The Endgame

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Knight_F018
two night and one king đź‘‘ VS only kingđź‘‘ ... checkmate OR stalemate which is the Possible?
Aron_08

two knights can't force a checkmate but checkmate is possible

 

MARattigan

Similarly

There are 14 mate positions in each corner and 4 on each edge square except those adjacent to a corner where no mate is possible. You might like to check that in all cases the lone king had an alternate move which doesn't allow an immediate mate. The pieces can't attack enough squares adjacent to or including the lone king's square to allow a mate or stalemate with the lone king not on the board's perimeter.

@Aron_08 is correct in saying two knights can't force a checkmate but a checkmate with two knights can be forced. E.g.

 

Aron_08
MARattigan Ă­rta:

Similarly

There are 14 mate positions in each corner and 4 on each edge square except those adjacent to a corner where no mate is possible. You might like to check that in all cases the lone king had an alternate move which doesn't allow an immediate mate. The pieces can't attack enough squares adjacent to or including the lone king's square to allow a mate with the lone king not on the board's perimeter.

@Aron_08 is correct in saying two knights can't force a checkmate but a checkmate with two knights can be forced. E.g.

 

Yes but checkmate can only forced when there's another black figure:

 

 

MARattigan

But your example isn't checkmate with two knights and one king vs only king as requested by OP. What is true is that a mate with two knights and one king vs only king can be forced only by capturing a black piece on the mating move as in the last example I gave in my previous post.

There are, of course, innumerable examples of forced mates with two knights and one king vs king and other pieces. I like this one.

Otto Bláthy
White to play and mate in 50

 

MARattigan

Stalemate is possible with two knights and one king vs only king and normally can be forced from any position with two knights and one king vs only king unless the lone king can force the capture of a knight as e.g. this with either side to play.

For example in the first positions given by @Aron08 and myself above:

 
Note that stalemate is possible with the lone king anywhere on the perimeter including next to a corner. 
 

But in some cases where the capture of the knight can't be forced, stalemate can be forced, but not stalemate  with two knights and one king vs only king. For example:

Black to play

 

The sequence above is actually drawn as a dead position on move 4, but (like my computer interface) I've ignored that. Strictly speaking stalemate can't be forced from this position either.


 

Aron_08

True, but why would you try to force a stalemate?

Aron_08
icyboyyy Ă­rta:

Two knights and king vs lone king is stalemate draw if the lone king plays well. Two knights and pawn is win if you know how to checkmate with two knights because the pawn prevents stalemate

Not every time, what about this?

( I had to make a move otherwise I couldn't post the diagramm)

Aron_08

Wait why is this marked as a draw?!

MARattigan
Aron_08 wrote:

True, but why would you try to force a stalemate?

Has been done. There's the story of two Russian GMs who finished up in a pointless endgame but weren't on speaks so nobody was offering a draw. I think it was Korchnoi who forced a stalemate. His comment after the match, "I stalemated him!"-

Apart from that, it's just out of interest.

MARattigan
Aron_08 wrote:

Wait why is this marked as a draw?!

You show us how to win the two knights v queen endgame with the knights. Can't be easy.

On the other hand:

 

Aron_08

In the following position after Kb8 ( is the best move) h1=Q and then it's easy

MARattigan
icyboyyy wrote:
Aron_08 wrote:
icyboyyy Ă­rta:

Two knights and king vs lone king is stalemate draw if the lone king plays well. Two knights and pawn is win if you know how to checkmate with two knights because the pawn prevents stalemate

Not every time, what about this?

( I had to make a move otherwise I couldn't post the diagramm)

Well ofc that would be winning for black but if the pawn isnt advanced then the strategy is I think to blockade the pawn with one knight, trap the king to the corner of the board that the knight is closest to with the other king and knight, and have the other knight jump out to checkmate the king. Its a pretty complicated mate tho

You don't need to insist the pawn isn't advanced.

 

MARattigan

@icyboyyy

Not necessarily. This for example is a draw whoever has the move.

This is also a draw whoever has the move.

Having said that, if the pawn is beyond the Troitzky line, the black king has no win/draw zone.

About 60% of positions are drawn. The majority of wins are for the side with the knights and in the majority of those the pawn has not advanced beyond the Troitzky line.

MARattigan

@icyboyyy

Not all KNNKQ positions are won for Black, just the great majority.

Don't ask me me why it's a draw, because I can't play the endgame. Just Nalimov says it is, but if he were to play Black against me he would be lying. 

The general result of the endgame is a draw contrary to Nalimov's opinion, which suggests there are quite a lot of people that also can't play this endgame. You don't find many references to wins by the side with the pawn in the two knights v pawn endgame, I think for that reason.

Tashhalfpint


How did this result in a stalemate ? I’m a beginner and assumed a checkmate but computer ended in a stalemate draw.

Automaton_Dragon

 

MARattigan
Automaton_Dragon wrote (#22):

 

Even quicker

Black to move

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