Wikipedia's entry on relative values of the chess pieces

[Kevin Pacey]

Here's the wiki on relative values of the chess pieces. Many different ones are suggested, as can be seen from the large table given at one point. It may be surprising for experienced players just how often a single bishop is rated as equal to a single knight on average; computer studies have led at least some authorities to believe that this is in fact true:

https://en.wikipedia.org/wiki/Chess_piece_relative_value

[Aris Marghetis]

Here's the wiki on relative values of the chess pieces. Many different ones are suggested, as can be seen from the large table given at one point. It may be surprising for experienced players just how often a single bishop is rated as equal to a single knight on average; computer studies have led at least some authorities to believe that this is in fact true:

https://en.wikipedia.org/wiki/Chess_piece_relative_value

Hello Kevin, from the way you wrote that, it seems that you feel a single bishop is NOT equal to a single knight. Assuming I read that right, how WOULD you compare them?

Thanks and regards, Aris.

[Kevin Pacey]

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.

[Aris Marghetis]

Thanks for the reply. Similarly many years ago, I believe at the Richmond Canadian Open, a GM told me at the bar something similar to what Sambuev had told you.

[Egidijus Zeromskis]

a single bishop is NOT equal to a single knight.

Parham Maghsoodloo (the current U20 champion) without a hesitation told that his favorite piece was a knight. When he has them on the board he finds easy ways to win :)
https://www.youtube.com/watch?v=kCKnPwGkgtQ
~13 min

On other hand one on one, a bishop should be stronger, it can trap the knight :)

3n4/8/8/3B4/8/8/8/8 w - - 0 1

(has a FEN stopped working?)

[Kevin Pacey]

...
(has a FEN stopped working?)

Repairs to the FEN possibly still pending, in case you missed the following thread:

http://www.chesscanada.info/forum/showthread.php?2808-Chesscanada-info-now-supports-PGN-files!&p=29484#post29484

[Kevin Pacey]

Most chess players who generally prefer a knight to a bishop either belong to history now (e.g. Chigorin, Sultan Khan), or they aren't really very strong players IMHO.

[Kevin Pacey]

...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....
To try to be clearer about this, I'd say it's since a knight takes at least two moves to cover a square of the same colour it wasn't already, whereas a B might often take only one move to do so.

[Kevin Pacey]

Here's one link re: a GM Larry Kaufman statistical study on material imbalances that concludes, among other things, that a single bishop is worth a single knight on average. I think something must be amiss for such a conclusion to have arisen. For one thing, the study involved looking at many games of 2300+ level players vs. 2300+ level players, meaning that at least some were with non-GMs conducting one side or the other of the (perhaps not always close to perfect) games played. This is apparently also where Kaufman's own chess piece values came from later on, as given within the Wikipedia link I gave with my first post of this thread:

https://www.danheisman.com/evaluation-of-material-imbalances.html