My question is this: how can I teach Rybka when the advantage of two bishops vs. bishop and knight is a big deal, and when it is not? The average value of this difference is nearly half a pawn, that is very clear from all my work. But clearly it swings a lot depending on the type of position. What factors, other than those mentioned above, are important in evaluating how large an advantage the bishop pair has? Please don't bother to mention advantages that apply to all positions, I'm assuming that things like king safety, space, and pawn structure are equal. I feel I'm missing something important here, so if you are a strong player and can formalize a suggestion, that would be welcome. Of course, to be useful the suggestion must be clearly expressed in words, not by saying something like "in positions like this diagram...". Computers don't understand "like".
What do you feel about that?
Also, it seems some more visitors have opinions on this trace:
By lonesometheblue Date 2008-05-29 11:46 "....4. ability to reach to enemy area (let say that first half of the board)"
By Soren Riis Date 2008-05-29 12:44 "... Here is an idea: In dynamic and open positions the opponent's weaknesses are easier to expose. The ability to expose weaknesses and/or control key squares that are spatially separated (e.g. on different side of the board) is superior for a bishop pair over B+N or N+N."
As for you remark that this conditions (highway) are not present in the opening; of course they aren't! Otherwise moves like X. ... Bxf3 you mentioned wouldn't be considered solid! Therefore, a slight evaluation advantage for BB side in the opening is ok AFAIK, it's just that this side should go for opening those highways, and depending of the outcome of this effort, the evaluation score must be corrected.
in a position when one side has BB and the other N(good)B, among other things scored (pawn structure, king safety, etc), I suggest additionaly "highway" component to be scored.
Fischer's experience had convinced him that allowing the bishop pair this early in the game is not dangerous for white and does not equalize for black. In the '72 World Championship Fischer played the Exchange Variation in only one game
which resulted in a draw.20 years later in their rematch Fischer played it twice against Spassky,winning one game and drawing the other.
I know that this is only one player's lifetime evaluation of the position but,still,considering the player,I doubt that he was wrong.
Larry, I realize that this might be off-topic but does your evaluation recognize the added value potential in having 2 knights operating against bishop/knight in middle and end game situations? I just assume that it already does.
I have never heard the claim that two knights vs. bishop and knight is any sort of advantage in any stage of the game. Jeremy Silman writes exactly the opposite, and I am inclined to agree with him. What is your source for this contention?
A single knight can never be linked to a pawn like a bishop can to achieve protected outpost status nor can 2 knights ever sweep the length of the board as the bishop pair can but I still contend that their are positions where 2 knights operating
in tandem are worth more than twice the value of one knight.
the power of a bishop pair increases dramatically the less material is on the board.
by less material I rather mean fewer pieces than material meassured in pawns.
maybe just use a simple function to reduce this 0.5 advantage to almost 0 in the opening, 0.2 for middlegame with ~ 24 pieces and 0.5 in positions with 10 pieces left.
some changes like this will change the style quite much I guess.
ok this is just playing around with values. I will think of a more sophisticated approach, which can be formulated as easy as possible.
my experience during analysis with rybka 2.3.2a was, that the bishops are weighted a bit too high - independant of the stage of the game.
your evaluation issue of the bishop pair was predicated on the search function being unavailable for your purposes. You sought a stand-alone means for valuing the bishop pair (basically against B/N OR NN conditions). We reviewed "good"
and "bad" bishops,interposing pawns to cog the bishop diagonals, open diagonal avenues that would enhance the dynamic possibilities of the bishop pair,circumstances where the presence of many pawns would impede those dynamics,circumstances where an active knight or knight pair would actually be better than the bishop pair,the inherently greater reach of the bishop than the knight,the advantages of the knight over the bishop for forking et.,etc.
In the end, the actual advantage of the bishop pair ,without search, seems extraordinarily elusive to pin down,let alone quantify by evaluation. Still, practice would seem to be rather conclusive that the bishop pair deserves a slight plus over
the B+N or the N pair.
This may be ,in fact, true if only because it's almost always easier for a bishop to force an exchange with a knight than the reverse.
Quantifying this advantage is your bailiwick,but I believe it's the only static advantage the bishop pair actually enjoys.
