It is indeed possible to trap the defending king on the edge with a king and knight but it takes a little maneuvering at times. Some examples:
I have trouble trusting Endgame Tablebases
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EndgameStudier Well, I am sure you can trust the Nalimov table base:
http://www.k4it.de/?topic=egtb&lang=en
Set up the position there and you can see how the black king can in fact be forced into a corner.
According to that tablebase your position takes 44 moves to win against best play.
EDIT: Way-of-Pain beat me to it although it is a different answer, but the point is the same which is that the black king can be forced into a corner.
Jesus Christ, the boards on this website are so full of glitches. Entire variations are missing from my puzzles even though they were visible last time I visited this page. Chess.com, just rip off lichess's study feature already because this is ridiculous.
EndgameStudier wrote:
Supposedly in this position, specifically with the black pawn on G6 and the two white knights where they are, (and any symmetrically equivalent positions..etc) is a forced win for white. I just posted in another thread about how 2 White Knights can win against an advanced pawn, which can take up to 17 moves, if the king is already on the side, but since 1 knight must blockade the pawn below what is called the "Troitsky Line" I don't see how white can force the black king to the edge with only a king and one knight. I am not a computer but I just don't see how that material is sufficient to force the king to the edge, and keep it there in the exact position for the other knight to jump in, I know computers say these are mates in 115 or 145...etc, but how?? I don't even see a viable pattern of restricting the kings movements at all with a king and one knight, even if the king is on the edge and just 3 squares from the corner, let alone on the center. If it is true then its very fascinating, but forgive me for doubting the supercomputers that say these are forced wins (excluding the 50 move rule).
It is mate in 89.
https://syzygy-tables.info/?fen=8/8/6p1/3k2N1/8/4K2N/8/8_b_-_-_0_1
Sep 18, 2020
0
#7
be wary of dogmaticaly follow an endgame table base type scenario. The technically-correct-next-move as shown in the table base is never the next move your opponent would choose to play. So, your plan based on blindly following the "..recommended..." is shot to sh*t, thus you have gained no advantage. Plus - YOU SHOULD NOT BE USING A TABLEBASE ANY WAY
Sep 21, 2020
0
#9
You're looking for "Collection of Chess Studies" by A.A.Troitzky, ISHI press (first published 1937, some years before any EGTBs). This contains a 60 page comprehensive analysis of this endgame. All you then need is a few years' practice, preferably against said EGTB, because the engines can't generally play it.
If you doubt it works try playing Black from your position against an EGTB and see if you can hold out for 44 moves.
You can do that here https://syzygy-tables.info/?fen=8/8/6p1/3k2N1/8/4K2N/8/8_w_-_-_0_1 by taking the White moves from the top of the list on the right. (Play your own Black moves.) If you're serious about learning it you should install the Nalimov 3-4-5 man EGTBs in your engine.
Fascinating, he must have tore his hair out solving all positions in this endgame. It took me an hour to figure out the solution for this without any help:
Also known as the "Troitzky Triangle"
Sep 22, 2020
0
#11
Black can actually survive for more than 50 moves in that position. But it'd require a really perfect defense.
Sep 22, 2020
0
#12
MARattigan wrote:
kingandqueen2017 wrote:
Black can actually survive for more than 50 moves in that position. But it'd require a really perfect defense.
Depends who's attacking.
But which position are you talking about? The initial position is mate in 44 and the last posted not very many.
In fact with the knights and pawn in the same positions as in the original diagram about 4% of positions will need more than 50 moves against perfect defence, but none can be drawn under the 50 move rule with a perfect attack.
Supposedly in this position, specifically with the black pawn on G6 and the two white knights where they are, (and any symmetrically equivalent positions..etc) is a forced win for white. I just posted in another thread about how 2 White Knights can win against an advanced pawn, which can take up to 17 moves, if the king is already on the side, but since 1 knight must blockade the pawn below what is called the "Troitsky Line" I don't see how white can force the black king to the edge with only a king and one knight. I am not a computer but I just don't see how that material is sufficient to force the king to the edge, and keep it there in the exact position for the other knight to jump in, I know computers say these are mates in 115 or 145...etc, but how?? I don't even see a viable pattern of restricting the kings movements at all with a king and one knight, even if the king is on the edge and just 3 squares from the corner, let alone on the center. If it is true then its very fascinating, but forgive me for doubting the supercomputers that say these are forced wins (excluding the 50 move rule).