The average value of the exchange (rook against a knight or a single bishop) is about 13/8 of a pawn. The advantage for the side with the rook is only 1 and 3/20 of a pawn if the opposing side has the bishop pair. If all the other minor pieces are still on the board, the value of the exchange drops by ¼ of a pawn. If, on the other hand, the queens and a pair of rooks have been exchanged off, it goes up by somewhat more than ¼ of a pawn. >

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Flear's Practical Endgame Play starts examination with some impressive statistics. In his own database of games by players rated over 2600, Flear counts 164 games with rook versus bishop and knight, the most common case.

< When pawns were equal, the rook won no games and lost 22; < with a one-pawn edge the Rook won 9 and lost 12; < with two pawns, the rook won 16 and lost 1. >>>

That’s a tremendous shift in results based on the number of pawns on each side. What accounts for such a disparity?

I dunno...let me take a flier

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check out <Rook vs. Two Minor Pieces> by Danish IM Esben Lund: His comments on Karpov vs Kasparov, 1985 after <47... h5>

click for larger view

<Kasparov writes that this endgame is objectively a draw, but that White will have to play very carefully to obtain it.<>>

Black should try to penetrate with his rook but must also do so without allowing too many pawn exchanges. However, I think White should, without too much difficulty, be able to prevent Black's rook from coming in.

48.Bc3 Rb8 49.Bb4 Rd8 50.Ke2 a3 51.Bc3 f6 52.Bb4 Kf7?!

"Kasparov criticizes this move as the king is poorly placed here later (the possibility of a knight check on d6 indirectly protects the pawn on f5). Instead he suggests 52...Kh7 with the idea that if White tries to use the same defensive idea as in the game, he will lose the kingside pawns and probably the game as well. 53.Bc3 Rb8 54.Bb4? (54.Nb4 Rb5 55.g4 Rb8 56.Kd3 Ra8 57.Na2 Ra4 58.Bb4 Kh6 59.Bd2+ and White has built up an impregnable fortress.) 54...Rb5! 55.g4 Rb8 56.Kd3 Rd8+ 57.Kc2 hxg4 58.hxg4 Rd4 59.Bxa3 Ra4 60.Kb3 Rxg4 61.Bc1 Rg3+ 62.Nc3 Rf3 63.Kc2 Rxf5 64.Kd3.

Kasparov writes that it is difficult to assess this endgame as there is no relevant material to compare it with, but Black would probably have excellent practical winning chances. I managed to find one position from the World Championship match between Steinitz and Zukertort - see next game." (Esben Lund)

53.Nc3 Rb8 54.Na2 Rb5 55.g4 Rb8 56.Kd3 Rd8+ 57.Kc4 Rd1 58.Bxa3 Ra1 59.Kb3 Rh1 60.gxh5 Rxh3+ 61.Nc3 Rf3

The problem with the king on f7 becomes evident in the line 61...Rxh5 62.Ne4 Rxf5? 63.Nd6+.

62.Bc1 Rxf5 63.h6 g6 64.Ne4 Rh5 65.Bb2 1/2

Lund continues with the Steinitz-Zukertort fragment and concludes that the rook and pawns most likely will win, and then returns to the position with after White's 64th move from Kasparovs analysis of <52...Kh7>.

However, his conclusion is confusing. First he writes: <The conclusion is that, instead of <52...Kf7?!>, <52...Kh7> probably leads to a win for Black with correct play.<>>, and then a few lines further down: <To recap, the game would still be a draw with precise play, but after <52...Kh7> Karpov would have to use a different defensive plan than in the game, as indicated in the notes - see the line beginning with <54.Nb4!>.<>>

Well, I admit, a lot of detail to pinpoint a minor mistake, since all in all Lund's lucid explanations are thorough and easy to understand.