My 2 cents only but a lot of consideration has gone into it .
and Larry's assessment thereof, opposed to Kramnik's position where White's remaining Fianchettoed Bishop is not so valuable -biting on them granite pawn chains-, a good illustration of this trade and, for my poor playing knowledge, it was certainly instructive!
This second trade-off is probably often the later trade though by the side having just BB against BN, where Larry's problem is more in the opening with BBNN against BBNN and one side having to assess giving up his Bishop pair when the other side retains it, so it comes down to exchanging a Bishop for a Knight there. One problem then for the side having this option is assessing both the function and the vulnerabilities of his remaining Bishop not just there but in the whole rest of the game! It is a strategic consideration and turning this into an eval one, excluding cases where you just follow existing opening practice/knowledge is very complicated, but also interesting, and of course search can help in practice but just not at the leafs of the search tree.
This probably touches on another point: that you do not want to double search issues too much in eval, so eval issues have to focus more on non-dynamical issues, just because dynamical issues get filtered out in search better, probably, when eval does not interfere too much with search. This is probably related also in not searching too deep?!? (i.e Pruning/Quiescence should be as soon as possible but not earlier than possible :-)) Anyway I think that this relates to part of the philosophy of what Larry is doing in Rybka: Rybka's Search Gap © CSTAL should be so good that the opponent is outsearched in majority of cases and Larry then has to focus on the non-dynamical issues remaining, you could call this positional characteristics but then as opposed to tactical characteristics, but non-dynamical versus dynamical is probably a more useful way to describe it. The plus of the approach is that the non-dynamical aspects of the evalution lend themselves well to testing at ultra-short time-intervals, you can ignore there most tactics and dynamical traits and leave those to Vasik's search. Ed Schröder already did that in Rebel testing but he did it with mostly games with 2 seconds per move for positional eval characteristics I believe, and Vasik and Larry just sped this process up tremendously :-)
Okay, so much for my analysis of Rybka's Search and Eval, was mostly meant to illustrate why in my opinion Larry probably feels he can ignore at least some dynamics in his work on Rybka's evaluation function, well he also has to, if he uses those 10/100/1000 games per second whatever it is to judge the percentages!
Coming back once more to the Function and Vulnerability of the remaining Bishop - sounds like the title of a lost Jane Austen book - which have to be assessed somehow by Search and Eval, I think weak squares, as illustrated by Felix and evaluation of the basis of pawn chains; can they be attacked and is the Bad Bishop likely to end up defending weak pawn chains of his own colour, are important also.
> and Larry's assessment thereof, opposed to Kramnik's position where White's remaining Fianchettoed Bishop is not so valuable -biting on them granite pawn chains-,
I suspect Kramnik agrees with Larry; it's just that Larry considers white's kingside pawns as part of the bishop's value, while Kramnik thinks the bishop makes the pawns more valuable by hiding the weaknesses.
It should also do so in a slightly conservative manner. This leads to:
1) More efficient search, with fewer switches from one move to another
2) Program outputs which are more reliable for analysis and more useful for humans in general
3) More easy-to-diagnose program behavior & better path to future improvement
> The static evaluator should do its best to estimate dynamic factors. This is a sort of axiom.
> It should also do so in a slightly conservative manner. This leads to:
> 1) More efficient search, with fewer switches from one move to another
> 2) Program outputs which are more reliable for analysis and more useful for humans in general
> 3) More easy-to-diagnose program behavior & better path to future improvement
First I have to say that I was quite surprised when you said that the pair of bishop is worth half a pawn. Seemed a bit high to me intuitively, but I trust you here. :) There are plenty of positions where your only advantage is the pair of bishops and it's worth a pawn or more. (I think there was a game Timman-Short in their candidates match, probably in 1993, which impressed me a lot at that time - though I was just a beginner then. Timman was a pawn up in an endgame, but Short had the pair of bishops and even played for a win. I do not recall whether he actually won the game, but he got some chances, I think.)
