/intuition.
Last edited by Kevin Pacey; 09-19-2018 at 07:20 PM.
Reason: Adding content
There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.
Hamlet (1.5.167-8), Hamlet to Horatio.