The Chess Mind

By Dennis Monokroussos.
This is a blog for chess fans by a chess fan, one who loves the beauty of the game and wants to share it with those who are like-minded.
Yet the chess mind is not only a chess mind, and other topics, such as philosophy, may appear from time to time. All material copyrighted.
A Bizarre Ending
I recently came across an old Karpov-Kasparov game from 1991, and it featured a material imbalance I'd never seen before in an endgame: two knights and a bishop against a rook, with no pawns for either side. Kasparov drew with the rook, but I wonder what's supposed to happen with best play. Here are my preliminary thoughts on the topic:

1. Because two knights vs. a king is a draw, White always has to watch for RxB sacs.

2. By analogy with B+N vs. K, the minor pieces will probably have more success generating mating threats if the weaker side's king is forced into a corner of the same color as the strong side's bishop.

3. The fact that Karpov didn't succeed in winning at a time when - I think - adjournments were still in place strongly suggests that the ending is (generally) drawn. There's no tablebase data on this ending, however (or if there is, it's brand new and not in my possession), so I don't know for sure.

John Nunn has a book treating pawnless endings - if any of you has that and could look up this ending and pass along the findings (if any), that would be great. (Likewise if anyone has genuine knowledge about this ending from some other source.)

Thanks, readers, and you can replay the game here.

Related Posts (on one page):

  1. Another Bizarre Ending
  2. A Bizarre Ending
Posted by Dennis Monokroussos on Thursday June 30, 2005 at 12:47am
Andrey:
6 piece tablebases give a draw. If you have two bishops and a knight, then it is a win, although I came up with positions that require more than 50 moves for White to win.
6.30.2005 2:00am
Andrey:
The maximum I could get is 60 moves to win (for 2B+N vs R). For 2N+B vs R you can cook up some positions that are lost. I only could come up with such positions if you put the king of the weakest side already into the corner of bishop's color (that is not enough of course). Then there are some positions where you need 11 (maybe more, but I could only get 11) moves to win (meaning that some trivial one-move win is not the only way this ending can be won).
6.30.2005 2:32am
Andrey:
Forget 11! Look at this position: (unfortunately, can't put a picture here) White: Kg6, Nf5, Ng5, Ba4. Black: Kf8, Rh1. Note that black king is far from the bishop's color corner. In this position, White to move checkmates in 30 moves! Black to move draws. After 1. Ne6 Kg8 2. Nh6 Kh8 (Rxh6 is the best, but suppose we want to keep the rook as long as possible) 3. Ng5 Rg2 4. Bc6 Rg1 5. Bb7 Rg3 6. Kf6 Re3 7. Bc8 Black has to give up his rook to avoid mate Ngf7 and Bf5.
6.30.2005 3:36am
mutlu:
Dennis, you can query 6-piece Nalimov tabebases online at this site for free:
http://www.k4it.de/index.php?topic=egtb&lang=en
6.30.2005 9:38am