Another example for what you describe would be this line: 1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. e3 Bg4 5. h3 Bxf3 6. Qxf3
Let's see: In both cases, the remaining bishop is really a good one - but I assume that Ryka can handle this. Black got rid of its only problem, and all the remaining black pieces have very natural squares. It's generally good to exchange pieces when you have less space - I assume that Rybka knows that?! (It can even become a disadavantage to have more space when there are only a few pieces left.) Moreover, in both cases d4 is weak. (This is probably less obvious in the line I gave, but still significant - often, white's e4 is countered by e5, and there is a problem with d4, especially as the position of white's queen is a bit unfortunate.)
Okay, but these characteristics are all more or less independent of the pair of bishops issue. There should probably be a bonus for each of them (for black). But I assume that there already is, but still, Rybka favors white too strongly in these positions. Maybe one more point which is related to the pair of bishops issue: Exchanging a bishop for a knight is often bad because it weakens the squares which were controlled by this bishop - the opponent's bishop does not have an antagonist. But here, because of the pawn structure, there is no such weakness.
You said that the eval drops a bit when there are many pawns on the board. The reasoning may be like this: The bishops get stronger when the position is opened. In a position with many pawns, they cannot really play out their strength. Thus there should be a penalty. But there is a significant difference between a blocked position and a position where the pawn structure is not yet fixed: in the latter case, the position can potentially open - thus the malus should be smaller here.
Now we are at the starting point of your problem: One hast to make a distinction between those 'pair of bishops many pawns unlocked pawn structure' positions where the pair of bishops is still a significant advantage, and those where it isn't. From a human perspective, the distinction is not that hard, in my view: It's about possible transformations. When you consider the position you gave: Black's pawn structure is very compact, and white does not really have the levers (I hope the term is correct) to put it under pressure and open lines - or diagonals. I don't know much about this line - mainly just some Fischer games - but I think that mostly, white will play e5 at some point. But this locks the position, and thus diminishes the value of the bishops. What about the other line: To give some space to the bishops, white will have to play e4 at some point. But then the weakness of e4 can become significant.
To conclude - finally: I can imagine that in these position, there may even be something like a horizon effect: E.g. in your line, Rybka probably has a malus for playing e5 and presumably doesn't see a way to bring about a favorable change in the pawn structure. Thus she will prefer leaving the pawn structure as it is. But it is hard to make progress this way. One way to solve this would be teach Rybka something about possible transformations - though intuitively, this is probably hard to formalize.
Or maybe you are not completely right about the strength of the pair of bishops after all: Maybe there is a strong correlation between the pair of bishops and some other factors in actual positions - such as the weakness of squares of the relevant color. Because the correlation holds in such a large number of positions, one tends to overlook that the bonus shouldn't be for the pair of bishops, but rather for the pair of bishops + x. (This is to say that a purely statistical analysis would be misleading here.)
I could still say a bit more, but I guess I already said too much. Sorry for the long and probably pointless post.
The one idea in your post that could conceivably be coded is the weak pawn notion. Maybe when both sides have a weak pawn (like mutual isolated "d" pawns), knights are relatively better than bishops. But this won't help the openings we are talking about; there are no weak pawns yet.
Yes, I did not doubt that - even mentioned it myself. I thought the openings we are talking about are such that there are many pawns, but a pawn structure which is not (yet) fixed. My basic idea was that it would be crucial to identify those of the positions of this kind where white is able to open the position - e.g. by checking for possible transformations of the pawn structure. There are no favorable transformations of pawn structure - especially in your example - thus, the position is likely to remain closed.
Your suggestion implies that the remaining bishop of the BN side tends to be a bad bishop
No, I don't think so. I said that the absence of a bishop typically leaves behind weak squares. This is completely compatible with the remaining bishop being a good bishop.
Maybe when both sides have a weak pawn (like mutual isolated "d" pawns), knights are relatively better than bishops
I doubt this rule. The case you mention is a special one, but here, the pair of bishops is also clearly an advantage. (The exception being that the bishop which can attack the opponent's isolated pawn cannot be saved from being exchanged for the opponent's bishop - in the resulting position, the knight is much stronger than the bishop.)
But this won't help the openings we are talking about; there are no weak pawns yet.
I was rather trying to say something about weak squares. The exchange of the knight clearly diminishes white's influence in the center - as a result, the square d4 becomes potentially weak.
When a bishop disappears and leaves behind weak squares, they are usually weak because the remaining bishop cannot cover them and hence tends to be "bad". Anyway, can you give a formal definition of a "weak square"?
