# Sufficient mating material, less a king?

As an extension to this question about can a rook and knight without a king stalemate a opposing king, and the traditional minimum-mating-material question, I had a puzzle question:

What are the minimum combinations of material (without a king) required to forcibly mate an opposing king?

• R + R/Q is clearly sufficient

• R + N + N/B maybe, as an extension from the above stalemate question

On the other hand, there are some sets that fail without a king:

• B(w) + B(b) (but 3 bishops should work, so long as one is on a different color)
• 3 bishops do not work to force a mate - the lone color bishop is not sufficient to force the king to a corner. Four bishops works though. Four knights, but not three (I think, after trying for a while). This would best be answered by an engine which can calculate without a King. Commented Jul 2, 2016 at 23:47

Assuming opponent has no pieces:

1. 4 or more knights

2. 4 or more bishops, at least 2 per side

3. At least 2 pawns, but it also depends on where the pawns are

4. 2 or more major pieces

5. Queen and a minor piece

6. Rook and 2 minor pieces

7. 4 minor pieces

8. Pawn+Minor pieces/2 Minor Pieces(depending on where the pawn is or a major piece

If opponent have pieces:

1. Queen(maybe rook)+Minor Piece vs 1 pawn

2. Queen(maybe rook)+2 pawns vs Rook+Bishop+Pawn

3. Q+R vs Rook and bishop or 2 minor pieces(for most positions)

• So it's 10 points or higher. Come to think of it, since K is ~4 points in strength, the traditional KBB/KBN is about 10 points. KR = 9 is exception. Commented Jul 5, 2016 at 16:10
• @jf328 Yes, without pawns Commented Jul 5, 2016 at 16:11
• In the 4 bishops case, you'll need at least two bishops from each colour, not one. Commented Jul 5, 2016 at 19:40
• @jf328 Then maybe we could set K as 5 points, but then some pawnless endgames where a minor piece up is enough, or Qv 4minor piece Commented Jul 6, 2016 at 3:04
• Note that KNN = 10 is also an exception. Commented Jul 6, 2016 at 8:38