We should reconsider the value of the Queen.................

[pichy]

So here White just plays e4
What is the value of the two queens?

For an engine, as well as - within certain limits - for a human, piece values (and also positional values) are needed only to get an approximated value of a position where the search (resp. the human analysis) can't go deep enough to determine the "true value" of the position. In your example above it is a forced mate in three plies for white, so neither engines nor (strong enough) humans need to consider any piece values here.

Therefore, your example does not say anything about pieces values that should be used by programs.

You are forgetting something very important. You are not following
these conditions in your example of the two Queens. Please read it again
[...]

I am not forgetting anything here, Jorge. I stated that your example is 100% unrelated to "piece values" since it is a mate in 3 plies. A similar statement applies to your other tactical examples where the queen value is fully unimportant (either the queen gets lost immediately, or the enemy can promote his passed pawn after white trades Q vs. RB). These examples are about search, not about the value of a queen when evaluating (leaf) positions.

We can surely debate about the choice of queen values in today's engines and possible improvements. Maybe you are right when stating that for some programs the queen value is too small. You can be sure, though, that this is not the case for the vast majority of the current "top" engines since their evaluation parameters are well-tuned. In any case, I don't say that your position is "wrong", the main issue I see with your posts (apart from the font size, of course) is the choice of your example positions which are unrelated to the points you want to make, in my opinion.

Sven

Some of you might be correct and I am not saying that the value of the Queen is too high, all that I am saying is that after the middlegame around move 40 or starting the endgame the value of the Queen disminish and it should not be left with the same value throughout the game.
The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well. Some examples follow.
• A queen versus two rooks
• In the middlegame they are equal
• In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn

We should reconsider the value of the Queen to no more than 8.5 in the endgame stage and here are some positions to look at

In the first position a Bishop and a Rook value at 8 points give us a draw [:wink/size]
[D]8/8/8/3kb3/3r4/3KQ3/8/8 w - - 0 1
[D]8/8/8/3kn3/3r4/2QK4/8/8 w - - 0 1
Here is another interesting position where the Queen is not as strong as two rook

[D]3k4/2rr4/8/8/8/8/8/3KQ3 w - - 0 1

I only recommend some adjustment to some engines not all of the top ones and the any Chess engine could easily be modified to adjust the value of the Queen depending on the stage of the game like Lasker recommended before the era of computer, for instance if the game has not reached the endgame which is normally after move 40 then this logic could be applied.


if(Condition)
Statement1;
else
Statement2;

Or something like this depending on the variable used for the Queen

if(Number of moves < than 40)
Statement1;value of Q=10.5
else
Statement2; value of set Q=8.5

[Andre]

This is the end of a study... A few moves earlier the position was

[D] Q7/2q5/1p6/2p5/P1k5/2P3p1/1P1KP3/7q w - - 0 1 [/D]

White plays 1.Qg8+ Qd5+ 2.Kc2 Qxg8 3.e4 and 4.b3 mate is next

The study starts with

[D] 8/8/1p2PQ2/k1pN4/p7/2PK2pq/PP2P1np/8 w - - 0 1 [/D]
Y. Dorogov, 1982
[Date "1982.??.??"]
[White "Dorogov, Y."]
[Result "1-0"]

1. e7 Nf4+ 2. Qxf4 Qh7+ 3. Kd2 h1=Q 4. Qxa4+ Kxa4 5. e8=Q+ Ka5 6. Qa8+ Kb5 7. Nc7+ Qxc7 8. a4+ Kc4 9. Qg8+ Qd5+ 10. Kc2 Qxg8 11. e4 Qg4 12. b3# 1-0

[syzygy]

Some of you might be correct and I am not saying that the value of the Queen is too high, all that I am saying is that after the middlegame around move 40 or starting the endgame the value of the Queen disminish and it should not be left with the same value throughout the game.
The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well.

Modern engines do not evaluate material by assigning each piece a fixed value and summing, but use complicated weightings to deal with imbalances.

Assuming you are correct about two rooks vs a queen (which I don't doubt, but I am not a good enough chess player to confirm it) and those engines are well-tuned, their evaluations will more and more favor the side with two rooks compared to the side with a queen as more material is removed from the board. In this way, there is also no need to artificially distinguish between middle game and end game at exactly 40 moves (or any other fixed number): the material that is still on the board decides what phase the game is in.