Your third comment, knight vs. lone bishop is favorable for the knight when the bishop is of the color that defends a weak pawn blocking an enemy weak pawn, could be tried. Of course this has nothing to do with the bishop pair.
In the Caro position, no definition of weak square would be likely to apply to d4, because White can set up his pawns on d3 and c3 if he wishes to cover d4. It may be temporarily a weak square, but not structurally.
One other try: I thought a bit and I am not sure whether there are many positions where both have 8 pawns and the pair of bishops is very relevant (I might be wrong). Of course, there are positions from 1.e4. But in 1.d4 positions, black is mostly able to keep his center intact, restricting the power of the bishops long term. The bishops are not only stronger in open positions, they are particularly quite dependent on an open center.
One more try concerning d4: :) Yes, of course, there cannot really be structural weaknesses in this position. But firstly, temporary weaknesses can be relevant as well, secondly and more importantly, my main point was that black has gained influence in the center.
Your third comment, knight vs. lone bishop is favorable for the knight when the bishop is of the color that defends a weak pawn blocking an enemy weak pawn, could be tried. Now I'm really curious - a pity that I do not have Rybka handy. Take this pawn structure: W:a2, b2, d4, g2, f2, h2 B: a7, b7, d5, f7, g7, h7 Now place a black bishop on a white square - say, e6, and give white a knight. Surely Rybka understands that this structure is really uncomfortable for black!?
Rybka 2.32a evaluates this as 0.04 at depth 22! That's really a surprise to me. Yes, it has been shown that black doesn't have to lose this, but it's really uncomfortable. By the way, there is a game Saidy-Fischer which Fischer won (he had the good knight with black). Of course, Saidy is no Fischer, so this doesn't prove anything, but Fischer's play was very instructive. And of course Karpov-Kasparov, if I recall correctly from their first WC match (Karpov won in great style, again with the knight). I honestly think you should have a look at this. 0.04 really seems to be too far off.
I´m sure you think about this game.
Karpov played the wonderful move 47. Ng2!!, but I´m absolutely sure, that this endgame is a draw by best play (see also Mark Dvoreckij, Die Endspieluniversität). And the very best: Rybka makes the right moves for black!
I have never seen any thorough annotations of this endgame, and I haven't analyzed it very carefully myself, either.
When you say that the endgame is drawn, do you mean this position? Again, I am curious how Rybka evaluates this. You do not always have to evaluate a position correctly to play it correctly.
The first issue is understanding that the knight is better than the bishop. Rybka 2.3.2a didn't understand this, while Rybka 3 does.
The second issue is that endgames often have this weird and somewhat mysterious quality that some theoretical advantages are only symbolic and can't really be played for a win, while in other cases the tiniest-looking advantage can actually be serious. Simply adding up some sort of features may not be good enough for these types of endgames.
This second issue will probably require some new heuristics or even some sort of different framework. It's not clear how it will all look - it's for later on.
We have to unify on the final result first. Muller&Lamprecht in Funtamenal Chess Endings write:
1 Ne3 Bb1 2 b4 gxh4?
2...Ke6 3 g4 hxg4 4 hxg5 gxf3 5 gxf6 (5 Kxf3 fxg5 6 Kg4 Kf6! 7 Nxd5+ Kg6!=) 5...Be4 6 Ng4 Kf7 7 Kg3 Ke6 8 Kf4 Kf7 9 Ke5 Bg6! 10 Kxd5 Bh5=
3 Ng2!! hxg3+ 4 Kxg3 Ke6 5 Nf4+ Kf5 6 Nxh5 Ke6 7 Nf4+ Kd6 8 Kg4 Bc2 9 Kh5 Bd1 10 Kg6! Ke7 11 Nxd5+?
11 Nh5 wins
I´m not convinced! Can you give the winning line or say what´s wrong with this line:
55. Nh5 Bxf3 56. Nxf6 Be4+! 57. Kg5 Bd3! 58.Nxd5+ Kd6 59. Nc3 Bf1! 60. Kf4 Bg2 61. Ke3 Bh3! 62. Ne4+ Kd5 63. Nc5 Bc8 64. Kd3 Bf5+ 65. Kc3 Bc8 which should be a draw.
