a bishop's worth

Actually a Knight can trap a Bishop Theodred, although it needs a small amount of aid in doing so.

I thought you could checkmate with two Knight's and a king.

You can't force the king into a checkmate with two N's + King vs. King... you can force the enemy King into checkmate with two N's + King vs. King + pawn, if the pawn is far enough from queening.  The extra pawn keeps the king from being stalemated as the mating pieces manuver to apply the checkmate. It is a difficult procedure, the situation arises rarely, and it isn't unheard of (although it is mildly embarassing) for very strong players to not know how to do it.

this site http://www.chessvideos.tv/two-knights-vs-pawn.php   has videos that will show you how to do it and an "endgame simulator" that will let you test youself.

I think everyone is saying that bishops are stronger than knights.  We seem to imply that knights need a given situation in order to really equal a bishop.  Leading to the question: Would you trade N+P for a B??

a knight in a blocked position can sometimes be as good as a queen

Hey Hammers show and prove that.

rich wrote:

The former world champion said Bishop, Rook, and Knight are equal ! Which I find very intriguing.

What? Where did a world champion or any master say that a bishop=rook=knight?

This is nonsense.

I think people should be made to tick a box when they join the site saying "I understand that a bishop and a knight are both worth 3 pawns".  If the position is totally closed and your opponent has a knight on an outpost, your bishops are still worth 3 points, and his knight is still worth 3 points.  This is called material.  The sides are materially equal.  The side with the great knights is however much better positionally than the side with the bad bishops.  To rectify this, the side with the bishops may try to exchange them for the knights.  This is to remove the positional advantage, and isnt because some piece has magically changed its material value.  The material value is like the mass of a piece.  It does not change with the position.  At the start of a game when the rook is totally hemmed in, it is still worth 5 points.  You would not trade it for even the most developed knight unless you had to.

If a game begins 1.e4 a5 2.d4 h5, we do not say that white is ahead in material because his pawns are worth more than his opponent's pawns.  The pawns are all worth 1 pawn.  White has a positional advantage.  Material is equal.

The material value is like the mass of a piece.  It does not change with the position.  At the start of a game when the rook is totally hemmed in, it is still worth 5 points.  You would not trade it for even the most developed knight unless you had to.

No Steven, I disagree, and better minds than mine disagree with you here as well. GM Andy Soltis wrote a book on this topic Rethinking the Chess Pieces, 2004, Batsford, ISBN 0-7134-8904-9.-- it's precisely about the changing valuation of pieces, and in fact one of the points he makes early on is that a hemmed in rook is very sac'able and is NOT worth 5 points in the early stages of the game. IM Jeremy Silman also discuss changing values of pieces -- he values a posted N differently depending on what rank it is posted on. He considers a N posted on the 6th rank generally to be valued at least equal to a rook.

I do understand what you're saying though... it's a bit of a semantic point... how much is a piece "worth" when it's the piece that delivers mate -- infinite? it's sort of a silly question.

Shango -- I think everyone is saying that bishops are stronger than knights -- I'm absolutely not saying that, nor are half the people here... it tells me you don't bother to read the replies to your own thread, or you don't take the time to understand them, which as a corollary tells me I've wasted my time here and I should not to bother responding in your threads in the future.

I'd say pieces have their static value (Q=9 R=5 etc) and a dynamic value, as dictated by the contours of the position. sstteevveenn's classic example of the value of a knight outpost vs a bishop that is totally hemmed in: the dynamic value at the time may show the knight being worth lots  more than the bishop.

You're both right and no doubt you know this.

As JG27Pyth plainly says, it's semantics...and because of this there may not be a shortage of people in the thread  who trip themselves and don't understand at all.

Your right steven, my pieces mass doesn't change no matter where i put them but their volume does.

(as in the area they can be in next, not exactly volume but XD)

In the nicest possible way, you're missing the point.  If something is sac-able it is by definition worth more points than the capturing piece.  It's a sacrifice.  You are gaining a positional advantage for your material sacrifice.  As soon as you introduce something artificial like changing piece values, you are massively overcomplicating the game.  We are not computers.  The knight on the 6th rank is a prime example.  How powerful it is is completely irrelevant.  If you give up your rook for the knight, you will be down in material, and if you havent got something for it, you will lose.  The knight on the 6th rank is a big positional advantage.  The knight is still worth 3 points.  A similar thing is said about pawns advancing down the board.  They become more powerful.  They do not become 'worth more points' though.  Even on the 7th, your opponent does not want to sac a rook for it.  It is just a pawn.  If he sacs a rook, he will be down in material and he will lose.  If he is forced to sac a rook for it, then the position is positionally lost. 

