## Rook+pawns vs two minors

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metax
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### Rook+pawns vs two minors

How many pawns does the side with the rook need to make the material configuration rook+pawns vs. two minors about equal, excluding bonuses and penalties based on bishop pair and/or rook pair redundancy issues in your opinion?

Traditional count implies a value of 1 pawn, which is definitely too little.
Kaufman values imply 1.5 pawns.
The following material values

{ P=1; N=3.75; B=3.75; R=5.50; Q=10.75 }

are basically increased Kaufman values, minor pieces and rook increased by 0.5 pawns and queen increased by 1 pawn. These values keep the value of the Exchange and the value of Q vs 2R, increasing the values of minor piece vs pawns, rook vs two minor pieces and queen vs three minor pieces. The first and the last are clearly favorable because the minor pieces are often undervalued in these cases. However, the values would imply a value of 2.5 pawns to equal two minors with the rook. Including a bishop pair advantage of 0.5 pawns and a rook pair penalty of 0.25 pawns and assuming a rather closed position, there may be cases where the rook needs over 3.5 pawns to equal the two minors, which seems almost certainly exaggerated.

So what do you think about all this?

diep
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### Re: Rook+pawns vs two minors

metax wrote:How many pawns does the side with the rook need to make the material configuration rook+pawns vs. two minors about equal, excluding bonuses and penalties based on bishop pair and/or rook pair redundancy issues in your opinion?

Traditional count implies a value of 1 pawn, which is definitely too little.
Kaufman values imply 1.5 pawns.
The following material values

{ P=1; N=3.75; B=3.75; R=5.50; Q=10.75 }

are basically increased Kaufman values, minor pieces and rook increased by 0.5 pawns and queen increased by 1 pawn. These values keep the value of the Exchange and the value of Q vs 2R, increasing the values of minor piece vs pawns, rook vs two minor pieces and queen vs three minor pieces. The first and the last are clearly favorable because the minor pieces are often undervalued in these cases. However, the values would imply a value of 2.5 pawns to equal two minors with the rook. Including a bishop pair advantage of 0.5 pawns and a rook pair penalty of 0.25 pawns and assuming a rather closed position, there may be cases where the rook needs over 3.5 pawns to equal the two minors, which seems almost certainly exaggerated.

So what do you think about all this?
typically you see that most top engines use rook is 2.5 pawns better than a piece. A few use 2.2 pawns, only amateur engines use less than 2.2 pawns.

Again just material we speak about nothing else. Some rooks can get a mighty amount of bonus when put on 7th rank in todays software.

Thanks,
Vincent

diep
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### Re: Rook+pawns vs two minors

In quit some games Diep vs Rybka where rybka wins, i observe that Rybka manages to get a rook versus diep a light piece and 2 pawns.

the rook nearly always wins.

it is really total overhappy with exchange up. So probably must be far over 2.3 pawns extra which is diep's difference.

{ 1000, 3875, 3875, 6175, 12350 }, /* 0 */

As a human i feel 2.3 pawns is a lot of difference, but its losing game after game past months in this manner, so i am really into figuring this one out for Diep.

The whole problem in computerchess is always the same. If there is some patzer that values a specific thing just a tad higher, he'll get it on the board.

Vincent

metax
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### Re: Rook+pawns vs two minors

I don't think that the Exchange is worth more than even 2 pawns in most cases.

Sven
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### Re: Rook+pawns vs two minors

metax wrote:The following material values

{ P=1; N=3.75; B=3.75; R=5.50; Q=10.75 }

are basically increased Kaufman values, minor pieces and rook increased by 0.5 pawns and queen increased by 1 pawn. [...] However, the values would imply a value of 2.5 pawns to equal two minors with the rook.
Which values do you mean by "the values would imply ..." here? If you mean minor=3.75/rook=5.50 then my calculator says 2 x 3.75 - 5.50 = 2, not 2.5. So probably you mean something else which I can't see yet.

As to your question: while traditional chess theory told us that R+P nearly equals two minors (except in case of a bishop pair), today it seems clear that it is closer to R+2P at least. To be honest: I don't know what the value should be but as a chessplayer I believe that values close to three pawns are highly exaggerated *for human chess play*. However, it may turn out to be quite different for engines. While parameter tuning for one engine may deliver good results with R+3P vs. two minors, another one may tend to more "human-like" R+2P or even less and get best results this way round.

I guess there is no "general answer" since the positional evaluation is so different between engines, which makes it nearly impossible in my opinion to compare only the pure material value constants of two engines.

I just made a small experiment with Rybka 2.2n2 (no R3 available here ): from the initial position I removed Nb1, Bc1 and Ra8, Pa7 and started a very quick analysis. The PV (e4 g6 Nf3 Bg7 c3 Nc6 Qa4 Nf6 e5 Nd5) showed a value of -0.95 after few seconds. Then I also removed Pc7, which gave -0.51 (Nf3 Nf6 e3 Nc6 c3 g6 d4 e6 Bd3 Bg7 O-O). Finally I removed Pd7 and the PV was "e3 Nc6 Bb5 Nf6 Nf3 e6 a4 Bd7 a5 Qb8 Nd4 Bd6" with a value of +0.01. So R+3P gave about an equal play, of course many positional factors add into this here. But interesting was that R+1P was not -2.00 but gave a PV with only about -1.00.