2. Rather than a grab of permanently weak Pd5 I would bring wK close to center f6,e5
3. Pa6 is also weak
After the gross blunder 58. Nxd5?? black jail is open.
What about Ng4-e5-c6-b8xa6-c5+?
Edit: Aha! Now I see 58.Ng4 Bf1! 59.Ne5 Bh3! it really looks like a draw.
To your points:
#1. There will be no pawn endgame.
#2. There is no way for white king to f6 or e5. Therefore I think 58. Nxd5 is forced. But okay, you can fight against :-)
#3. Pa6 will be defended by black bishop.
To your idea:
58. Ng4 Bf1 59. Ne5 Bh3 60. Nc6+ Kd6
And now I see this: Edit: Aha! Now I see 58.Ng4 Bf1! 59.Ne5 Bh3! it really looks like a draw. This is new! :-). So, forget my post!
1.Nh5 Be4 2.Nf4 (!Ng6-e5) Kf7! 3.Nh3 Ke6 4.Nf2 Bc2 (Bf5 5.Ng4 Be4 6.Ne5)(Bg2 5.Nd3) 5.Ng4 Bf5 6.Kf4! (6.Ne5 Bh3) Be4 7.Ne5 Bf5 8.Nd7! Bc2 9. Nb8 Kf6 10.Nxa6 Bd3 11.Nc5 Bc2 12.Nd7+ Ke6 13.Ne5 Kf6 14.Ng4+ Ke6 15.Ne3 Bb3 16.Kf3 Kf6 17.Ke2 Kg5 18.Nd1 Kf4 19.Nc3 Kf5 20.Kd2 Bc4 21.a4 bxa4 22.Nxa4 Ke6 23.Nc3 Kd6 24.Kc2 Kc6 25.Kb2 Bd3 26.Ka3 Bf1 27.Ka4 Bg2 28.b5+
Is this position won for White? I believe yes, but I can´t prove it :-(.
PS: In your line, Black is defending very bad, I think (so 15. Bb3??). Bishop has to go first behind own pawns!
1.Nc5 Be8 2.Nd3 Bd7 3.Ne5 Be6 4.Ng4+ Kg6
(Bxg4 5.Kxg4 Kg6 6.Kf4 Kf6 7.Ke3)
5.Ne3 Kf6 6.Nd1 Bd7
(Bc8 7.Nc3 Bd7 8.Nxd5+ Ke6 9.Nc3 Bc6 10.d5+ Bxd5 11.Nxb5 don't ask me to prove this :)
(Ke6 8.Kg5 and N->c5 wins a4 or f5)
(Be8 8.Nxd5+ Ke6 9.Nc7+)
8.a4! bxa4 9.b5 Bd7 10.b6 Bc6 11.Nxa4! Ke6 12.Nc5 Kd6 13.b7
Please, show me the winning line (after Pa6 is lost; see below).
Just one idea: Step 1: Transfer white's knight to c3: For example 68. Nc5 Bc6 69. Nd3 Bd7 70. Nb2 Bc6 71. Nd1 Be8 72. Nc3, and now black has to give up control over g5 because Ke6 is forced(Bc6 73. a4 bxa4 74. b5 Bd7 75. b6 Bc6 76. Nxa4)
Step 2: Push away black's king with king and knight - this is typical in these positions: 73. Kg5 Bd7 74. Ne2 Ke7 75.
Nf4 Bc6 76. Kf5 Kd6 77. Kf6 Be8 78. Ng2 Bh5 79. Ne3 Be2 80. Nf5+ Kd7 81. Ke5
Step 3: Get one of black's pawns: ...Bf3 82. Nd6 Kc6 83. Nc8
I think that in principle, black's best defense is not to cover b5 and d5 from behind. But still, if he tries to cover them from c4, white can, e.g., play a4 at some point, then bring his king to the queenside to support his pawn. Looks like an easy win.
> One other try: I thought a bit and I am not sure whether there are many positions where both have 8 pawns and the pair of bishops is very relevant (I might be wrong).
There are plenty of those. For example, 1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. Qc2 0-0 5. a3 Bxc3+ 6. Qxc3. White is quite far behind in development and yet is playing for an advantage, simply because he has the bishop pair.
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