For how long can lone bishop stop king, knight and pawn?

Question

Recently I found quite surprising evaluations for me, especially in KNPP vs. KB, where the defending side could hold a draw just with waiting moves, not winning one of the pawns immediately. The h+f pawns with bishop holding promotion square is probably one of those theoretically most important and straightforward draws, but I saw many with pawns being on different files with one file gap and even pawns many files away like c+g.

I just wonder if there was some research on this topic and if there could be some rule said when position is drawn and when it is lost, in both KNP vs. (K)B and KNPP vs. KB. It looks like the bishop can stop some pawns almost forever, giving the king enough time to go sightseeing, grab a very distant pawn and return with very little stress to achieve a draw.

Answer 1

The reason why endgames are difficult, despite there being only a few pieces left on the board, is that many positions can only be evaluated by accurate calculation rather than by appealing to any rule. Rueben Fine in Basic Chess Endings says that KNPP vs KB "is in general a fairly simple win. The exceptions come only with a blockade" He then analyses seven examples of marginal cases. One very surprising example is that doubled pawns always win, a rare case of a universal rule. But even then, some accurate moves have to be found.

But some general advice is possible. For the superior side. Make active use of your King. Send him on ahead of the pawns and then escort them through. For the defender, try to keep your bishop on the longer of the two diagonals that control a crucial square. That will give a better chance of having waiting moves available. But always calculate.