It is lost. You can enter all positions of six pieces into a tablebase, like this online one.
It's mate in at most 39 moves, for example:
[FEN "4N1K1/5P2/6k1/8/6n1/8/N7/8 w - - 0 1"]
1.f8=N+ Kf5 2.Kg7 Ke4 3.Nb4 Kd4 4.Kf7 Kc5 5.Na6 Kd4 6.Nac7 Ne5 7.Kf6 Nc4 8.Ke6 Na5 9.Nd6 Nc4 10.Nf5 Kd3 11.Nd5 Na5 12.Nf6 Nc4 13.N8d7 Kd2 14.Nd5 Ke2 15.Kf6 Kd2 16.Nc5 Kc2 17....
This was a great game! Hou Yifan brilliantly outplayed her opponent Fabiano Caruana in a very positional middle game, and mind you using the Petroff's defence in the opening, which is Caruana's specialty by any stretch of the word! The endgame was very tricky, and Caruana proved his resilience and held the game to a draw in a very resourceful way, despite ...
Well, simply put, they chose to follow the USCF "Article 14: The Drawn Game rule 14E: Insufficient material to win on time, 14E3: King and two knights."
While it is not a forced mate, there is a mating position that is possible, thus they could have easily followed the FIDE rule, and allowed the side with the knights to continue playing.
It was probably a ...
An exhaustive computer search shows that as expected K+N cannot in general
force stalemate against a lone K.
In fact, the defending King can avoid stalemate as long as it's not on
one of the six-square triangular neighborhoods of the corners
shown in the following diagram
[Title "Danger Zone"]
[fen "kkK2Kkk/kK4Kk/K6K/8/8/K6K/kK4Kk/kkK2Kkk w - - 0 0"]
Let's assume that white is the side with the two knights, and black has the single pawn. The endgame study composer A. A. Troitzky gave an analysis (in a lengthy supplement to his 1937 Collection of Chess Studies) that established what is now known as the "Troitzky line":
So long as a white knight has the black pawn securely blockaded on one of these ...
In the general case K+N vs K+P is of course a draw - or a win for the pawn if it can promote unhindered.
There is however a famous construction were the knight can force a mate against a king stuck in front of its own well-advanced rook pawn:
[fen "8/3N4/8/8/8/p7/k7/2K5 w - - 0 1"]
1.Nc5 Ka1 2.Kc2 Ka2 3.Nd3 Ka1 4.Nc1 a2 5.Nb3#
There are many ...
I have looked at tablebases but the moves are somewhat bizarre
That's the problem with tablebases; they're efficient but they can't 'play' human chess. This particular endgame is one-sided enough that it's almost never required to play the best move.
Just drive the opponent's king to the edge of the board, as you would do with king+queen vs. king; just be ...
Just for the record, the longest win in this endgame is 7 moves:
[FEN "8/8/8/8/p7/8/N7/k1K5 w - - 0 1"]
1. Nb4 a3 2. Nc2+ Ka2 3. Nd4 Ka1 4. Kc2 Ka2 5. Ne2 Ka1 6. Nc1 a2 7. Nb3#
The idea in this position (and other similar positions) is to stalemate the king in the corner; that forces a pawn move and when the pawn reaches a2, you'll need to have ...
It is, of course, objectively a draw. But according to the FIDE rules, the game can be declared a draw (without agreement of both opponents) only if there's no sequence of moves that can lead to a mate. Here the sequence leading to mate exists, even thought it is really illogical. Here is just a random example:
4k3/8/7n/4K3/8/6N1/8/8 w - - 0 1
1. Kf6 Kf8 2....
It is probably not only about position, but how about playing for 7 hours, and you are positionally killing your opponent, and you slip up, throwing away all that work?
Here are a couple positions that still probably qualify:
[FEN "7k/7P/8/6K1/4B3/8/8/8 w - - 0 1"]
You would think that white should be able to win, but no.
Or black here.
If you can fork your opponent's king and knight with your knight, then your opponent must either take your knight or allow you to take theirs on the next turn. Since that gets you down the KN vs K one way or the other, this forces the draw.
However, the answer to the literal question is no: there is no situation in KN vs KN where the only legal move is to ...
Always keep your K and Q on opposite colour squares, or have your K diagonally 1 gap away from the N, so that you will never be forked.
Beyond that, just as Glorfindel said, fork the N if it's allowed or drive opponent's K to the edge and checkmate.