I think really we agree, at least in principle.  Maybe I should give an example.  Lets say someone has a mass of 100kg, and their opponent has a box that can withstand 981N of force.  The man is like say a knight, and the box is like a bishop.  They are equal.  Now, change the position a bit, say, take them somewhere with the gravity of jupiter say, the mass of the box and the man are the same, but now, the box is positionally lost, the man will crush it, because his weight has increased.  The man has not changed his mass.  He has just gained a favourable position. 

What's more, I'm certain that these people do not calculate material any differently.  They are merely trying to illustrate how the power of a piece may change.  But this is what we all know to be position.  Nobody assigns new values to pieces as they move around the board, except perhaps in very extreme circumstances such as a totally dead, and never coming back, bishop.  They simply evaluate the position.  They have 'more active pieces'.  The reason better placed pieces are "worth more" in an artificial sense, is that you can often trade them to 'win material'.  You can cash in your positional advantage for a decisive material one that is less likely to disappear.  If you have artificially introduced some on the fly values, you would never make this trade.  You could trade your knight for a rook, and not win material.  Ludicrous!  I'm still not saying you would make this trade every time.  But if you did make this trade, you would always win material.  This is why when we speak of material, we should always talk about the 'mass' of a piece, and not the 'weight'.  Other things are already covered in our positional assessment.  Material is material.  If we're so good we can calulate everything as we go in just one number, why give them these material values at all, we can just look at the board and assign a value to the position just like a computer.

I was aware of silman talking about this actually, and it really gets on my nerves how he is clearly very knowledgeable but can talk such utter nonsense.  His system, is seemingly just another example of something that might sound nice but that takes something that works and strips it of all practical purpose.  I hope it is simply a bit of a careless way of trying to get people to think about the positioning of their pieces.  Really this is a problem of having 2 different values for the pieces.  Yes a knight on the edge of the board is worth less to the position than the knight in the centre, but it still has a fixed material value of 3.  Perhaps you will understand why this annoys me, if you think of a physics professor getting confused between mass and weight of an object and then passing that confusion on to others.  All of a sudden crazy things start happening, and none of the calculations in physics works anymore because everyone is putting the weights into the equations rather than the masses. 

I think goldenrod expresses it very succinctly:

"I'd say pieces have their static value (Q=9 R=5 etc) and a dynamic value."

Taking Steven's metaphor: Static value = mass  Dynamic value = weight (as determined by the gravity of the situation *chortle guffaw self-satisfied chuckle*)

If we're so good we can calulate everything as we go in just one number, why give them these material values at all, we can just look at the board and assign a value to the position just like a computer -- well, yes, precisely, that is exactly what Rybka et. al do -- and they didn't program themselves. Humans devised this way of looking at things, and it works rather well if Rybka's ELO is to be believed. I don't know how topalov or kramnik evaluate pieces, but I'll bet it's got a dynamic component.

Well, this was my point- that only a computer could calculate like this, and if it did, it would have to not calculate anything positionally because then it would be calculating the positional stuff twice.  It is perhaps a nice idea to have dynamic values, but the material value should always be the constant one because none of us is a computer.  The dynamic value should be nothing more than a curiosity.  It serves no practical purpose.  After deciding the material is equal, we look at the position, and simply evaluate that our bishop is better than his knight, or whatever, so we try usually to avoid trades, unless by avoiding a trade, we have to make our bishop worse than his knight, etc.  It is worth knowing if you dont have the experience, that a knight on a good outpost is very powerful, say like a rook, but it's no better than the confused physicists to actually give it this value in your calculations. 

Well... I agree with you right up to the very end. As long as you are talking "practical" chess, I agree... and I look at things exactly as you say... I think of the "real" (mass) material value and look at the dynamics of the situation without calculating specific dynamic values, rather I just say: ok my knight is good here, or his bishop is 'bad' etc.  Ok. So we agree there, but philosophically, I depart at your final sentence:

...but it's no better than the confused physicists to actually give it this value in your calculations.

Disagree completely.  The confused physicist is plain wrong... he's made a garble of weight and mass, his results will not make sense, his students will make idiots of themselves. This is NOT analogous to a chess player making dynamic evaluations. Those are merely impractical.

The mass = static value metaphor breaks down -- Mass is real, it is an intrinsic property of matter. Static value of chess pieces is NOT real. The static value is an abstraction thrust upon the chess piece to help us dim-witted humans get a handle on things -- but intrinsically chess pieces have NO static value. Nowhere in the rules of chess does it say a N is 3 points but a Rook is 5... no points of any kind exist in the rules of chess, and in chess terms pieces do not have any static existence. (How many points is a N valued when it's in the box between games?)  On the contrary the only real value a piece has is it's dynamic value -- it may be impractical to calculate it, but it is the real value.

