Lonely queen

[hgm]

Indeed, this is why I mainly applied the method to opening positions where almost all material is still on the board, so that pieces protect each other and their Pawns pretty well. Sometimes (like in this case) you just want to know end-game values, however. I guess the games could be analyze to see if any Pawns were lost within, say, 5 moves. But that would be a lot of work, or would require specially written software.

Effects of Pawn eval can usually be eliminated by using only (line or point) symmetric Pawn structures. But it would be more difficult to decide which Pawn to delete as 'standard Pawn odds'. It can still be pretty useful to establish beyond any doubt that a certain combination of material is tronger than another one (e.g. that Archbishop (B+N) crushes Rook + Knight in the presence of (equal) multiple Pawns, which is very counter-intuitive).

[Lyudmil Tsvetkov]

Hi,

I'm done with my tests of queen vs 3 minors. I performed several tests where I altered the number of rooks on the board.

Here are the numbers

http://macechess.blogspot.de/2013/12/qu ... art-2.html

Hi Thomas.
Thank you very much.

So my original impression that the Q is stronger than 2Ns+B in a pure setting was more or less precise, but obviously more pieces change things. Your numbers are very useful, but there might be some tiny bit of inconclusiveness about them concerning the exact values probably because of the engine used. It is possible that ICE playes with some of its pieces better than with others. My impression is that the stronger the engine in general, the better it plays with the queen.

Do you plan to do any other tests involving this time rooks as part of the Q vs 3 pieces (not just 3 minors) imbalance, as this was the primary goal of our research, although we learned some other things thanks to you? It would be interesting to still measure the value of the imbalance in the case of Q vs R+2Ns, 2Rs+N, R+B+N, and R+2Bs.

[tpetzke]

Hi,

maybe later I do some more stuff in that area, but not right now.

Imbalances of Q vs RRM are already very hard to measure, because you have to remove some pawns for the side with the minors. Otherwise the queen side will almost always lose.

But if you remove pawns for the side with the more pieces, the rooks get half open files, if additional minors are added also the bishops develop more quickly. So whatever you measure is polluted by a lot of things.

BTW: You can easily repeat that test with stockfish to verify the values, just created a little opening file with the imbalance present, let stockfish play a few hundred games and do the math. No programming skill at all required for that.

Thomas...

[hgm]

Indeed, trying to balance with many Pawns never worked well for me. The value of Pawn chains is just too variable. I sometimes have the feeling that with huge imbalances in piece material, Pawns are nothing but toast for the side with the piece advantage, and adding more of them hardly has any effect. K+Q vs K + 10 (2nd or 3rd-rank) Pawns is just a massacre; the Pawns don't stand any chance at all. A full minor ahead might already be too much.

[Lyudmil Tsvetkov]

Hi,

maybe later I do some more stuff in that area, but not right now.

Imbalances of Q vs RRM are already very hard to measure, because you have to remove some pawns for the side with the minors. Otherwise the queen side will almost always lose.

But if you remove pawns for the side with the more pieces, the rooks get half open files, if additional minors are added also the bishops develop more quickly. So whatever you measure is polluted by a lot of things.

BTW: You can easily repeat that test with stockfish to verify the values, just created a little opening file with the imbalance present, let stockfish play a few hundred games and do the math. No programming skill at all required for that.

Thomas...

Hi Thomas.

I do not think removing pawns is in any way an obstacle. You could easily set up a position where nothing is attacked, good to start for both black and white, no development issues, etc.

I would gladly do the tests myself, but unfortunately I am not good at maths, doing statistics, etc. Besides, someone has to play Stockfish.

Anyway, big thanks again, wherever you have the desire to do some further tests, we will all be very happy to read some new report from you.

Frohe Weihnachten!

[hgm]

I would gladly do the tests myself, but unfortunately I am not good at maths, doing statistics, etc.

As if that would be needed in any way for observing the number of wins in a 1000-game match...

[Evert]

I have repeated the experiment Thomas did with Jazz using a very similar setup to his: black always has the minors, white always has the queen, but I award the first move to black half the time. This way I can simply count the score of white (or black).

The numbers I get are the following. First, with all rooks present on the board I get

Code: Select all

QN  - BBNN 42.16 - 57.84
QNP - BBNN 53.98 - 46.02

This gives the extra pawn a relatively low value of 11.82. Now to calculate the value of the 3M-Q imbalance:

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QN  - BBNN 42.16 - 57.84 -> +0.66
QB  - BBNN 41.09 - 58.91 -> +0.75
Q   - BBN  30.28 - 69.72 -> +1.67
Q   - BNN  41.88 - 58.12 -> +0.69

The draw rate is about 30-35 percent.

If I delete both rooks (but use the same value of the pawn as above rather than recalculating it, I'll probably do that later today):

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QN  - BBNN 63.19 - 36.81 -> -1.12
QB  - BBNN 63.47 - 36.53 -> -1.14
Q   - BBN  57.56 - 42.44 -> -0.64
Q   - BNN  65.84 - 34.16 -> -1.34

The draw rate increases to about 50% (60% for Q-BBN).
Because with this starting position many black pawns are undefended in the initial setup, I repeated the test Q-BBN with the black rook pawns advanced to the third rank (so they're defended). This gives:

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Q   - BBN  52.50 - 47.50 -> -0.21

The draw rate is 60%.

