R vs B and N

I recently played over an interesting ending from Donaldson-Bisguier that relates to a  couple of previous posts I made concerning minor piece against Rook endings.

Minor Piece for Rook - Part 1

Minor Piece for Rook - Part 2

In the below position (White to move) Bisguier stated that he felt he could win the game with either color.  I take that to mean he felt that, as the stronger player, he could win it from either side.   Regardless of generalities these endings are very difficult and we are speaking of averages so many other factors are likely to influence the results.
To sum up:

In the opening:

2 minor pieces = R = 2P’s

2B’s = R + 2-1/2 P’s

In the ending (with P’s, but no additional pieces):

2 minor pieces = R + 1/2 P

2B’s = R + 1-1/2 P’s

The R has the least value in the opening and Purdy observed that the biggest jump happens “with the last exchange of pieces just before the ending.”  He said that if you add a piece to each side, the minor pieces increase in value.

In Basic Chess Endings, Fine wrote, “Three pieces versus a Rook (with equal P’s) is normally a draw, but in favor of the pieces because they have more play.”  Purdy observes that this is true but 2N’s and a B aren’t as good as a N and 2B’s because a B+N or 2N’s, without other pieces, are generally not a good team.

If all this sounds complicated and difficult to remember, it is.  This is why I think Bisguier said that against a weaker player, he could win with either color.

In the starting position, which is complicated even more because of the extra material, the engine evaluation was about 1-1/2 P advantage to White, Black is about to win another P leaving a highly unbalanced material situation that is very difficult to play.