The Chess Mind

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.

A few days ago, I expressed my surprise that the ending with two knights and a bishop against a rook was a draw. (Thanks to Andrey and mutlu for their very helpful comments!)

Yet even stranger, in a way, is that four knights vs. queen is a win for the knights. The material disparity, as traditionally conceived, is smaller, and that would seem to favor the queen against the knights. On the other hand, if the strong side has a 4-1 advantage in total toys, as opposed to the 3-1 edge in the earlier case, that numerical advantage may just be the crucial factor in favor of the Liliputians.

If you'd like to see how that unusual ending works out, go here and scroll down to entry 282.