40a_R+B:R+N (the little inequality) II

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40a_R+B:R+N (the little inequality) II
Compiled by whiteshark

What difference does it make ?

" This is by far the most common NQE, with 8.8% of all 2600+ encounters involving this particular material imbalance. It's therefore evident that, as it's so relevant to practical play, it's an area a serious player would be wise to study.

The fact that the properties of a bishop differ from those of a knight lends itself to a number of generalities concerning the relative strength of these pieces. If we take an empty chessboard and place a bishop and a knight randomly in the central arena, we notice that the bishop can have as many as 13 possible moves whereas a knight can at best only have eight.

The logical deduction would be that the bishop is potentially a better piece, and it's true that most GMs, if given the choice, will take the bishop.

As we know, however, there are a number of positions where a knight can at least hold its own, so chess commentators have developed a consensus view of the relative merits of the minor pieces in different types of position:

1 . A bishop is generally stronger than a knight when the position is open, if the pawns are broken, or play is on both flanks.

2. A knight is often better than a bishop in fairly closed positions, if play is on a limited front, or if the bishop is restricted by its own pawns.

If we tum our attention to the main subject of this chapter, in which each side has a rook as well as a minor piece, then a common view in books is that rook and bishop are worth more than rook and knight. Having surveyed many examples of this NQE I'm not sure that I agree. The broad arguments that I've mentioned above are frequently overturned, for instance by a slight alteration in the pawn structure, a better-placed king or by several other factors."

Glenn Flear, Practical Endgame Play beyond the basics (chapter 12)

= ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ =

"In general the line-up of rook plus bishop is rather stronger than rook and knight <to a large extent this depends on structure>, but a few grandmasters for example Evgeny Sveshnikov, think the reserve. Rook and knight is stronger when there are <fixed weaknesses> or, for example, when there are <doubled pawns>."

Alexander Beliavsky + Adrian Mikhalchishin in <Winning Endgame Strategy>

= ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ =

Müller/Lamprecht say that 15% of all games reach an ending of rook and minor piece vs rook and minor piece, so that you can expect to get such one in every tournament.

Their statistics, with relative percentage frequencies, rounded:

♖♗ vs ♖♘ (45%) ♖♗ vs ♖♗ (22%) some coloured ♗
♖♗ vs ♖♗ (13%) opp. coloured ♗
♖♘ vs ♖♘ (20%).

= ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ = ♖ ♗ = ♖ ♘ =

educational video http://www.youtube.com/watch?v=iQum... Karpov's ensuing technique is absolutely brilliant, patiently massaging black's pawn weaknesses until he senses the critical moment to sacrifice his queenside pawns to form a potentially winning mating net around black's king on the kingside. Karpov's positional pressure and subsequent technical conversion in this game is extremely instructional as he wears down Kramnik's defense with a long series of threats to finish the game with a devastating tactical sequence.

