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.
The ones that are not possible are:
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.
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.