What is very nice about this approach is that an engine playing with two rooks against a queen will actively seek to trade down material (since that will increase its evaluation), while an engine playing with a queen against two rooks will attempt to avoid exchanges of material.

On the other hand, your suggestion of how to implement the rules you propose will only bump the evaluation of the side with two rooks after 40 moves have been played, whether that side trades down or not. Effectively, it will only tell the side with two rooks to avoid a draw by repetition. It will not tell the engine that trading down is good or bad.

[pichy]

Some of you might be correct and I am not saying that the value of the Queen is too high, all that I am saying is that after the middlegame around move 40 or starting the endgame the value of the Queen disminish and it should not be left with the same value throughout the game.
The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well.

Modern engines do not evaluate material by assigning each piece a fixed value and summing, but use complicated weightings to deal with imbalances.

Assuming you are correct about two rooks vs a queen (which I don't doubt, but I am not a good enough chess player to confirm it) and those engines are well-tuned, their evaluations will more and more favor the side with two rooks compared to the side with a queen as more material is removed from the board. In this way, there is also no need to artificially distinguish between middle game and end game at exactly 40 moves (or any other fixed number): the material that is still on the board decides what phase the game is in.

What is very nice about this approach is that an engine playing with two rooks against a queen will actively seek to trade down material (since that will increase its evaluation), while an engine playing with a queen against two rooks will attempt to avoid exchanges of material.

On the other hand, your suggestion of how to implement the rules you propose will only bump the evaluation of the side with two rooks after 40 moves have been played, whether that side trades down or not. Effectively, it will only tell the side with two rooks to avoid a draw by repetition. It will not tell the engine that trading down is good or bad.

You made a good point, and I have to reconsider since I am in the process of making pieces evaluation changes based on the stage of the game, sure enough 40 moves doesn't determine that the game has reached the endgame, but only how many pieces are left will make the determination.

PS: Thanks

[syzygy]

You made a good point, and I have to reconsider since I am in the process of making pieces evaluation changes based on the stage of the game, sure enough 40 moves doesn't determine that the game has reached the endgame, but only how many pieces are left will make the determination.

PS: Thanks

You're welcome!

And thanks for reminding me that I really should add such rules to my engine. I think this can make a difference in many games. (But first I need to tell it about king safety )

[pichy]

You made a good point, and I have to reconsider since I am in the process of making pieces evaluation changes based on the stage of the game, sure enough 40 moves doesn't determine that the game has reached the endgame, but only how many pieces are left will make the determination.

PS: Thanks

You're welcome!

And thanks for reminding me that I really should add such rules to my engine. I think this can make a difference in many games. (But first I need to tell it about king safety )

After analyzing several ending positions I believe that Howard Stauton and peter Pratt pieces evaluation might be the most realistic on average throughout the game.

Howard Staunton in The Chess-Player's Handbook notes that piece values are dependent on the position and the phase of the game (the queen typically less valuable toward the endgame), but gives these values, without explaining how they were obtained (Staunton 1870, 30–31):
pawn 1.00
knight 3.05
bishop 3.50
rook 5.48
queen 9.94
In the 1817 edition of Philidor's Studies of Chess, the editor (Peter Pratt) gave the same values.

[Adam Hair]

The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well. Some examples follow.
• A queen versus two rooks
• In the middlegame they are equal
• In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn

According to long time control engine matches between engines greater than 2700 Elo (CCRL scale) and with an Elo difference of 50 or less, with no minor pieces the 2 rooks are worth about 0.3 pawns more than the queen. If you add a pawn to the queen, then the queen + pawn is worth 0.7 pawns more than the 2 rooks.

Of course, the above situation (Q vs 2 R with no minors) depends on how many pawns are on the board. The rooks have their greatest advantage when there are 2 or 3 pawns on the board for each side (+0.5 pawns for the rooks vs a queen).

[pichy]

The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well. Some examples follow.
• A queen versus two rooks
• In the middlegame they are equal
• In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn

According to long time control engine matches between engines greater than 2700 Elo (CCRL scale) and with an Elo difference of 50 or less, with no minor pieces the 2 rooks are worth about 0.3 pawns more than the queen. If you add a pawn to the queen, then the queen + pawn is worth 0.7 pawns more than the 2 rooks.

Of course, the above situation (Q vs 2 R with no minors) depends on how many pawns are on the board. The rooks have their greatest advantage when there are 2 or 3 pawns on the board for each side (+0.5 pawns for the rooks vs a queen).

