K+2 Kts vs K = DRAW with correct play by the defender. All the Kts can do is stalemate the lone King. BUT, with a K+P after the King is stalemated the pawn moves while the Kts get repositioned for checkmate. The longest such mate requires 66 moves and in 1992 FIDE abolished all exceptions to the 50 move rule because no one knows any of them including most GMs, at least according to me - and at least one GM named Karpov.
As Botvinnik said in this book, Lilienthal had gotten that endgame 3 times in his career already by that point...and was unable to win it any of those times...
Nimzovitch erroneously traded down into this ending with a K+RP, which loses even if it's on the 6th-rank, but Nimzo didn't know this back in 1913 (I wonder if anyone else did)
Lilienthal may have been a slow learner in the endgame, but he had an even record with Capablanca: +1 -0 =2
I've never even seen it occur once...hard to believe Andrei had it happen to him three times...
Cool...this is going to help me on the chess tournament.
I'm so pumped up!!!
What about if the black king is for example on h1 the white King is on g3 and the two white knights are on f2 and h3
This position is interesting because White can win even though the black pawn has advanced well beyond the Troitsky line.
White to play and win.
Well, in some cases it can be forced, if Black has a pawn
you have to get the king to the corner first mate. and how can you do that with 2 knights?
its hardly doable with a knight and a bishop.
well its still a draw even if that is true... which i dont believe
the 50 move rule mate
White to move? That's a bit odd.
In any case, this position isn't reachable unless Black is being highly cooperative and/or a total idiot...
EDIT: Ninja'd by marvellosity. But what you said isn't quite true - the position can be legally reached, but it requires Black to help.
The position is not only legal but forcible- E.g. White's quickest win from this position is as shown.
With the Black king on a1/h1 I've several times finished up on both sides of the corresponding positions while practising the two knights v. pawn endgame.
the cheakmate is impossibe i dont know if pepole can do it
I think it can only be forced if the side without the two Knights has a pawn (or a piece in a usless position)- because these is otherwise a stalement position, which the pawn move eliminates.
Strictly speaking pawns and or pieces, for instance the addition of a black pawn or piece on b6 in the above position would not change the mate.
Incidentally, though the elimination of stalemate by the move of an opposing piece is necessary to force a mate position with only the kings and two same coloured knights, this is not always necessary for other mates with two knights against opposing material, e.g. White cannot afford to let the pawn move in the following diagram.