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The FIDE chess rules describe that "The game is draw when a position is reached from which a checkmate cannot occur by any possible series of legal moves" (FIDE rule 9.6). This rules is sometimes referred to as "Insufficient mating material rule", and the material that results in draw based on this rule is described in Draws in all games. So this covers the case where even a helpmate (or checkmate by unskilled play) is not possible with the present material. So:

What is sufficient mating material, whereby a skilled player can force another skilled player into checkmate?

Some combinations are well known, like:

  • K + Q vs. K
  • K + R vs. K
  • K + B(w) + B(b) vs. K

But is for example K + N + B vs. K sufficient mating material ?

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6  
Just looking at the title, I really want to answer this question with "Barry White". –  IQAndreas Mar 16 at 2:44
    
Or that musical by Benny Andersson, Björn Ulvaeus and Tim Rice. –  Mr Lister Mar 16 at 15:27

5 Answers 5

up vote 15 down vote accepted

Most basic first - this rule is the reason that King vs King is an immediate draw. Neither side has a piece to check with, let alone checkmate with. A position that is a draw because neither side can win is called a "dead position".

Playing against a bare king, a bishop or a knight is insufficient to checkmate with, and therefore K+B v K and K+N v K is always a dead position. Most online playing sites end there, and consider everything else winnable.

K+Q v K, K+R v K, K+B+B v K, K+B+N v K are all endings in which white can even force mate. Because you ask for it explicitly, here is an example of a mate with N and B:

[FEN "k7/8/NKB5/8/8/8/8/8 b - - 0 1"]

There are some special cases. K+N+N v K is tricky -- white can't force mate, but mate is still possible:

[FEN "6k1/8/6K1/4N3/4N3/8/8/8 w - - 0 1"]

White plays 1.Nf6+, and black avoids mate by going to f8. But if he goes into the corner with 1...Kh8??, then 2.Nf7# mates.

So K+N+N v K is basically always given an immediate draw by the player with the knights in a slow game, because he knows he won't win. It will be awarded a draw by the arbiter if black claims one based on rule G.6 [the old "10.2", before july 1 2014], if the other requirements of that rule are met, and it's trivial to make 50 moves without losing. But if black runs out of time, black loses. And in a blitz game where nobody is writing down moves to count them, that may happen.

K+B v K+B is also tricky:

[FEN "5B2/8/8/8/8/7K/8/6bk w - - 0 1"]

With the bishops on the same color, mate isn't possible. It's an immediate draw.

[FEN "8/5B2/8/8/8/7K/8/6bk w - - 0 1"]

But with opposite colored bishops it is: 1.Bd5# mates.

In most other endgames it is possible to think of a way that one or both sides can be mated. In particular, if there are pawns, it is usually possible that one of them promotes and checkmates later. but there are exceptions:

[FEN "4k3/8/8/p1p1p1p1/P1P1P1P1/8/8/4K3 w - - 0 1"]

To a human it's immediately obvious that the kings will never be able to cross to the other side, so this is a dead position. Engines have no clue, though. Mine thinks white is minutely worse.

And in the recent question about sequences of forced moves, limulus proposed this position with an "infinite loop" of forced moves:

[FEN "8/6p1/1p3pPk/1P3Pp1/1Pp3p1/KpP3P1/1P6/8 - - - 0 0 "]

Neither king can break out of its jail -- so this is just another example of a dead position. Immediate draw.

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10.2?! There is no 10.2 in the laws of chess. Is this the USCF thing about "insufficient losing chances"? That's not a thing in the rest of the world. –  kahen Dec 10 at 11:10
    
My answer predates July 1, article numbers have changed. –  RemcoGerlich Dec 10 at 11:40
    
Quickplay finish has moved to appendix G, it's now G.6. I'll edit. –  RemcoGerlich Dec 10 at 11:43

The quote

The game is draw when a position is reached from which a checkmate cannot occur by any possible series of legal moves

Is a good summary in itself. It is not just how much material e.g. white has, black's material is also important. For example, let's say white has a K+N and black has K and h-pawn. Black's time runs out. Black loses on time, because

You can theoretically reach a position with the available material where black is checkmated

When one of the players only has a king left, then the situation is different. The following material is judged as enough for a checkmate when the side with the lone King runs out of time.

  1. K+pawn vs K
  2. K+knight+knight vs K
  3. K+bishop+knight vs K
  4. K+the bishop pair vs K
  5. K+rook vs K
  6. K+queen vs K

(Edited to be more precise)

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In the K+knight+knight vs K case, as pointed out in other other answer to question, then mate is still possible, so I don't think K side can claim draw. –  Morten Zilmer Mar 15 at 14:02
    
@MortenZilmer Yeah, that was my guess too. I edited my answer. Let's see if more interesting cases will pop up! –  Rauan Sagit Mar 15 at 14:07
1  
"Considered enough for a checkmate"? That's not a matter of opinion! Also, the bishops must be on opposite-coloured squares: king plus any number of bishops on the same coloured squares, versus king is a dead position. –  David Richerby Dec 10 at 12:16

RemcoGerlich's answer is quite exhaustive, but I would like to add that unsymmetric theoretically drawn positions can arise. These are situations where one player may still checkmate, but the other cannot, e. g.