If you let this endgame to be played out to the end what do you think the outcome will be without using tablebase, Komodo is evaluating the position as favorable to White, but I gave Black to Houdini and White to Komodo and it ended in a draw search depth set to 34:

[D]4k3/5r2/8/8/8/8/3P2Q1/1r2K3 w - - 0 1

FEN: 4k3/5r2/8/8/8/8/3P2Q1/1r2K3 w - - 0 1

Komodo3-32:
1 00:00 4 39.999 -0.21 Ke1e2
2 00:00 858 8.579.999 -0.07 Ke1e2 Rf7e7+ Ke2d3 Re7d7+ Kd3c2
3 00:00 1.366 13.659.999 +0.02 Ke1e2 Rf7e7+ Ke2d3 Re7d7+ Kd3c2 Rb1b6
4 00:00 3.114 31.139.999 +0.02 Ke1e2 Rf7e7+ Ke2d3 Re7d7+ Kd3c2 Rb1b6
5 00:00 5.054 0 -0.01 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1c1 Ke2d3
5 00:00 5.054 50.539.999 -0.01 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1c1 Ke2d3
6 00:00 6.268 0 0.00 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1f1 Ke2d3 Rf7d7+ Kd3c2
6 00:00 6.268 62.679.999 0.00 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1f1 Ke2d3 Rf7d7+ Kd3c2
7 00:00 13.956 894.611 +0.04 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Ke2d3 Rb1b4 Qd5c5
7 00:00 13.956 894.611 +0.04 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Ke2d3 Rb1b4 Qd5c5
8 00:00 29.926 383.665 +0.08 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5e5 Rb1f1 Ke2d3 Rf1f4
8 00:00 29.926 383.665 +0.08 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5e5 Rb1f1 Ke2d3 Rf1f4
9 00:00 50.043 458.268 +0.07 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5h4+ Kh7g7 Qh4g4+ Kg7f8 Qg4d4 Kf8g8 Ke2d3
9 00:00 50.043 458.268 +0.07 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5h4+ Kh7g7 Qh4g4+ Kg7f8 Qg4d4 Kf8g8 Ke2d3
10 00:00 123.799 466.812 +0.07 Ke1e2 Ke8f8 Qg2d5 Rb1f1 Ke2d3 Rf1f5 Qd5d4 Kf8g8 Kd3c2 Rf5b5 Qd4e4
10 00:00 123.799 466.812 +0.07 Ke1e2 Ke8f8 Qg2d5 Rb1f1 Ke2d3 Rf1f5 Qd5d4 Kf8g8 Kd3c2 Rf5b5 Qd4e4
11 00:00 244.797 506.196 +0.06 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8d4 Rb6d6 Qd4c5 Rf7f6 Ke2d1 Ke7f8 Kd1c2
11 00:00 244.797 506.196 +0.06 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8d4 Rb6d6 Qd4c5 Rf7f6 Ke2d1 Ke7f8 Kd1c2
12 00:00 372.430 518.992 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Qc3c5+ Rf7e7+ Ke2d3 Rb6f6 Kd3c2 Kf8f7 Qc5d5+ Kf7g7 Qd5c4
12 00:00 372.430 518.992 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Qc3c5+ Rf7e7+ Ke2d3 Rb6f6 Kd3c2 Kf8f7 Qc5d5+ Kf7g7 Qd5c4
13 00:01 504.340 521.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Kd1c2 Kf8g7 Qc3g3+ Rf6g6 Qg3e5+ Rf7f6 Qe5d4
13 00:01 504.340 521.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Kd1c2 Kf8g7 Qc3g3+ Rf6g6 Qg3e5+ Rf7f6 Qe5d4
14 00:01 758.570 534.353 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3a3+ Kf8g7 Qa3g3+ Rf6g6 Qg3e5+ Rg6f6 d2d4 Kg7f8 Kd1c2 Rf6f1
