In general, the second rook is worth less than the first (there is some redundancy), but two rooks are much better specifically against a queen because once they are connected the queen can't bother either one. Of course there are exceptional positions, but it is nearly always a good idea to trade off your second rook for the opponent's sole rook when there are no queens on the board. With queens it becomes more complicated.Dann Corbit wrote: ↑Mon Jan 28, 2019 10:46 pmTwo rooks have a certain synergy together.
E.g.
One rook on the 7th is good. Two rooks on the 7th rank is savage. Utter devastation is just around the corner.
E.g.
Endgame KRRvk compared to KRvk
Both times the side with rook(s) win, but you can win much faster if the weaker king starts in the center of the board with 2 rooks than with 1.
They are also great for battery (e.g. Alekhine's gun variants).
If you have to have a duplicate of something then a queen would be wanted because of her power.
But if you could not have a queen, I would pick a rook, unless there was a driving reason to pick something else (e.g. one of those kinky knight underpromotion only mates).
How powerful is the Queen compared to 2 Rooks ?
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Re: How powerful is the Queen compared to 2 Rooks ?
Komodo rules!
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hgm
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Re: How powerful is the Queen compared to 2 Rooks ?
Although I do agree with the final conclusion, I am rather skeptical about the 'explanation'. I have always thought this concept of 'redundancy' to be a red herring, and that what sometimes is ascribed to redundancy in reality is due to the 'leveling effect' proposed by Ralph Betza: stronger pieces lose value when up against weaker opponent pieces.
When there is two Rooks against one, and the outcome is still at stake, the side with one Rook must have some other material in compensation. And if Queens are explicitly excluded, this must be minors. But the presence of these minors then devaluates both opponent Rooks, while the lone Rook is not bothered by minors (or by fewer minors), and thus effectively worth more. So trading it is a good deal for the player with two Rooks.
The leveling effect would predict the same for two unequal pieces of Rook value. E.g. a Rook plus a piece that moved as Knight or step one square diagonally. There would be no redundancy in that case (the pieces do not share a single move!), but it would still be favorable for the player that has R + augmented N to trade Rooks against an opponent that has R + B-pair.
A similar effect is very obvious in Capablanca Chess, where it is bad (like in orthodox Chess) to trade your Q for R+B if the other two super-pieces (Archbishop and Chancellor) are no longer present, but quite favorable when all A and C are still on the board: the remaining A and C devaluate because of the opposing R an B, while they are not so much impressed by an opposing Q. (More the other way around...) So trading A and C becomes quite favorable for the player that still has Q, while A and C are not really redundant w.r.t. Q (and in any case not more than w.r.t. R + B, which share the same moves with them as Q does).
When there is two Rooks against one, and the outcome is still at stake, the side with one Rook must have some other material in compensation. And if Queens are explicitly excluded, this must be minors. But the presence of these minors then devaluates both opponent Rooks, while the lone Rook is not bothered by minors (or by fewer minors), and thus effectively worth more. So trading it is a good deal for the player with two Rooks.
The leveling effect would predict the same for two unequal pieces of Rook value. E.g. a Rook plus a piece that moved as Knight or step one square diagonally. There would be no redundancy in that case (the pieces do not share a single move!), but it would still be favorable for the player that has R + augmented N to trade Rooks against an opponent that has R + B-pair.
A similar effect is very obvious in Capablanca Chess, where it is bad (like in orthodox Chess) to trade your Q for R+B if the other two super-pieces (Archbishop and Chancellor) are no longer present, but quite favorable when all A and C are still on the board: the remaining A and C devaluate because of the opposing R an B, while they are not so much impressed by an opposing Q. (More the other way around...) So trading A and C becomes quite favorable for the player that still has Q, while A and C are not really redundant w.r.t. Q (and in any case not more than w.r.t. R + B, which share the same moves with them as Q does).
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Graham Banks
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Re: How powerful is the Queen compared to 2 Rooks ?
I'll stick with my observations.Dann Corbit wrote: ↑Mon Jan 28, 2019 7:48 pmNote that two rooks are 2578 so a bit better than the queen in midgame. But it's close enough where it doesn't matter much.
Note that two rooks are 2756 so significantly better than the queen in the endgame.
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Nordlandia
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Re: How powerful is the Queen compared to 2 Rooks ?