H Ree vs U Geller, 1968
(C00) French Defense, 57 moves, 1/2-1/2
V Sanduleac vs M Dambacher, 2015
(C53) Giuoco Piano, 65 moves, 0-1
V Sanduleac vs L Schandorff, 2003
(B17) Caro-Kann, Steinitz Variation, 78 moves, 0-1
Carlsen vs Short, 2004
(D37) Queen's Gambit Declined, 54 moves, 1-0
R Koehler vs C Braun, 2016
(E76) King's Indian, Four Pawns Attack, 61 moves, 0-1
Geller vs Najdorf, 1953
(B92) Sicilian, Najdorf, Opocensky Variation, 57 moves, 1-0
Najdorf vs Averbakh, 1953
(E17) Queen's Indian, 41 moves, 0-1
Xiong vs J van Foreest, 2017
(E62) King's Indian, Fianchetto, 64 moves, 1-0
T Lei vs M Ragger, 2017
(E60) King's Indian Defense, 84 moves, 0-1
Korchnoi vs Huebner, 1984
(D55) Queen's Gambit Declined, 52 moves, 1/2-1/2
I Malakhov vs V Artemiev, 2016
(B22) Sicilian, Alapin, 110 moves, 1/2-1/2
Rapport vs Aronian, 2016
(A06) Reti Opening, 87 moves, 1-0
H Jonkman vs Tiviakov, 2002
(B22) Sicilian, Alapin, 49 moves, 0-1
Gelfand vs S Maze, 2017
(E04) Catalan, Open, 5.Nf3, 57 moves, 1-0
A Machulsky vs A Yusupov, 1978
(C42) Petrov Defense, 69 moves, 1/2-1/2
V Laznicka vs M Ragger, 2017
(A48) King's Indian, 126 moves, 1/2-1/2
Abdusattorov vs Bluebaum, 2017
(C03) French, Tarrasch, 46 moves, 0-1
E Iturrizaga Bonelli vs H Olafsson, 2017
(E04) Catalan, Open, 5.Nf3, 67 moves, 1-0
J van Foreest vs A Moskalenko, 2017
(B30) Sicilian, 44 moves, 1/2-1/2
F Doettling vs S Siebrecht, 2005
(E60) King's Indian Defense, 45 moves, 1-0
Shirov vs V S Gujrathi, 2016
(B12) Caro-Kann Defense, 60 moves, 1-0
Gheorghiu vs R Byrne, 1980
(D58) Queen's Gambit Declined, Tartakower (Makagonov-Bondarevsky) Syst, 47 moves, 1/2-1/2
S Brynell vs J Vang Glud, 2017
(D58) Queen's Gambit Declined, Tartakower (Makagonov-Bondarevsky) Syst, 72 moves, 0-1
L Babujian vs R Aghasaryan, 2017
(D58) Queen's Gambit Declined, Tartakower (Makagonov-Bondarevsky) Syst, 69 moves, 1/2-1/2
Psakhis vs S Semkov, 1982
(D42) Queen's Gambit Declined, Semi-Tarrasch, 7.Bd3, 112 moves, 1-0
B M Ochsner vs J Pfreundt, 2017
(B33) Sicilian, 70 moves, 1-0
Gelfand vs Harikrishna, 2017
(E06) Catalan, Closed, 5.Nf3, 52 moves, 1-0
Giri vs Karjakin, 2017
(D37) Queen's Gambit Declined, 76 moves, 1/2-1/2
Ivanchuk vs E Inarkiev, 2010
(B13) Caro-Kann, Exchange, 45 moves, 0-1
N V Pedersen vs E Najer, 2005
(A31) English, Symmetrical, Benoni Formation, 53 moves, 0-1
RB4:RN3
Aronian vs V Gashimov, 2012
(A70) Benoni, Classical with 7.Nf3, 48 moves, 1-0
Tal vs Knaak, 1979
(E96) King's Indian, Orthodox, 7...Nbd7, Main line, 58 moves, 1-0
Tal vs Larsen, 1979
(B16) Caro-Kann, Bronstein-Larsen Variation, 51 moves, 1/2-1/2
M Lewicki vs V Malaniuk, 2012
(C53) Giuoco Piano, 45 moves, 0-1
Psakhis vs Kupreichik, 1984
(D31) Queen's Gambit Declined, 60 moves, 0-1
Rapport vs Jakovenko, 2017
(E20) Nimzo-Indian, 86 moves, 0-1
Q L Le vs Naiditsch, 2017