14 00:01 758.570 534.353 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3a3+ Kf8g7 Qa3g3+ Rf6g6 Qg3e5+ Rg6f6 d2d4 Kg7f8 Kd1c2 Rf6f1
15 00:02 1.309.882 541.720 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4
15 00:02 1.309.882 538.247 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4
16 00:04 2.199.003 518.240 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
16 00:04 2.199.003 518.240 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
17 00:06 3.161.019 530.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
17 00:06 3.161.019 530.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
18 00:10 5.458.408 541.636 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g5+ Kg7f8 Qg5d5 Kf8g7 Qd5e5 Rf7b7 Qe5c5
18 00:10 5.458.408 541.636 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g5+ Kg7f8 Qg5d5 Kf8g7 Qd5e5 Rf7b7 Qe5c5
19 00:24 13.576.984 549.443 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1f1 Qh2d6 Kf8f7 Qd6d5+ Re7e6 Kd3c2 Rf1f6 Qd5h5+ Kf7g7 Qh5g4+ Kg7f8 Qg4b4+ Re6e7 Qb4c5 Kf8f7 Qc5c4+ Kf7g7 Qc4c8 Re7f7 Qc8g4+ Kg7f8
19 00:24 13.576.984 549.443 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1f1 Qh2d6 Kf8f7 Qd6d5+ Re7e6 Kd3c2 Rf1f6 Qd5h5+ Kf7g7 Qh5g4+ Kg7f8 Qg4b4+ Re6e7 Qb4c5 Kf8f7 Qc5c4+ Kf7g7 Qc4c8 Re7f7 Qc8g4+ Kg7f8
20 00:35 19.625.224 558.873 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b2 Rc1c6 Qb2b7+ Kd7d6 Qb7b8+ Kd6d7 Qb8a7+ Rc6c7 Qa7d4+ Kd7c8 Qd4h8+ Kc8b7 Qh8b2+ Kb7c8 Qb2f6 Re7d7+ Kd3e2 Rc7c2 Qf6a6+ Kc8c7 Qa6a5+ Kc7c8 Qa5a8+ Kc8c7
20 00:35 19.625.224 558.873 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b2 Rc1c6 Qb2b7+ Kd7d6 Qb7b8+ Kd6d7 Qb8a7+ Rc6c7 Qa7d4+ Kd7c8 Qd4h8+ Kc8b7 Qh8b2+ Kb7c8 Qb2f6 Re7d7+ Kd3e2 Rc7c2 Qf6a6+ Kc8c7 Qa6a5+ Kc7c8 Qa5a8+ Kc8c7
21 00:54 30.537.120 566.079 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b7+ Rc1c7 Qb7d5+ Kd7c8 Qd5f5+ Kc8b7 Qf5b5+ Kb7c8 Qb5b6 Rc7d7+ Kd3c2 Rd7b7 Qb6g6 Re7d7 Kc2d1 Rb7c7 Qg6f6 Rd7e7 Qf6a6+ Kc8b8 Qa6b5+ Kb8c8
21 00:54 30.537.120 565.916 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b7+ Rc1c7 Qb7d5+ Kd7c8 Qd5f5+ Kc8b7 Qf5b5+ Kb7c8 Qb5b6 Rc7d7+ Kd3c2 Rd7b7 Qb6g6 Re7d7 Kc2d1 Rb7c7 Qg6f6 Rd7e7 Qf6a6+ Kc8b8 Qa6b5+ Kb8c8
22 01:23 47.270.442 565.245 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3d5 Rb7d7 Qd5a5
22 01:23 47.270.442 565.245 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3d5 Rb7d7 Qd5a5
23 02:25 83.027.682 570.498 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3g8+ Kb8a7 Qg8d8 Re7c7 Kd1e2
23 02:25 83.027.682 570.494 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3g8+ Kb8a7 Qg8d8 Re7c7 Kd1e2



