Knight Pairs and Bishop Pairs

I always hear talk that losing a Bishop pair is costly because they work so well in tandem. Makes sense. They cover different colors and criss-cross. Some chess authors assign the pair extra value.

Why do I never hear of a benefit of having a pair of Knights, or the cost associated with losing a Knight-pair? Can't they work well in tandem too? Seems to me they can.

Also, where do I learn how to use Bishops in tandem and Knights in tandem?

It is an empirical fact that having a material imbalance of a single Knight versus a single Bishop is almost perfect equality (both sides win equally often), while with a pair of Knights vs a Pair of Bishops the Bishops win much more frequently. But when you then handicap them by an extra Pawn, the score reverses, and NNPx beat BBx about as often as BBx beats NNx. In general, for any imbalance where one side has one Bishop and the other side has none, the score of the Bishop's side improves when giving both sides an extra Bishop (so that the one originally already having a Bishop now has a pair), by about half as much as when you give him an extra Pawn. No such effect is observed for Knights.

So empirically, a Bishop pair turns out to be worth half a Pawn more than the sum of its components.

Now one could of course try to rationalize this empirical fact by all kind of arguments. Just as one can rationalize that a Bishop is worth less than a Rook, by the maximum or average number of squares they can attack, the fact that the Bishop is color bound and the Rook is not, or that the Rook can force mate on a bare King, and the Bishop can not. Such arguments are risky, as they are difficult to quantify, and are often completely wrong, no matter how reasonable they sound.

A rationalization of the value of the B-pair bonus would be to see it instead as a single-B penalty: Setting B=3 and pair bonus=0.5 is equivalent to setting B=3.5, and single-B penalty=0.5. As long as you only have 0, 1 or 2 Bishops. The penalty is more easy to rationalize by the color binding: it obviously is a disadvantage that you cannot exert influence on half the squares, which gives the opponent the opportunity to set up a defence on that color. For a Knight you would not have that.

Note, however, that 7 Knights have the upper hand over 3 Queens.

Its quite interesting.  sometimes you hear authors saying as soon as there is a disparity between minor pieces, one side has the advantage of two bishops, but its not always the case.  The position needs to be open or capable of being opened for two bishops to have any kind of advantage.

If you manage that then two bishops can be very effective in supporting heavy pieces on an attack on the king, they can be used to infiltrate weak squares, provoke pawn weakness etc etc

http://www.chess.com/blog/robbie_1969/chess-strategy-advantage-of-two-bishops

Well first, I'm going to suggest a wonderful book all about piece imbalances called "Rethinking the Chess Pieces" by Andrew Soltis.  This will deffinately answer your question far better than any of us.

But to give some of an answer to your question.  Bishops are generally considered better than knights becuse of thier range and scope.  they can simply control more of the board than knights, making them faster.  Naturally if you have the bishop pair you can then control the whole board with them.

Knights on the other hand, are sneaky little batards and are the only piece that doesn't require a straight line to attack.  You can't block them by putting a pawn in the way of their line: file, diagonal, or rank.  You have to control their movement squares so they can't reach certain parts of the board.  Because of the way they move, two knights generally don't work well together.  The Litmus test for this is the fact that two knights CANNOT checkmate the king by themselves.  It is just physically impossible.   Now, there are ways that they can work in tandum, such as if you have two knights on the same rank, or file they will cover four consecutive squares.  But that's about it.  The knight's real advantage is the fact that they jump from one color to another, so you don't need two knights to cover the whole board like you do with bishops.  Thus they are redundant, and therefore you don't need both.  This is why you often see masters trying to trade one of their knights for a bishop so that you get rid of the redundancy of your pieces, and weaken your opponent by denying him the bishop pair.  this is one of the things talked about in Rethinking the Chess Pieces.  You also see this theme in the openings of the Nimzo Indian and the Berlin Defense of the Ruy Lopez.  In these openings, the knight is pinned by the enemy bishop.  You don't do anything about it and you let the bishop take the knight.  Their compensation is the doubled pawns which result, and your compensation is the removal of redundancy and the claiming of the bishop pair.

Now that mosf of the above is general principle.   All of this changes and depends once you factor in the pawn structure.  If the center is open, or there are few pawns on diagonals, then you have great scope for your bishops.  However, if you are able to close the center, and block those diagonals by creating color complexes, then you have really neutralized the mobile advantage fo the bishops and the knights rule supreme because they can get around those pawns, and they really love outposts.  Now this depends on a lot of factors, but as i said it is mainly dependent on the pawn structure.

