# Where can I find a list of all theoretically possible piece combinations where checkmate is possible? (e.g. bishop and knight and pawn vs knight)

There are obvious ones that I know, like queen and rook (or either) vs lone king, and I also know you can't checkmate with only a bishop or knight, for instance.

But what if you have a rook and bishop vs a knight, is that possible? What if it's vs a knight but with eight pawns? I mean the list is endless. In short, I just want to know when it's a good idea just to say it's a draw vs other times you just keep trying and trying to get a checkmate. Thank you.

• To keep this list somewhat manageable, I think you should limit the number of pieces or otherwise restrict it. Also, by "checkmate is possible" do you mean that there has to be a forced mate sequence or would you also include piece combinations that can be mate if the opponent cooperates? – user1583209 Dec 16 '16 at 22:52
• Food for thought then, cause I guess I was mixing the two, both forced mate sequence and opponent cooperation. This whole thing occurred because I was doing some easy chess puzzles online (I'm an amateur) and one person was suggesting another line works as well because then you end up with rook and pawn vs knight, and that's a win, and I put it in the chess engine I had and went through like 20 moves and still did not seem to result in a win as they kept dancing around a pawn on e7. I wanted to know if this is a win, and so that's the genesis of my question.... – JSavant Dec 16 '16 at 23:07

The ones that are not possible are:

1. King + Bishop vs King
2. King + Knight vs King
3. King + Bishop vs King + Bishop if the bishops are on the same color square.

For the bishops, imagine black king on h1, black bishop on g1, white king on g3, white bishop on f3 giving mate. That isn't possible if the black bishop is also on a white square, say f1.

Otherwise, checkmate is possible with a given material balance.

For instance, of course rook and bishop vs knight can lead to checkmate, because checkmate with a lone rook is possible, and it is possible that the rest is captured.

Any material balance that includes a pawn can lead to checkmate, because pawns can turn into queens.

• Thanks, so it means rook vs knight is also possible? – JSavant Dec 16 '16 at 23:08
• @JSavant: sure, not necessarily forced, but it's obviously possible. – RemcoGerlich Dec 17 '16 at 22:36

I just want to know when it's a good idea just to say it's a draw vs other times you just keep trying and trying to get a checkmate.

I don't think you should base your decision on whether to play on, on the piece combination only. A few things that can happen are:

• A position might be theoretically won, but it is not easy if the opponent defends well (e.g. queen and king vs rook and king). The winning side might struggle giving mate within the 50 move limit.

• A position might be a theoretical draw, but very difficult to hold for the defender. You would want to play on in this case

• For some piece combinations also the position of pieces matters (e.g. central pawn vs side pawn).

• Some opponents might not be familiar with best play. In this case it is worth playing on drawn or lost positions.