Perhaps the better metaphor for static and dynamic value is Newtonian vs. Relativistic physics. If I ask you the time, I ask you for the time in your frame of reference, trusting it will apply to my frame of reference. That is practical... but if I wanted the most accurate time possible, I'd need to calculate the difference in our frames of reference -- done correctly this produces a better result, NOT a confused wrong-headed result.

No the analogy works fine, but perhaps you didnt quite get what I meant by it.  Whether the pieces have a real value or not is irrelevant.  It's just an analogy.  It's no more relevant than whether the masses making up the universe are part of some godly game.  The whole point of the analogy, is that if you plug in the 'weight' values into "shall I make a trade" equations for example, you will often come to stupid conclusions.  Often, you will get your knight onto a strong outpost, and it will be a big enough positional advantage to win a pawn.  But you wont make the trade of piece for piece and pawn because you have used the wrong value, and think you have a rook's worth of material.  You may be left without a plan, and may end up losing.

Mass is likely to be equally irrelevant as it happens and is no more fundamental to the objects of the universe than the value of the pieces is to them.  It is simply something we have observed.  This particle has mass x etc.  We dont yet know why, although it will be interesting to see what the LHC turns up.  The value of the pieces has to do with how they move on a chess board.  The value of the mass of a particle probably has to do with how it interacts with the Higgs field.  If we were gods, perhaps we could look at every single interaction in the universe and we would no longer need to worry about such clumsy notions as mass.  However, this is irrelevant. 

Relativity is another excellent example that can be compared to the values of the chess pieces.  When you ask what the mass of a particle is, you get a value depending on the particle.  When you speed the particle up, it is as if it has a higher mass, greater than its rest mass.  But if you start treating this relativistic mass as the real mass, then you're going to have some problems, because really it is just the rest mass, and some kinetic energy, just as a knight on the outpost, is its material value, and some positional value. 

As an example of how things can go wrong by introducing unnecessary additives, you need look no further than "centrifugal force."  If you are swinging something around on a piece of string, with the tension in the string acting as the centripetal force keeping the object from flying off, and for some bizarre reason you decide to invent a centrifugal force to balance this, with the idea that it's somehow keeping the object from being pulled inwards by the centripetal force, you might find you are much happier that your string system now works, but in reality you have just destroyed your understanding of the rest of the universe because Newton's first law of motion now doesnt hold true, according to which your object on the end of the string, should be moving tangentially to the circle, because the forces now balance.  In essence you have counted something twice because you have just made up this centrifugal force out of nowhere and added it to the natural tendency of the object on the end of the string, and it's lead you to the wrong conclusion, that the object should be moving in a straight line, whereas you can see it moving around in a circle.  Or to put it another way, you now have an object circling for no apparent reason!  What happens if the need arises to cut the string?  Now you're in trouble, because now you have a centrifugal force, and no centripetal force to balance it!  Your improved centrifugal force system is now going to tell you that your object is going to accelerate off some other way, whereas what really happens is now is when it's going to move tangentially.  The ony way for your made up system to make sense is if you come to the decision to scrap the thing you arbitrarily introduced in the first place, which prompts the question "why introduce it in the first place?"

@ JG27Pyth: You wrote: 3 points for a B or N, is remarkably accurate...of course this value can change.  You also wrote: You can't force a king into a checkmate with two N's + K--v--K...you can force the enemy king into a checkmate with two knights + King + pawn, if the pawn is far enough from queening.

Aren't you saying right here in your own great words that the knight or knights need help?!  And not to mention some assisting situation. 

And if it wasn't an intriguing question, I wouldn't have so many competent minds lending thought.  I asked this question because in my decisions I feel the bishop is nearly as powerful as the rook and half the value of the queen.  It may be foolish; but it is an idea, and I am myself when I play.

um, how many times has anyone faced a knight, knight, king vs. king? i think the real value of a queen is it's ability to manuever through diagnals and files, so it gets 1 more pawn for maunuvearability (bishop 3 + rook 5 + queen mauneuveerability 1)

and in the opening phase, the  knight and bishops arealmost more than a rook, but if your playing against a stronger player and your down a rook in the opening, he knows to make it the endgame before you know it!

Well, chess is a complicated game.  Two knights by themselves are not enough to checkmate.  This is just how chess is, and is another thing you need to remember.  A really bad bishop, or 'tall pawn' will be far worse than a knight.  So just as you need to remember not to leave yourself with 2 knights against a bare king, you also need to remember not to get your bishop badly jammed up.  There are many other examples in chess endgames that refute your line of reasoning.  If you are left with a pawn on the 7th rank supported by your king, and your opponent has just queened and it's his move, it turns out, that the best pawns to have are rook pawns or bishop pawns.  With these you will draw, with all others you will lose.  So in this position these pawns are better than other pawns.  The rook pawn is better than a centre pawn in these positions.  This doesn't however make these pawns better in other positions.  In other endgames you may find you cant win specifically because you have a rook pawn.