(E73) King's Indian, 49 moves, 1/2-1/2
V Fedoseev vs D Andreikin, 2017
(D37) Queen's Gambit Declined, 59 moves, 1-0
V Akopian vs Y Wang, 2010
(C42) Petrov Defense, 74 moves, 0-1
#net
I Aloni vs Fischer, 1968
(E43) Nimzo-Indian, Fischer Variation, 44 moves, 0-1
Andersson vs S B Hansen, 1999
(B39) Sicilian, Accelerated Fianchetto, Breyer Variation, 53 moves, 1-0
Korchnoi vs Huebner, 1973
(D58) Queen's Gambit Declined, Tartakower (Makagonov-Bondarevsky) Syst, 43 moves, 1/2-1/2
Svidler vs Caruana, 2009
(C80) Ruy Lopez, Open, 43 moves, 0-1
J de la Villa Garcia vs Suba, 1989
(B80) Sicilian, Scheveningen, 59 moves, 1/2-1/2
Z Tsydypov vs A Saveliev, 2012
(C00) French Defense, 53 moves, 1-0
Jakovenko vs Svidler, 2017
(C50) Giuoco Piano, 52 moves, 1-0
B Adhiban vs J van Foreest, 2017
(D26) Queen's Gambit Accepted, 62 moves, 1-0
E Valdimarsson vs N Grandelius, 2016
(D00) Queen's Pawn Game, 47 moves, 1-0
Z Ma vs V Malakhov, 2017
(B08) Pirc, Classical, 83 moves, 1/2-1/2
V H Nguyen vs Z Ma, 2012
(A46) Queen's Pawn Game, 42 moves, 1-0
Svidler vs E Romanov, 2017
(B42) Sicilian, Kan, 46 moves, 1-0
A Loginov vs Korneev, 2013
(B42) Sicilian, Kan, 44 moves, 0-1
Miles vs J Ochkoos, 2001
(D00) Queen's Pawn Game, 57 moves, 1/2-1/2
A Yusupov vs Rozentalis, 1995
(E54) Nimzo-Indian, 4.e3, Gligoric System, 50 moves, 1-0
Averbakh vs Taimanov, 1948
(E29) Nimzo-Indian, Samisch, 65 moves, 1-0
Aronian vs Shirov, 2007
(D20) Queen's Gambit Accepted, 67 moves, 1/2-1/2
Goryachkina vs D Yuffa, 2016
(A56) Benoni Defense, 53 moves, 1/2-1/2
Carlsen vs Grischuk, 2015
(B92) Sicilian, Najdorf, Opocensky Variation, 66 moves, 0-1
H Rolletschek vs E Frosch, 2002
(C69) Ruy Lopez, Exchange, Gligoric Variation, 53 moves, 0-1
Simagin vs Korchnoi, 1955
(D77) Neo-Grunfeld, 6.O-O, 61 moves, 1-0
Andersson vs Spassky, 1971
(A06) Reti Opening, 51 moves, 1/2-1/2
S Ivanov vs V Yemelin, 1998
(E34) Nimzo-Indian, Classical, Noa Variation, 55 moves, 1/2-1/2
G Meier vs J Vykouk, 2018
(A15) English, 61 moves, 1-0
K Ruben vs S Khan, 1930
(E15) Queen's Indian, 74 moves, 1-0
instructive
L Sawlin vs D Kollars, 2018
(C55) Two Knights Defense, 75 moves, 1/2-1/2
S Milliet vs B Ider, 2013
(C18) French, Winawer, 53 moves, 0-1
Geller vs Kasparov, 1979
(B07) Pirc, 64 moves, 1/2-1/2
V Spasov vs Tal, 1990
(C07) French, Tarrasch, 53 moves, 1-0
Bareev vs J Polgar, 2007
(A46) Queen's Pawn Game, 47 moves, 1/2-1/2
Saemisch vs Tartakower, 1925
(D44) Queen's Gambit Declined Semi-Slav, 60 moves, 1/2-1/2
R Alvarez Ibarra vs Suba, 1992
(A70) Benoni, Classical with 7.Nf3, 38 moves, 0-1
L Vogt vs Andersson, 1975
(B84) Sicilian, Scheveningen, 46 moves, 0-1
großes Kino
Tartakower vs M Marchand, 1920
(A13) English, 60 moves, 1-0
A Dimitrova vs O Gritsayeva, 2018
(C04) French, Tarrasch, Guimard Main line, 66 moves, 0-1