Here is another interesting position where the Queen is not as strong as two rook

[D]3k4/2rr4/8/8/8/8/8/3KQ3 w - - 0 1

[pichy]

The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well. Some examples follow.
• A queen versus two rooks
• In the middlegame they are equal
• In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn

According to long time control engine matches between engines greater than 2700 Elo (CCRL scale) and with an Elo difference of 50 or less, with no minor pieces the 2 rooks are worth about 0.3 pawns more than the queen. If you add a pawn to the queen, then the queen + pawn is worth 0.7 pawns more than the 2 rooks.

Of course, the above situation (Q vs 2 R with no minors) depends on how many pawns are on the board. The rooks have their greatest advantage when there are 2 or 3 pawns on the board for each side (+0.5 pawns for the rooks vs a queen).

If you let this endgame to be played out to the end what do you think the outcome will be without using tablebase, Komodo is evaluating the position as favorable to White, but I gave Black to Houdini and White to Komodo and it ended in a draw search depth set to 34:

[D]4k3/5r2/8/8/8/8/3P2Q1/1r2K3 w - - 0 1

FEN: 4k3/5r2/8/8/8/8/3P2Q1/1r2K3 w - - 0 1

Komodo3-32:
1 00:00 4 39.999 -0.21 Ke1e2
2 00:00 858 8.579.999 -0.07 Ke1e2 Rf7e7+ Ke2d3 Re7d7+ Kd3c2
3 00:00 1.366 13.659.999 +0.02 Ke1e2 Rf7e7+ Ke2d3 Re7d7+ Kd3c2 Rb1b6
4 00:00 3.114 31.139.999 +0.02 Ke1e2 Rf7e7+ Ke2d3 Re7d7+ Kd3c2 Rb1b6
5 00:00 5.054 0 -0.01 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1c1 Ke2d3
5 00:00 5.054 50.539.999 -0.01 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1c1 Ke2d3
6 00:00 6.268 0 0.00 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1f1 Ke2d3 Rf7d7+ Kd3c2
6 00:00 6.268 62.679.999 0.00 Ke1e2 Ke8f8 Qg2a8+ Kf8g7 Qa8e4 Rb1f1 Ke2d3 Rf7d7+ Kd3c2
7 00:00 13.956 894.611 +0.04 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Ke2d3 Rb1b4 Qd5c5
7 00:00 13.956 894.611 +0.04 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Ke2d3 Rb1b4 Qd5c5
8 00:00 29.926 383.665 +0.08 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5e5 Rb1f1 Ke2d3 Rf1f4
8 00:00 29.926 383.665 +0.08 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5e5 Rb1f1 Ke2d3 Rf1f4
9 00:00 50.043 458.268 +0.07 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5h4+ Kh7g7 Qh4g4+ Kg7f8 Qg4d4 Kf8g8 Ke2d3
9 00:00 50.043 458.268 +0.07 Ke1e2 Ke8f8 Qg2d5 Kf8g8 Qd5g5+ Kg8h7 Qg5h4+ Kh7g7 Qh4g4+ Kg7f8 Qg4d4 Kf8g8 Ke2d3
10 00:00 123.799 466.812 +0.07 Ke1e2 Ke8f8 Qg2d5 Rb1f1 Ke2d3 Rf1f5 Qd5d4 Kf8g8 Kd3c2 Rf5b5 Qd4e4
10 00:00 123.799 466.812 +0.07 Ke1e2 Ke8f8 Qg2d5 Rb1f1 Ke2d3 Rf1f5 Qd5d4 Kf8g8 Kd3c2 Rf5b5 Qd4e4
11 00:00 244.797 506.196 +0.06 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8d4 Rb6d6 Qd4c5 Rf7f6 Ke2d1 Ke7f8 Kd1c2
11 00:00 244.797 506.196 +0.06 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8d4 Rb6d6 Qd4c5 Rf7f6 Ke2d1 Ke7f8 Kd1c2
12 00:00 372.430 518.992 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Qc3c5+ Rf7e7+ Ke2d3 Rb6f6 Kd3c2 Kf8f7 Qc5d5+ Kf7g7 Qd5c4
12 00:00 372.430 518.992 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Qc3c5+ Rf7e7+ Ke2d3 Rb6f6 Kd3c2 Kf8f7 Qc5d5+ Kf7g7 Qd5c4
13 00:01 504.340 521.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Kd1c2 Kf8g7 Qc3g3+ Rf6g6 Qg3e5+ Rf7f6 Qe5d4
13 00:01 504.340 521.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Kd1c2 Kf8g7 Qc3g3+ Rf6g6 Qg3e5+ Rf7f6 Qe5d4