The tablebase says that it is mate in 38 moves after f8N+. That is for perfect play of both sides. If black does not play perfectly it might be shorter (same for white).
Since it is a chess problem/study, it does not really matter how easy it is to win, though I would not expect it to be too difficult (against a human player).
The Wikipedia page on the Nightrider contains an example from T. R. Dawson, published in the British Chess Magazine in 1925, where a king, knight and nightrider force a mate against a lone king. I guess a similar procedure would work for two nightriders, but you have to be a little more careful to avoid stalemate.
The rules applied on chess.com are explained here. Basically the rule says that if there are no pawns and the material is insufficient to force a mate on the lone king, then the game is declared a draw.
This is contrary to FIDE rules and leads to some positions that are actually winning by force being declared draws, as noted here by Nigel Short. Actually, ...
I can think of some:
Time trouble causing blunders in general.
Objectively you can have an advantage, but then having to convert/transform it could require an impractical level of calculation (such that no human could ever realistically win over the board with such an advantage).
Some argue stalemate in general is wrong. Why should trapping the king be a ...
You left out THE single biggest factor in the position, at least initially: The knight has zero mobility. That said, she did, indeed miss two opportunities to win involving a queening scenario, but they were very tricky for a human.
I remember this endgame when they played it, and now, the winning idea comes back to me.
[Event "Grenke Chess Classic 5th"]
The position is indeed a draw - but your edit suggests a far more interesting question. Why would Houdini give such an evaluation when the position is a known book draw? @EdDean touched upon the answer, explaining the interpretation of the point evaluation.
Houdini, along with other chess engines, will analyze the position many moves deep. The depth is ...
It takes at most 33 moves to win this endgame from any position (excluding positions where bishop or knight can be captured). See https://en.wikipedia.org/wiki/Bishop_and_knight_checkmate and references there.
So, no, a forced draw is not possible in this endgame. However if the defending side is playing perfectly (e.g. an engine with tablebase), it could ...
Here's how to forcibly checkmate the bare King on f8 or e8
(added later: or on g8 or h8) once it's been cornered on h8.
First put Kg6 and Nd7, so the other Knights can roam freely
as long as they don't accidentally checkmate or stalemate
the cornered King; then:
[Title "h8 to f8 (or g8 or h8)"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]
(1. Kh6 Kg8 ...
Here's an example of how to do it, plus some general guidance.
I can't find a single game in my 7 MM games database where it was managed, though a couple of players have tried it and come pretty close.
The key difficulty (beyond knowing what to do) is managing the timing; knights can't lose a move, so you can end up being ready to mate in a good position, ...
This has been already solved by Helmut Conrady, his elegant 15-page solution is available here.
It is filled with diagrams and examples as you wanted.
Let me know if you have any questions regarding the diagrams or explanations given.
EDIT: In reply to the edited version of the question and the three positions added:
For the position to be winnable under 50 ...
To get the following position as a checkmate, the last move must be Nb3#.
[fen "8/8/8/8/8/1NN5/2K5/k7 b - - 0 2"]
Prior to Nb3#, black must have made a non-king move, so must have moved something to b3. If it were anything other than a pawn, it could choose to avoid the b3 square, so it's not a forced win for white. If it were a pawn on b4, it could ...
One thing I think is an injustice of chess is the rule enabling a player being able to get a 50-move draw even if their position is lost. (A "blessed loss" position; a "cursed win" from the point of the other player, who deserved the chance to try to execute a win.)
I am not aware of being able to use an engine to calculate the possibility of such moves and no it is not possible to do this with one knight.
The easiest way to figure this out is by backtracking the position by one or two moves. No matter in which position the white king or knight were before this situation arose, black was not obligated to move to the ...
EDITED ( January 7th, 2014 ):
Based on the member shivsky's comments I have edited the entire solution.
Does White have a win here, or is this a draw?
Yes it is won for White.
So what should White's plan be in this position?
At first, I wanted to provide an answer with 1.a4 and simply force the win, but I do not have computer strong enough to ...
At tournament level, Black can safely resign. If you wanna play some more moves, taking a pawn with 1...Kxe5 looks reasonnable.
I see no trick with stalemate nor with the d-pawn, e.g. 1...Nf4 2.Ke4 [2.Kxd4+-] d3 3.Kxf4 d2 doesn't promote because of 4.Ra6+ Ke7 5.Rd6 +-
1...Ne7 can be a trap [2.Kxd4?? Nc6+ with a probable draw (or not even, see Annatar's ...