V Akopian vs Bacrot, 2009
(B30) Sicilian, 57 moves, 1-0
Bacrot vs Tiviakov, 2009
(B36) Sicilian, Accelerated Fianchetto, 69 moves, 1-0
Zugzwang
Spielmann vs Reti, 1925
(C65) Ruy Lopez, Berlin Defense, 30 moves, 1-0
RB4:RN3
Karpov vs Huebner, 1972
(B42) Sicilian, Kan, 74 moves, 1-0
R Haria vs J Christiansen, 2018
(C01) French, Exchange, 63 moves, 1/2-1/2
N+1
Uhlmann vs Fischer, 1970
(A65) Benoni, 6.e4, 34 moves, 0-1
RB3:RN4||
A Zaitsev vs Stein, 1971
(D90) Grunfeld, 72 moves, 1/2-1/2
Larsen vs N Krogius, 1966
(A05) Reti Opening, 63 moves, 1-0
P Panagopoulos vs A Prameshuber, 1954
(C18) French, Winawer, 50 moves, 1/2-1/2
H Bharathakoti vs Sutovsky, 2018
(D70) Neo-Grunfeld Defense, 61 moves, 1/2-1/2
R Praggnanandhaa vs G Meier, 2018
(C11) French, 110 moves, 1/2-1/2
Avrukh vs Kamsky, 2007
(A64) Benoni, Fianchetto, 11...Re8, 53 moves, 0-1
AlphaZero vs Stockfish, 2018
(A35) English, Symmetrical, 236 moves, 1/2-1/2
B+1
N Grandelius vs R Svane, 2018
(A19) English, Mikenas-Carls, Sicilian Variation, 49 moves, 1-0
Vachier-Lagrave vs Anand, 2018
(C83) Ruy Lopez, Open, 40 moves, 0-1
--> Q
T Karolyi vs Hjartarson, 1981
(D58) Queen's Gambit Declined, Tartakower (Makagonov-Bondarevsky) Syst, 95 moves, 1-0
Alekhine vs Vidmar, 1936
(D65) Queen's Gambit Declined, Orthodox, Rubinstein Attack, Main line, 71 moves, 1-0
Karpov vs Smyslov, 1977
(C82) Ruy Lopez, Open, 69 moves, 1/2-1/2
T Shaked vs S Boring, 1991
(A12) English with b3, 45 moves, 0-1
Khismatullin vs A Sarana, 2019
(B23) Sicilian, Closed, 55 moves, 0-1
RB4:RN3||
Y Yu vs Rapport, 2019
(C07) French, Tarrasch, 75 moves, 1/2-1/2
Timman vs C Lutz, 1994
(B52) Sicilian, Canal-Sokolsky (Rossolimo) Attack, 92 moves, 1/2-1/2
Radjabov vs Kasparov, 2004
(C45) Scotch Game, 58 moves, 1/2-1/2
Bogoljubov vs K Richter, 1933
(A46) Queen's Pawn Game, 77 moves, 1-0
A Becker vs Keres, 1937
(A46) Queen's Pawn Game, 51 moves, 1-0
Alekhine vs Euwe, 1922
(D02) Queen's Pawn Game, 50 moves, 1-0
E Cordova vs Sevian, 2017
(A04) Reti Opening, 82 moves, 1-0
Romanishin vs Marjanovic, 1980
(A08) King's Indian Attack, 58 moves, 1-0
K Piorun vs Lupulescu, 2021
(D40) Queen's Gambit Declined, Semi-Tarrasch, 45 moves, 1-0
Bogoljubov vs Alekhine, 1921
(A50) Queen's Pawn Game, 54 moves, 0-1
Rublevsky vs Zvjaginsev, 2016
(C42) Petrov Defense, 66 moves, 0-1
6:6
J Plaskan vs M Mingachev, 2006
(C42) Petrov Defense, 47 moves, 1/2-1/2
Saemisch vs J H Donner, 1968
(A48) King's Indian, 62 moves, 0-1
D Frolyanov vs S Sargsyan, 2021
(B10) Caro-Kann, 51 moves, 0-1
R Reynolds vs B Garfinkel, 1988
(C17) French, Winawer, Advance, 57 moves, 1-0
3+3:4:2
Caruana vs Duda, 2022
(B90) Sicilian, Najdorf, 51 moves, 1/2-1/2
M Bagi vs Nisipeanu, 2022
(C01) French, Exchange, 83 moves, 1/2-1/2
111 games

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