Answers.Body: <p>Assuming opponent has no pieces:</p>
  
  <ol>
  <li><p>4 or more knights</p></li>
  <li><p>4 or more bishops, at least 2 per side</p></li>
  <li><p>At least 2 pawns, but it also depends on where the pawns are</p></li>
  <li><p>2 or more major pieces</p></li>
  <li><p>Queen and a minor piece</p></li>
  <li><p>Rook and 2 minor pieces</p></li>
  <li><p>4 minor pieces</p></li>
  <li><p>Pawn+Minor pieces/2 Minor Pieces(depending on where the pawn is or a major piece</p></li>
  </ol>
  
  <p>If opponent have pieces:</p>
  
  <ol>
  <li><p>Queen(maybe rook)+Minor Piece vs 1 pawn</p></li>
  <li><p>Queen(maybe rook)+2 pawns vs Rook+Bishop+Pawn</p></li>
  <li><p>Q+R vs Rook and bishop or 2 minor pieces(for most positions)</p></li>
  </ol>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-07-05T16:10:35.227Z
Answers.Text: 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.
Answers.UserDisplayName: jf328
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Answers.CreationDate: 2016-07-05T16:11:11.737Z
Answers.Text: @jf328 Yes, without pawns
Answers.UserDisplayName: Ariana
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Answers.CreationDate: 2016-07-05T19:40:22.123Z
Answers.Text: In the 4 bishops case, you'll need at least *two* bishops from each colour, not one.
Answers.UserDisplayName: Glorfindel
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Answers.CreationDate: 2016-07-06T03:04:11.687Z
Answers.Text: @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
Answers.UserDisplayName: Ariana
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-07-06T08:38:19.683Z
Answers.Text: Note that KNN = 10 is also an exception.
Answers.UserDisplayName: Glorfindel
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-07-06T08:48:07.640Z
Answers.Text: @Glorfindel KBB*
Answers.UserDisplayName: Ariana
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Answers.CreationDate: 2016-07-06T08:56:35.537Z
Answers.Text: No, I meant King + 2 Knights = 10 points, but not sufficient enough to enforce mate.
Answers.UserDisplayName: Glorfindel
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Answers.CreationDate: 2016-07-06T09:23:40.677Z
Answers.Text: @Glorfindel Oh ok
Answers.UserDisplayName: Ariana
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Answers.LastActivityDate: 2016-07-09T10:55:54.920Z
Answers.LastEditDate: 2016-07-09T10:55:54.920Z
Answers.UserDisplayName: Ariana
Body: <p>As an extension to this question about <a href="https://puzzling.stackexchange.com/questions/36874/can-whites-rook-and-knight-without-moving-white-king-force-stalemate">can a rook and knight <em>without a king</em> stalemate a opposing king</a>, and the <a href="https://chess.stackexchange.com/questions/5028/what-is-sufficient-mating-material">traditional minimum-mating-material question</a>, I had a puzzle question:</p>
  
  <p>What are the minimum combinations of material (without a king) required to forcibly mate an opposing king? </p>
  
  <ul>
  <li><p>R + R/Q is clearly sufficient</p></li>
  <li><p>R + N + N/B maybe, as an extension from the above stalemate question</p></li>
  </ul>
  
  <p>On the other hand, there are some sets that fail without a king:</p>
  
  <ul>
  <li>B(w) + B(b) (but 3 bishops should work, so long as one is on a different color)</li>
  </ul>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-07-02T23:47:42.607Z
Comments.Text: 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.
Comments.UserDisplayName: Daniel
Tags: <checkmate><material>
Title: Sufficient mating material, less a king?
ThreadText: # Sufficient mating material, less a king?
  
  (Asked by: username_0 on 2016-07-01)
  
  As an extension to this question about [can a rook and knight *without a king* stalemate a opposing king](https://puzzling.stackexchange.com/questions/36874/can-whites-rook-and-knight-without-moving-white-king-force-stalemate), and the [traditional minimum-mating-material question](https://chess.stackexchange.com/questions/5028/what-is-sufficient-mating-material), 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)
  
  **Tags:** checkmate, material
  
  > **Comments:**
  > **username_1**: 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.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2016-07-05. Score: 4
  
  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)
  
  > **Comments:**
  > **username_3**: 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.  
  > **username_2**: @username_3 Yes, without pawns  
  > **username_4**: In the 4 bishops case, you'll need at least *two* bishops from each colour, not one.  
  > **username_2**: @username_3 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  
  > **username_4**: Note that KNN = 10 is also an exception.  
  > **username_2**: @username_4 KBB*  
  > **username_4**: No, I meant King + 2 Knights = 10 points, but not sufficient enough to enforce mate.  
  > **username_2**: @username_4 Oh ok  
  
  ---
  
  