Theory: Piece Value

This thread is for discussion of the first theory bit on piece values.

I was a bit annoyed that they simply dump a table of relative values on us. On the positive side, I've looked up their claims in the key sources, and they are basically right. The key places to verify what they are saying is Kaufman's classic article The evaluation of material imbalances and Soltis' book 'Rethinking the Chess Pieces.' The latter is quite good with lots of historical analysis and quotes that are very fun.

In a nice review of Soltis' book at Amazon, one reader had some great insights:

The central point in RETHINKING THE PIECES is that you win chess games by making your pieces worth more than your opponent's pieces. Everyone gets that idea. But how do you do that? Soltis tries to answer this question thoroughly, giving plenty of clear examples of his points.

Soltis argues that your pieces are worth more than their normal value when they achieve great mobility, when they have ready targets, and when they coordinate their actions. Conversely, your pieces become worth less than their normal value when they lose mobility, when they lack targets, and when they fail to work together.

Soltis also maintains that your pieces are worth less than their normal values when they suffer from a change in board range and from redundancy. These ideas are certainly not that hard to grasp.

This quote helps explain the discrepancy between opening/middlegame values and endgame values for Bishops and Knights. As pawns are removed from the board, Bishops increase in strength because their mobility increases. This is especially true if there are pawns on both sides of the board, as their great range compared to Knights is helpful. On the other hand, if all the pawns are clustered in one area, the Knight can be more powerful than the Bishop, even in an endgame.

Soltis goes over many such things. I frankly have only superficially looked over the book.

One thing that worries me is that this material in ICS is too advanced for me. Not that I don't understand it, but it won't help me that much. I still lose games because I drop pieces to simple 1-3 move tactics. All this subtle crap about Knights versus Bishops and the two Bishop advantage is of no use if I'm down a piece.

I'm hoping that the tactics lessons, and my independent working on tactics puzzles, will help with my gross tactical retardation.

What i like in the piece value theory pdf, they talk about some material imbalances and equivalences and the first game to study (Kramnik-Topalov) is dealing with 2R+P vs R+2N which nowhere appear in the course. LOL.

Moreover why is it, we have to consider (2R+P vs R+2N) and not (2R+B+P vs R+B+2N) or even (R+P vs 2N) considering that R & B are present on both sides ?

Anyway their explanations and games comments are good and clear.

Hey Hanging King, they don't mention the bishops because both sides have one so its not relevant to the assessment of material imbalance.

It's like on the playchess server they don't list all captured pieces but only display the material imbalance so if you exchange a pair of knights and a couple pawns each nothing will show on the captured piece as your material is identical but if you trade bishop for knight they will show as they represent a material imbalance.

I really like that way of doing things, helps you focus on the true differences in the position.

It's the same here, the imbalance in the position is 2R + P vs R +2N.

As both sides have bishops they don't represent part of the imbalance of the position and so including them in the evalution confuses the issue.

I am still having a headache of trying to fully grasp why we must learn that table. Nobody can cram that all in his head or remember it for the rest of his/her life.

So i wonder, did you all try to get this table into your head or did you just took it as information?

I agree chesstiger, it is a bit much all in one table.

I found the discussion of the strength of Bishops relative to Knights in the endgame helpful (the stuff on the first page). The table I frankly don't find all that helpful. Soltis spends an entire book on such stuff (Rethinking the chess pieces), and I spent one night comparing what he said to what they say. Basically they both agree, which is good.

However, without more examples, explanation, principles, it is a fairly useless table, and I'm not sure if they make much use of it.

It depends, for example if you take the R+P vs B+N it is a very common case.

For example light bishop is threatening f7, sustained by knight on g5, when black king is castled. Can the white exchange in f7, gaining a pawn and a rook for a bishop and a knight ? The answer is NO according to the table.

I guess we can find examples for other occurences in the tables, that appear in commonly encountered situations on the board. and this is what we have to remember, in my opinion.

Remember this is only the first month BDK. It doesn't matter if you don't understand the table right away, and they are going to spend the next 13 explaining everything to us.

Think of it like joining science class. If on day one of your first chemistry class as part of your notes they gave you a copy of the periodic table you wouldn't be expected to understand it all, and they wouldn't be expected to explain it you in great detail. It's just an impotant piece of information to file away and it will be of practical use later on throughout the course, no need to get annoyed about them dumping it on you on day one!


Also it should be stressed that the first month of this course we learnt the thinking method in chess which can be outlined as firstly, a proper evaluation of the position, and secondly an effective analysis of that evalution with a subsequent plan.

The thinking method and positional evaluation lectures are actually what the entire course is about. The first thing we need to evaluate when thinking about the position is king safety, and thus that is the main subject of month two.

If you look at the position of material equality table, that is an outline of the entire course right there, king safety and the next nine months are are all about teaching us the positional knowledge necessary to best make those evaluations.

Then once we have fully understood the key positional factors and concepts the remaining four months is going to be an extensive analysis of hundreds of positions where use the knowledge we have learnt to put the thinking method into practice.

What I mean is, that month 1 is just an overview of the whole.

So don't worry about anything you don't understand in month 1 because the next 12 months are all about going into detail each part that makes up that whole.

If we stick with it over the entire course (I wont say a year because I think this will take at least two to actually finish) by the end I'd certainly expect to be rated over 2000 at least, I think the course has the potential to be that good.

Just bear in mind that we won't understand everything fully straight away, patience and persistance are the key elements here!

Bilbo: very interesting take on the course, and what is going on in the first month. Excellent post, thanks for taking the time to write it!