Silman says that the battle between Minor Pieces is a major part of the game.  it's one of the Imbalances in his system which he talks about in the Amateur's Mind and How to Reassess Your Chess.

Hope this helps.

That all makes sense. Thanks.

The only part that was new to me was that Knights may actually JUMP OVER other pieces. That's great to know.

Just teasing. Thanks for info. Actually, robbie, it was your post above that is in your blog that promted me to ask this question.

A good argument for the knight pair is Lasker-Chigorin, Hastings 1895. Look it up, it's very instructive.

Bishop and knight mates are *the* most difficult of the basic (piece-only) mates: that's common knowledge and there's no arguing that. The reason bishops and knights don't work together well is due to their mismatched lines of force (https://www.youtube.com/watch?v=hWwuy-aiK1M). The only place where I've seen anything hinted about knights working well with *any* other piece is in mates with knight and queen, where one book mentioned those two pieces work well together.

So in answer to your question, I believe that knights don't work well in tandem, not with each other, and not with any other piece. (I'll have to take a look at Soltis' book that Senchean mentioned above, though--sounds interesting.)

----------

(p. 109)
Bishop and rook: Morphy's Mate

The final mating pattern presented here involves the rook and bishop. The two
pieces complement one another because the rook controls files and ranks while
the bishop controls diagonals. It takes time for most of us to develop a sense for
which pieces work well together and which ones don't (queen and knight do,
bishop and knight don't, for example), but one of the keys to chess mastery is
understanding this relationship between pieces. Morphy's mate is an example
of the bishop and rook working well together.

Eade, James. 1996. Chess For Dummies. Foster City, CA: IDG Books Worldwide, Inc.

Thanks, JMB. Here's a link to where you can play through that game...

http://www.chessgames.com/perl/chessgame?gid=1036398

That *is* a pretty instructive game, though Black's success looked mostly to me to be that he restricted White's bishops with Black's pawn structures, which made the knights more valuable in such a locked position. I didn't read the comments on the game yet, though.

2 bishops vs 1 knight is a win

2 knights vs nothing is a draw

Spassky often seemed to prefer knights to bishops and he has won many games with the knight(s) . 

I have read that some GMs consider Knights to be more valuable than Bishops (not just in a very closed game) and harder to play against. Although the empirical data may show a Bishop-pair to have more value than a Knight-pair, that is on average over a large sample size. I would imagine that one could become exceptionally skilled at using Knights in tandem, but I'm guessing at this.

That Lasker game is interesting. I note that in Lasker's Manual of Chess, Chigorin games are mentioned many times...however, that Knight game seems to have been inadvertantly left out by Lasker. ;)

Bishops are better in most games because of their space and wonderful pair. Knights are useful as well but I haven't seen it as much as bishops. Just my two cents.

http://www.chess.com/forum/view/daily-puzzles/1222015---gessner-vs-whitaker-chicago-1916

This daily puzzle is a great example of the knights working together and a knight sacrifice.  Plus it speaks to the whole idea of how knights are able to attack around defenses.

Ah, so when the board is full of pawns, the pawn structure is locked and looks like swiss cheese, then the knights are good eh?

There are moments in a game where you can show your style, but after those moments pass, and the logic is locked in, the player who better meets the needs of the position is superior. Certain players may often choose a certain way when they have a choice, but when there is no choice they don't hesitate. Shirov would grind you down in a winning endgame and Leko would hit you with a sacrificial mid game attack.

Spassky would sac his knights and Fischer would sac his bishops, etc.

Thinking about it in terms of being good with bishops or knights is incorrect IMO. It's being good at chess that counts.

Hi Chicken_monster, I will be doing a 'how to play gainst the two bishops', in next video - and as someone mentioned the Lasker v Chigorin game of Hastings will be one of the games reviewd as awell as a Smyslov v Euwe, 1946 :D

The game is instructive but it contains a lot of errors by todays standards.

Looking forward. I have you on track. Thanks.

You make some good points about there being moments to show style and having a choice.  I also agree about there being a point when the logic sets in.  And even the fact that being good at chess is what counts.  But the thread isn't about being better at knights OVER bishops, its more about having a proper understanding of them, and how they relate to each other within the position.  If it helps someone improve their knight or bishop play great.  But that improvement also helps there over chess ability.