What is sufficient mating material?

Question

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 ?

Answer 1

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 (see an overview of basic checkmates on Wikipedia). 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.

Answer 2

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)

Answer 3

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#

Answer 4

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.

Answer 5

AFAIK sufficient mating material is considered as such if a "helpmate" can be demonstrated in any number of moves. Put another way, it is as if the player that ran out of time is out of the game, and now the other player controls both sides. If a checkmate position can be reached this way, that other player wins the game, otherwise it's a draw.

Answer 6

The minimum needed is Knight and Bishop, though N+N+KvK+P is also possible. Perhaps N+KvK+P will sometimes happen, but the standard minimum is N+B