It is not representative, and it is also about search, not only about material value constants, I know. I just found it interesting.

Sven

BubbaTough
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### Re: Rook+pawns vs two minors

diep wrote:In quit some games Diep vs Rybka where rybka wins, i observe that Rybka manages to get a rook versus diep a light piece and 2 pawns.

the rook nearly always wins.

it is really total overhappy with exchange up. So probably must be far over 2.3 pawns extra which is diep's difference.

{ 1000, 3875, 3875, 6175, 12350 }, /* 0 */

As a human i feel 2.3 pawns is a lot of difference, but its losing game after game past months in this manner, so i am really into figuring this one out for Diep.

The whole problem in computerchess is always the same. If there is some patzer that values a specific thing just a tad higher, he'll get it on the board.

Vincent
So Vincent, are you saying your program considers a rook and knight to be worth significantly more than 2 bishops and a pawn? Because that has not been my finding at all. I find Kaufman's estimate of the exchange being worth a pawn and the exchange to be much closer to right than the values you are showing...which also matches my intuition as a chess player.

-Sam

lkaufman
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### Re: Rook+pawns vs two minors

"most top engines use rook 2.5 pawns better than a piece. A few use 2.2 pawns, only amateur engines use less than 2.2". Rybka 3 uses almost exactly 2 pawns on average, though the value is heavily phase-dependent. Doch (latest private version) uses 1.97 on average. For Stockfish it's hard to say, because the terms are so dependent on each other, but I believe the true value used is somewhat below 2. I don't know about Naum 4 and Deep Shredder 12 and Fritz 12, but I haven't noticed them valuing Exchange vs. pawns much differently than Rybka 3 in general. So what "top engines" use values as high as 2.2 (not to mention 2.5)? I don't know any.
If some engines do use such high values and have proven them to work best in actual play, I would be most interested in why they work in those engines but not in others like Rybka. I don't think that the engines differ in such a fundamental way as to require radically different piece values. It's strange.
It is clear though, that the value is higher for engines than for humans. If we use Rybka's value of 2, it's clearly higher than the par value for humans, which is probably about 1.75.

BubbaTough
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### Re: Rook+pawns vs two minors

lkaufman wrote:"most top engines use rook 2.5 pawns better than a piece. A few use 2.2 pawns, only amateur engines use less than 2.2". Rybka 3 uses almost exactly 2 pawns on average, though the value is heavily phase-dependent. Doch (latest private version) uses 1.97 on average. For Stockfish it's hard to say, because the terms are so dependent on each other, but I believe the true value used is somewhat below 2. I don't know about Naum 4 and Deep Shredder 12 and Fritz 12, but I haven't noticed them valuing Exchange vs. pawns much differently than Rybka 3 in general. So what "top engines" use values as high as 2.2 (not to mention 2.5)? I don't know any.
If some engines do use such high values and have proven them to work best in actual play, I would be most interested in why they work in those engines but not in others like Rybka. I don't think that the engines differ in such a fundamental way as to require radically different piece values. It's strange.
It is clear though, that the value is higher for engines than for humans. If we use Rybka's value of 2, it's clearly higher than the par value for humans, which is probably about 1.75.
Yes, but by the time endgame rolls around, the minor piece usually has a nice mobility bonus, and if you have 2 extra pawns probably one of them is passed. If you have a knight, it often has a nice outpost. I would guess that these type of factors are usually weighted pretty highly in most strong programs, so that unless there is something wrong with your position, in rook vs. minor and 2 pawns the side with the minor + pawns is actually up in score by a non-trivial amount even if only looking at the material differences it looks about even.

-Sam

lkaufman
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### Re: Rook+pawns vs two minors

In both Rybka and Doch we made some effort to bias the piece-location tables to offset mobility and such factors in all game phases, so that the nominal piece values will be reasonably realistic. For programs I'm not so familiar with, I would just go by the evaluation of some neutral position you might set up, not by the nominal values (which I probably don't know anyway). Also, when I talk about "average" values, I mean with half the material left on the board; of course they are different in the opening and the endgame.

BubbaTough
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### Re: Rook+pawns vs two minors

lkaufman wrote:In both Rybka and Doch we made some effort to bias the piece-location tables to offset mobility and such factors in all game phases, so that the nominal piece values will be reasonably realistic. For programs I'm not so familiar with, I would just go by the evaluation of some neutral position you might set up, not by the nominal values (which I probably don't know anyway). Also, when I talk about "average" values, I mean with half the material left on the board; of course they are different in the opening and the endgame.
OK, a couple simple examples from Doch12:

2 pawns for the exchange
[d]8/4rk2/5pp1/8/2N1PP1P/3PK3/8/8 w - - 0 1
at ply 1: +0.34
1 pawn for the exchange
[d]8/4rk2/5pp1/8/2N1PP2/3PK3/8/8 w - - 0 1
at ply 1: -0.45

so even though you tried to balance things, picking a couple typical positions without trying to game things you can see the values look pretty different than what you are saying. This is because of the passed pawn and knight outpost I would guess, but that is going to usually be the case in minor piece + pawns for rook situations.

-Sam