Finally, I calculated the bare Q-BBN value without other material on the board. This is very crude because I have to begin in a position where all minors are fairly close to the king so one of them isn't lost immediately. This setup is very drawish (85% of games are drawn), but the minors are just ahead by +0.3.

Conclusions:

• QM-BBNN/Q-BNN are about equal, at 0.7. The bishop pair doesn't give a large bonus when opposed by a minor.
• The bishop pair makes a significant difference in Q-BBN (and the value of the extra pawn probably needs to be measured again).
• Without rooks but with many pawns on the board, the queen side has a significant advantage, more than a pawn with this scaling (which is probably off). The bishop pair matters significantly only when there are no minors on the queen side.
• Without rooks, it makes a large difference whether pawns are defended in pawn chains or not.
• Without pawns, the queen is at a disadvantage if the minors are well protected. However, a single pawn probably makes a considerable difference here (needs to be tested).

More later

[tpetzke]

That is interesting, so in general the conclusions are the same, the values a bit different.

Thanks for posting

Thomas...

[Evert]

A few things to follow up on my previous post.

I've measured the score for Q-BBN with an extra pawn for the queen side. This gives

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QP  - BBN  54.28 - 45.72

which gives the pawn a value of 24, which gives the Q-BBN imbalance as

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Q   - BBN  30.28 - 69.72 -> +0.82

which includes the bishop pair bonus.

Because I am also interested in the often-mentioned "elephantiasis effect" (I'd like to construct a piece value model based on it, but everything I've tried has failed so far), I decided to also measure QNN-NNNBB (which would not be a realistic material combination in normal chess). Compare:

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Q    - BNN    41.88 - 58.12 -> +0.69 (previous)
QN  - BBNN  42.16 - 57.84 -> +0.66 (previous)
QNN- BBNNN 42.71 - 57.29

In other words, the material advantage of the minor side seems to decrease steadily as we add more knights and the position becomes more balanced (although I would guess that the difference here is within the statistical error bar). On the one hand, this is reasonable (the relative difference in strength becomes smaller), on the other hand, based on the elephantiasis idea I would expect the value of the queen to be depressed more by the presence of the extra knights, but this does not seem to be the case. Perhaps I'm misunderstanding something, or perhaps I should measure the value of the pawn in the QNN-BBNNN case to express everything in "pawn units" rather than winning percentages.

However, this result does agree with the idea that trading pieces benefits the side that is ahead (in this case, the minors side).

I have also measured QNP-BBNN without rooks:

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QNP - BBNN 44.78 - 55.22

which gives the value of the pawn as 18.41. Using this scaling for the rook-free imbalances gives

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QN  - BBNN 63.19 - 36.81 -> -0.72 
QB  - BBNN 63.47 - 36.53 -> -0.73 
Q   - BBN  57.56 - 42.44 -> -0.41
Q   - BNN  65.84 - 34.16 -> -0.86 

Finally, I've measured Q-RR and QR-RRR (the latter again because I'm interested in the elephantiasis idea):

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Q   - RR    65.45 - 34.55
Q   - RRP   51.09 - 48.91
QR  - RRR   54.76 - 45.24
QR  - RRRP  46.00 - 54.00

So the value of a pawn is 14.36 and 8.76 respectively. So

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Q   - RR    65.45 - 34.55 -> -1.08
QR  - RRR   54.76 - 45.24 -> -0.54

Here, again, the addition of the extra piece reduces the advantage of the side that is ahead, which in this case agrees with the idea that the addition of the extra rook depresses the value of the queen. However, I find it hard to reconcile these data with the elephantiasis idea. Perhaps there is something I am overlooking.

Conclusions

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[*] Trading (equal) pieces is good for the side that benefits from the material imbalance. This is not new or shocking, but it seems to dominate over an "elephantiasis effect".
[*] A queen is much stronger than two rooks (over +1) with all pawns on the board. This advantage should drop when pawns disappear from the board, but the effect is much stronger than I would have expected.

[hgm]

..., on the other hand, based on the elephantiasis idea I would expect the value of the queen to be depressed more by the presence of the extra knights, ...

This would indeed be the prediction for the 'raw elephantiasis'.

But with 1 vs 4 minors, and even more so with 2 vs 5, there are very many possibilities to trade a Knight for one of the opponent's minors. Unless that opponent would change to a trade-avoiding strategy, but that would be close to impossible in the 2 vs 5 case, and seriously devaluate his 4 minors in the 1-4 case, which then start to suffer from elephantiasis themselves. This is quite unlike adding a Rook on both sides (QR-RBNN), where trade-avoidance with the Rooks only devaluates a single Rook, rather than 4 minors, while the Rook that seeks the trade is itself hindered by the presence of the opposing minors. The damage inflicted by trade-avoiding of a single Rook for a severely handicapped Rook is much smaller than that inflicted by an unimpeded Knight on 4 minors. Making the latter not worth it, so that quick trading becomes unavoidable, and the extra elephantiasis of the Queen will hardly get the chance to manifest itself.

So in short: 'effective' elephantiasis is the cost of trade-avoiding strategy, and when such a strategy for a certain class of pieces becomes too costly, it should be abandoned. But then trading will be unavoidable, so that the effective elephantiasis should be calculated based on the remaining pieces.