Here is piece values for Gothic Chess (alternative to capablanca chess). The value for archbishop should be around 7 +/-
Source: http://www.angelfire.com/ultra/georgecm ... Chess.html
Fischer Random: http://www.symmetryperfect.com/shots/te ... -chess.pdf
Capablanca Random: http://www.symmetryperfect.com/shots/te ... s-capa.pdf
Source: http://www.angelfire.com/ultra/georgecm ... Chess.html
Fischer Random: http://www.symmetryperfect.com/shots/te ... -chess.pdf
Capablanca Random: http://www.symmetryperfect.com/shots/te ... s-capa.pdf
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Nordlandia
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Re: How powerful is the Queen compared to 2 Rooks ?
Rook plus pawn versus two bishops borderline position.
Originally it was black to move but SF displayed an advantage of -1.75. With white to move the advantage shrinked to -1.2 - 1.3. Those numbers is sustainable.
Originally it was black to move but SF displayed an advantage of -1.75. With white to move the advantage shrinked to -1.2 - 1.3. Those numbers is sustainable.
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Chessqueen
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Re: How powerful is the Queen compared to 2 Rooks ?
I will try with 5 pawns next, but of course I need at least 100 games according to Dann Corbit. I believe that with two equal programs like SF10 vs SF10 or Komodo vs Komodo a Queen can find too many squares to keep the two Rooks busy, but two Humans GMs probably the two Rooks with 5 pawns and Queen with 5 pawns, could be dificult for any GM to find the best moves or squares to force a drawlkaufman wrote: ↑Mon Jan 28, 2019 4:48 pmWith no minor pieces on the board and an average number of pawns (five per side), two rooks are nearly a pawn better than the queen. But on a full board the queen is indeed better than two rooks, as GM Roman Dzindzichashvilli taught me before computers were strong enough to answer the question. On average thruout the game the queen is a bit weaker.
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Chessqueen
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Re: How powerful is the Queen compared to 2 Rooks ?
I stopped the game since the score was 0.00 for the last 30 moves and I knew that SF10 could easy reach 50 moves with no advancement. I believe that with two equal programs like SF10 vs SF10 or Komodo vs Komodo a Queen can find too many squares to keep the two Rooks busy, but two Humans GMs probably the two Rooks with 5 pawns and Queen with 5 pawns, could be difficult for any GM to find the best moves or squares to force a draw.lkaufman wrote: ↑Mon Jan 28, 2019 4:48 pmWith no minor pieces on the board and an average number of pawns (five per side), two rooks are nearly a pawn better than the queen. But on a full board the queen is indeed better than two rooks, as GM Roman Dzindzichashvilli taught me before computers were strong enough to answer the question. On average thruout the game the queen is a bit weaker.
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Nordlandia
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Re: How powerful is the Queen compared to 2 Rooks ?
Trivial edge for white. Q is stronger than RNP but again supressed by redundancy.
Slight edge for black.
Maybe winning for white.
Slight edge for black.
Maybe winning for white.
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hgm
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Re: How powerful is the Queen compared to 2 Rooks ?
Totally wrong. As you can easily observe yourself an Queen vs Archbishop + Pawn imbalace is on average favorable for the side with the Archbishop. An in en-games A vs R+N and equal Pawns the Archbishop usually wins too, and an extra Pawn on the R+N side is needed to make it about equal.Nordlandia wrote: ↑Tue Jan 29, 2019 9:29 amHere is piece values for Gothic Chess (alternative to capablanca chess). The value for archbishop should be around 7 +/-
Source: http://www.angelfire.com/ultra/georgecm ... Chess.html
Fischer Random: http://www.symmetryperfect.com/shots/te ... -chess.pdf
Capablanca Random: http://www.symmetryperfect.com/shots/te ... s-capa.pdf
Accurate measurements show that Q-C ~ 50cP and Q-A ~ 75cP.
Also, non-royal King is not better than Knight in the opening.
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Nordlandia
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Re: How powerful is the Queen compared to 2 Rooks ?
Your implying black is the favourable side here.
2a2k4/pppppppppp/10/10/10/10/PPPPPPPP1P/4QK4 w - - 8 8
For the queen white has archbishop + pawn as compensation.
Capablanca Chess Pieces in staunton:
I have to say that the chancellor looks pretty much like the queen. It resembles more like an amazon if you ask me.
2a2k4/pppppppppp/10/10/10/10/PPPPPPPP1P/4QK4 w - - 8 8
For the queen white has archbishop + pawn as compensation.
Capablanca Chess Pieces in staunton:
I have to say that the chancellor looks pretty much like the queen. It resembles more like an amazon if you ask me.
Code: Select all
https://upload.wikimedia.org/wikipedia/en/e/e6/Gothic_chess_set_staunton.jpg