Yes, thanks, Bilbo. The idea that I had to have that table memorized immediately was scaring me, too!

I think the main points to keep in mind are that knights get weaker in the endgame relative to bishops and major pieces, bishops get stronger in the endgame relative to knights and pawns get stronger in the endgame as more pieces disappear from the board and it becomes easier to promote them.

That seemed to be the gist of it, but of course, the table is more precise than these generalized rules.

I am amazed that noone yet took the following example:
1R=1B+1P ("=" as relative equal in both of the lines)
1R=1N+2P
both on endgames.

I came to conclusion that this part of the table would be wrongly done. I doubt that generally Bishop is about 1 pawn valuable than Knight on endgame. According to piece value table if the material is even on endgame and you trade your N plus 1 pawn to B the material would be still balanced. At least this is the way I interpret it.

And of course like in ICS material this is about positions where may be many other pieces as well. For example 1Q or R+3 pawns on both sides and the generally N+1P=B.

If the table is general values, it should be very precise, because otherwise it may cause many mistakes. Of course in chess it always depends on the position...

I just think that the difference in B and N on endgame would be more like half pawn than full pawn. I would be happy if someone could explain this to me. Are other titled players, especially IMs and GMs agreeing on this N+P=B on endgame?

-Jari

I don't think you can simplify the equations like this.
X=Y and X=Z doesn't mean that Y=Z in the endgame.

What they say is that X can be kept in respect with Y and also with Z. But that doesn't mean that Y and Z are equivalent against another piece than X.

So here against a rook, the bishop has a slight advantage because it has a long ray of action, and a bishop protected by 1 pawn is untakable by a rook, because of reciprocal protection (bishop protects the pawn, and pawn protects the bishop).

For the knight to achieve the same thing is more complicated, because there is no such reciprocity, and an additionnal pawn will be required.

That's how i see it.

Very well thought Hangingking, I think you are completely correct. A bishop and pawn could well hold out against a rook because of the reason you gave whereas its impossible for a knight to both defend and be defended by a pawn, thus the rook can always attack one of them.

Sounds like Rock paper scissors to me

I was just starting reading "The Piece Value" and I found a contradiction:

"During opening and middlegame, we have a set of values and, during the endgame, we have another set. This is because during the endgame, the ROOK, the BISHOP and the PAWN change their values. All the above 3 pieces increase in value, especially the pawn."

So far so good, then a small table comes stating that a Bishop is worth more than 3 pawns in opening/middlegame and then relative equal to 3 pawns in the endgame.

Is just me that needs a good knight of sleep, or was this a contradiction? First it states that the bishop increase the value in the endgame, then the table states otherwise.

Pawns increase their value more than Bishops do, that's why a Bishop is equal to 3 pawns in the endgame. Just read again the last sentence of the ICS quote: All the above 3 pieces increase in value, especially the pawn.

Thanks Tweety, that explains everything

The same is said about the rook.

It does seem somewhat contradictory. The conundrum is comparing these pieces to pawns, which, as was stated, increase most in value as the game goes on.

So in the endgame, a pawn is worth more, so being relatively equal to 3 ENDGAME pawns is probably more value than 3½ OPENING/MIDDLEGAME pawns.

What the table should do is compare everything to something constant, perhaps points.

I've just done this lesson and had the same initial reaction and then looked for a way to simplify it (and not try to learn the table by rote).  As BorgQueen suggests, I looked for a "common currency" (points or whatever) to make sense of it...then I gave up when I realised that actually if you use the good old N=3, B=3, R=5, Q=9 stuff, and add in that B is a bit stronger than N, and B,R and especially P get stronger in endgame, then you get pretty close.  The deviation is less than 1P and the Qualitative factors of the position could easily create swings bigger than this.  This seems to be aligned to the ethos of the course materials which seem to teach that positions are assessed in terms of both Quantity and Quality (see making decisions in chess), and imply that Qualitative factors are perhaps even more important.
My problem is that I am so materialistic, that I don't have the courage to go into positions where I have a "Quantitative disadvantage" (e.g. B+P vs R) even though I have Qualitative positional compensation.  I guess its yet another thing to practice
Cheers
Jazzmouse

I thought the whole point of the Piece Value article was to say that piece value is relative to a variety of factors.  

We all know the traditional Piece Value, the one they associate with the Opening and MiddleGame:

P = 1
N = 3 1/2
B = 3 1/2
R = 5
Q = 9

But they say that long-range pieces gain piece value during the endgame, so given the chart and equivalences, I worked out another (rough) assignment of values for the endgame

P = 1 1/2
N = 3
B = 4
R = 5/12
Q = 10

This should just about satisfy all the equivalences and inequalities in the chart.  

But, again, 'the endgame' is just one rough factor.  Another will be which other pieces you have remaining.  Take for example their "play coordinating piece", either a rook or queen, which is said to be nearly essential for the weaker side to coordinate his defense and attacks.  Generally, you wouldn't want to give up a rook (5 1/2) for a bishop + pawn (5 1/2) in the endgame if you're the weaker side because you'd lose the special 'coordinating' feature of a major piece.  So, all things are not equal despite PME (Positions with Material Equivalence).  

We all want an easy formula -- hence we come up with rough piece value assignments -- but chess is more complicated than that and so we have to understand in which situations each piece is more or less valuable.  We can then determine its value given these principles, and not rely on inaccurate charts.  In other words, we have to learn to read positions and then know which pieces are better suited for our plans in such positions.

I was looking over this table again and I forgot why in the end game column the queen is valued as "=R+B+(P)" ....