14 00:01 758.570 534.353 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3a3+ Kf8g7 Qa3g3+ Rf6g6 Qg3e5+ Rg6f6 d2d4 Kg7f8 Kd1c2 Rf6f1
14 00:01 758.570 534.353 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3a3+ Kf8g7 Qa3g3+ Rf6g6 Qg3e5+ Rg6f6 d2d4 Kg7f8 Kd1c2 Rf6f1
15 00:02 1.309.882 541.720 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4
15 00:02 1.309.882 538.247 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4
16 00:04 2.199.003 518.240 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
16 00:04 2.199.003 518.240 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
17 00:06 3.161.019 530.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
17 00:06 3.161.019 530.442 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g1+ Kg7h7 Qg1d4 Kh7g7 Qd4g4+ Kg7f8
18 00:10 5.458.408 541.636 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g5+ Kg7f8 Qg5d5 Kf8g7 Qd5e5 Rf7b7 Qe5c5
18 00:10 5.458.408 541.636 +0.05 Ke1e2 Ke8f8 Qg2h2 Rb1b6 Qh2h8+ Kf8e7 Qh8c3 Ke7f8 Ke2d1 Rb6f6 Qc3c8+ Kf8g7 Qc8c5 Rf7d7 Kd1c2 Rd7f7 Qc5g5+ Kg7f8 Qg5d5 Kf8g7 Qd5e5 Rf7b7 Qe5c5
19 00:24 13.576.984 549.443 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1f1 Qh2d6 Kf8f7 Qd6d5+ Re7e6 Kd3c2 Rf1f6 Qd5h5+ Kf7g7 Qh5g4+ Kg7f8 Qg4b4+ Re6e7 Qb4c5 Kf8f7 Qc5c4+ Kf7g7 Qc4c8 Re7f7 Qc8g4+ Kg7f8
19 00:24 13.576.984 549.443 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1f1 Qh2d6 Kf8f7 Qd6d5+ Re7e6 Kd3c2 Rf1f6 Qd5h5+ Kf7g7 Qh5g4+ Kg7f8 Qg4b4+ Re6e7 Qb4c5 Kf8f7 Qc5c4+ Kf7g7 Qc4c8 Re7f7 Qc8g4+ Kg7f8
20 00:35 19.625.224 558.873 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b2 Rc1c6 Qb2b7+ Kd7d6 Qb7b8+ Kd6d7 Qb8a7+ Rc6c7 Qa7d4+ Kd7c8 Qd4h8+ Kc8b7 Qh8b2+ Kb7c8 Qb2f6 Re7d7+ Kd3e2 Rc7c2 Qf6a6+ Kc8c7 Qa6a5+ Kc7c8 Qa5a8+ Kc8c7
20 00:35 19.625.224 558.873 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b2 Rc1c6 Qb2b7+ Kd7d6 Qb7b8+ Kd6d7 Qb8a7+ Rc6c7 Qa7d4+ Kd7c8 Qd4h8+ Kc8b7 Qh8b2+ Kb7c8 Qb2f6 Re7d7+ Kd3e2 Rc7c2 Qf6a6+ Kc8c7 Qa6a5+ Kc7c8 Qa5a8+ Kc8c7
21 00:54 30.537.120 566.079 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b7+ Rc1c7 Qb7d5+ Kd7c8 Qd5f5+ Kc8b7 Qf5b5+ Kb7c8 Qb5b6 Rc7d7+ Kd3c2 Rd7b7 Qb6g6 Re7d7 Kc2d1 Rb7c7 Qg6f6 Rd7e7 Qf6a6+ Kc8b8 Qa6b5+ Kb8c8
21 00:54 30.537.120 565.916 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8b7+ Rc1c7 Qb7d5+ Kd7c8 Qd5f5+ Kc8b7 Qf5b5+ Kb7c8 Qb5b6 Rc7d7+ Kd3c2 Rd7b7 Qb6g6 Re7d7 Kc2d1 Rb7c7 Qg6f6 Rd7e7 Qf6a6+ Kc8b8 Qa6b5+ Kb8c8
22 01:23 47.270.442 565.245 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3d5 Rb7d7 Qd5a5
22 01:23 47.270.442 565.245 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3d5 Rb7d7 Qd5a5
23 02:25 83.027.682 570.498 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3g8+ Kb8a7 Qg8d8 Re7c7 Kd1e2
23 02:25 83.027.682 570.494 +0.05 Ke1e2 Ke8f8 Qg2h2 Rf7e7+ Ke2d3 Rb1c1 Qh2f4+ Kf8e8 Qf4b8+ Ke8d7 Qb8a7+ Kd7d8 Qa7a8+ Rc1c8 Qa8a5+ Rc8c7 Qa5b6 Re7d7+ Kd3e2 Rd7e7+ Ke2d1 Kd8c8 Qb6f6 Kc8b7 Qf6b2+ Kb7a7 Qb2a3+ Ka7b8 Qa3b3+ Rc7b7 Qb3g8+ Kb8a7 Qg8d8 Re7c7 Kd1e2



Here is another interesting position where the Queen is not as strong as two rook, this is a better test position
[D]3k4/2rr4/8/8/5Q2/8/8/3K4 w - - 0 1

[Guenther]

Each and every position you showed so far is either a 5 or 6men endgame.
I guess you have recently discovered them, this is fine but bad for a discussion about Q values.

Guenther