Sufficient mating material, less a king?

Question

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

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

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. — Daniel, Jul 02 '16 at 23:47

Ariana · Answer 1 · 2016-07-09T10:55:54.920

4

Assuming opponent has no pieces:

4 or more knights
4 or more bishops, at least 2 per side
At least 2 pawns, but it also depends on where the pawns are
2 or more major pieces
Queen and a minor piece
Rook and 2 minor pieces
4 minor pieces
Pawn+Minor pieces/2 Minor Pieces(depending on where the pawn is or a major piece

If opponent have pieces:

edited Jul 09 '16 at 10:55

answered Jul 05 '16 at 15:49

Ariana

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. – jf328 Jul 05 '16 at 16:10
@jf328 Yes, without pawns – Ariana Jul 05 '16 at 16:11
1

In the 4 bishops case, you'll need at least two bishops from each colour, not one. – Glorfindel Jul 05 '16 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 – Ariana Jul 06 '16 at 03:04
Note that KNN = 10 is also an exception. – Glorfindel Jul 06 '16 at 08:38
@Glorfindel KBB* – Ariana Jul 06 '16 at 08:48
No, I meant King + 2 Knights = 10 points, but not sufficient enough to enforce mate. – Glorfindel Jul 06 '16 at 08:56
@Glorfindel Oh ok – Ariana Jul 06 '16 at 09:23

1 Answers1