[FEN "kq6/8/KB6/8/8/8/8/8 b - - 0 1"]

You will not find a mating position for white but it is quite clear that black still may. Of course, this does not qualify for article 9.6 of the FIDE rules but is still important when one player's flag has fallen. If black's flag would fall in that situation, the result would be a draw, but if white's flaw fell, he would have lost the game.

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If a player's flag falls (whether in blitz or normal play) may he demand that the other player demonstrate that there would be some legal combination of moves by both sides by which the fallen-flag player could be checkmated? In most situations it would be obvious, but if it isn't, could the fallen-flag player demand that the opponent either demonstrate a win or accept a draw? –  supercat Mar 20 at 3:21
    
"In dubio pro reo" holds in chess as well, so the player claiming draw must prove to the arbiter (if his opponent disagrees) that a given position cannot be won by the opponent (although that is not easy in non-standard cases). –  chaosflaws Mar 20 at 19:53
    
What form would such proof take? If there have been e.g. 170 moves played, then if a helpmate in five moves exists the opponent seeking victory would generally be able to demonstrate it. If none exists, how would that be proven short of enumerating all possible five-move sequences? –  supercat Mar 20 at 20:09
    
Basically, the rule stated above applies, but I think, the arbiter has to use common sense here. If he is convinced by the arguments brought forth by the player whose flag fell (far short of enumerating all moves - there are a lot of shortcuts) he should make it a draw - and only in that case. The other player has nothing to do with it. –  chaosflaws Mar 22 at 20:59
    
@supercat: why the five move limit? I'm not aware of any 175 move rule, and if there is one, it's not relevant to assessing the possibility of checkmate. Usually with a little bit of material left (say a pawn on either side) mate is possible. –  RemcoGerlich Mar 30 at 14:39

K+N+B, K+B+B, K+R, K+Q, and K+N+N are. The latter is a helpmate.

K+N and K+B are insufficient.

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K+pawn vs K is also enough for a checkmate. Also, your answer assumes that the opponent only has a King remaining. While the question doesn't clearly state this (although it hints it). Cheers. –  Rauan Sagit Mar 15 at 14:43
    
K+P is not enough for mate. Unless the pawn can be queened. But that's covered. If Black can have other pieces, then it gets harder quicker, and situational. For example, K+N+N vs K+P is sometimes a forced win for the side with the knights. –  Tony Ennis Mar 15 at 17:46
    
I base this on the rules that are valid when the opponent's time runs out. As well as the rules that are valid when you want to "claim a draw". As far as I know, you cannot demand a draw in a K+pawn vs K situation. The side with the pawn can claim to play for a win and the 50 move rule will be used. Cheers. –  Rauan Sagit Mar 15 at 17:49

One interesting forced mate which nobody has mentioned is K+N+N v K+P.

Provided the pawn is not far advanced the side with the 2 knights drives the opposing king towards a corner. At a certain point when the driving can be completed by K+N the other knight blockades the pawn. The K+N finish driving the opposing king into a corner, building a prison, say a1+b1 (i.e. the opposing king can only alternate between a1 and b1), with king on b3 and knight on a2. The blockading knight then comes over to help deliver checkmate with stalemate avoided because the pawn can move.

Similar game shown below:

[FEN "2k5/7p/2K1N3/5N2/8/8/8/8 w - - 0 1"]

1. Ne7+ Kb8 
2. Kb6 h5 
3. Nc5 h4
4. Nd7+ Ka8
5. Nd5 h3
6. Nc7#
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This answer is confusing because it is about forced mates, whereas the question is about possible mates (helpmate if necessary). –  RemcoGerlich Dec 10 at 12:30
    
@RemcoGerlich: Another answer pointed out that K+N+N v K is not sufficient to force a mate, so black could get a draw. However, this answer points out that black may loose if a pawn is added, which is peculiar. –  Morten Zilmer Dec 10 at 12:46
    
@MortenZilmer: but it's not an answer to the question. Replying to an answer with another answer like this is not a good fit for the Stack Exchange format. –  RemcoGerlich Dec 10 at 13:43
    
@RemcoGerlich: But since K+N+N v K+P actually is sufficient mating material in the shown start position, I would think it is a valid answer. –  Morten Zilmer Dec 10 at 13:58
    
But so is K+N+N v K. –  RemcoGerlich Dec 10 at 13:59

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