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R and K. v. B and K, no pawns

R and K. v. B and K, no pawns

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z

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Draw or can R and K win by careful manoevouring?

s

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Depends on the position (as usual)

If the weaker side's king is on the edge of the board, mating threats can be combined with threats of taking the bishop to force the weaker side to part with his bishop.

I am not sure but I doubt you can force the weaker side's king to the edge when it is in the middle of the board.

c

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Originally posted by schakuhr
Depends on the position (as usual)

If the weaker side's king is on the edge of the board, mating threats can be combined with threats of taking the bishop to force the weaker side to part with his bishop.

I am not sure but I doubt you can force the weaker side's king to the edge when it is in the middle of the board.
Uh, kinda right, but not really.

It depends on the corner. So if black has the B + K (assume the bishop is dark squared) and white has the R+K than black needs to get his king to a light squared corner of the board in order to draw. For example, the square F1. This way, the dark squared bishop can block checks from the rook.

p

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Here are 35 examples.

http://www.personalchesstraining.com/main.php?request=possBoards&track=41

g

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Unless there's something special about the position, then K&R vs. K&B is a theoretical draw. K&R vs. K&N is also a theoretical draw.

Of course, the greatest injustice in chess is the fact that K+N+N vs. K is an easy draw.

p

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Originally posted by gaychessplayer
Unless there's something special about the position, then K&R vs. K&B is a theoretical draw. K&R vs. K&N is also a theoretical draw.

Of course, the greatest injustice in chess is the fact that K+N+N vs. K is an easy draw.
I'm glad you pointed out these other positions; many times underpromotion to a knight is the only way to draw against a rook.

g

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Originally posted by petrovitch
I'm glad you pointed out these other positions; many times underpromotion to a knight is the only way to draw against a rook.
Sorry, but I didn't understand your post. Were you being sarcastic about what I said , or were you making a joke that I don't understand? (It wouldn't be the first time that I didn't understand a joke on this site. 😛)

IC

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http://en.wikipedia.org/wiki/Pawnless_chess_endgames

Fine's rule

In his landmark 1941 book Basic Chess Endings, Reuben Fine inaccurately stated that in endgames without pawns, at least the advantage of a rook (or equivalent material) is required to win, with two exceptions in which less of an advantage is sufficient (chapter IX of the first edition). The advantage of a rook corresponds to a five-point material advantage using the traditional relative value of the pieces (pawn=1, knight=3, bishop=3, rook=5, queen=9). The two exceptions noted by Fine are (1) the double exchange — two rooks versus any two minor pieces, and (2) four minor pieces versus a queen. (Fine & Benko 2003:585). It turns out that there are several exceptions, but they are endgames that rarely occur in actual games (except for perhaps a queen versus a rook).

A four-point material advantage is often enough to win in some endings without pawns. For example, a queen wins versus a rook (as mentioned above, but 31 moves may be required); as well as when there is matching additional material on both sides, i.e.: a queen and any minor piece versus a rook and any minor piece; a queen and a rook versus two rooks; and two queens versus a queen and a rook. Another type of win with a four-point material advantage is the double exchange—two rooks versus any two minor pieces. There are some other endgames with four-point material differences that are generally long theoretical wins, but the fifty move rule comes into play in competition because in general more than fifty moves are required to either checkmate or reduce the endgame to a simplier case: two bishops and a knight versus a rook (68 moves); and two rooks and a minor piece versus a queen (82 moves for the bishop, 101 moves for the knight).

A three-point material advantage can also result in a forced win, in some cases. For instance, some of the cases of a queen versus two minor piece are such positions (as mentioned above). In addition, the four minor pieces win against a queen.

There are some long general theoretical wins with only a two- or three-point material advantage but the fifty move rule usually comes into play because of the number of moves required: two bishops versus a knight (66 moves); a queen and bishop versus two rooks (two-point material advantage, can require 84 moves); a rook and bishop versus a bishop on the opposite color and a knight (a two-point material advantage, requires up to 98 moves); and a rook and bishop versus two knights (two-point material advantage, but it requires up to 222 moves!) (Müller & Lamprecht 2001:400-6) (Nunn 2002:325-29).

Finally, there are some other unusual exceptions to Fine's rule involving underpromotions. Some of these are (1) a queen wins against three bishops of the same color (no difference in material points), up to 51 moves are required; (2) a rook and knight win against two bishops on the same color (two point difference), up to 140 moves are needed; and (3) three bishops (two on the same color) win against a rook (four point difference), requiring up to 69 moves, and (4) four knights win against a queen (85 moves). This was proved by computer in 2005 and was the first ending with seven pieces that was completely solved.

z

127.0.0.1

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Originally posted by cmsMaster
Uh, kinda right, but not really.

It depends on the corner. So if black has the B + K (assume the bishop is dark squared) and white has the R+K than black needs to get his king to a light squared corner of the board in order to draw. For example, the square F1. This way, the dark squared bishop can block checks from the rook.
Here is a game where I employed this tactic to draw.
Game 4444240

Unfortunately it has no history but it was a very interesting game. French, after playing f6 and fxe, I played Rxf3 to create attacking chances and the game eventually became B + N + 7 pawns vrs R + R + 4 pawns which somehow simplified down into the drawn bishop vrs rook ending.

b

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Originally posted by Ice Cold
http://en.wikipedia.org/wiki/Pawnless_chess_endgames

(pawn=1, knight=3, bishop=3, rook=5, queen=9). The two

A four-point material advantage is often enough to win in some endings without pawns.
how do you have a 4 point advantage without pawns?

z

127.0.0.1

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Originally posted by bdh191
how do you have a 4 point advantage without pawns?
One example would be:
N + N + B + B vrs Q + N

however, the point is that if you have that 4 point advantage it should be enough to win. Whereas say a 2 point advantage (R vrs B) or even some 3 point (B + B vrs B) may not be enough.

JoL
Curb Your Enthusiasm

London

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Originally posted by zebano
One example would be:
N + N + B + B vrs Q + N
....
A simpler one would be Q v R

z

127.0.0.1

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Originally posted by JonathanB of London
A simpler one would be Q v R
lol. Mine isn't even an advantage. I listed "equal" material.

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