First, proof that such a position exists at all. The black king is in the corner, the white king takes away g7 and g8, one knight covers h7, and the other gives check from g6. Nowhere to go - mate.
The position is genuine, there is no mistake in it. The problem is elsewhere: for it to arise, the black king had to walk into the corner by itself and stay there - and it is under no obligation to do so.
Take one knight off the board - the one that was giving check. That leaves king and knight against king, and here is what happens.
That is the whole point. To drive the king into the corner, the stronger side has to take away all its squares - and the moment every square is taken and there is no check, you get stalemate. So the last knight has to arrive with check on exactly the move when the net closes.
And that is impossible to arrange against sensible defence. While the second knight travels to the right square - and a knight needs several moves to change its post - the king simply walks out of the corner: the net is not closed yet, so it still has one free square. You cannot close the net in advance, because that is stalemate.
Hence the rule for the defender: do not go into the corner of your own accord. Stay nearer the centre or along the edge, not in the corner, and there will be no mate.
There is a subtlety here that makes two knights behave differently from a single bishop or a single knight.
In practice that means an hour and a half of pointless play if your opponent is stubborn. Usually the players simply agree a draw at this point. All the ways a game can end in a draw - draws in chess.
There is an exception, and it sounds paradoxical: an extra pawn for the weaker side can be its undoing.
The logic goes like this. Stalemate is only possible when there is no legal move at all. If the defender has a pawn, there is always something to move - and the stalemate defence collapses. The stronger side blockades the pawn with one knight, calmly brings up the king and the second knight, and at the decisive moment lifts the blockade: the pawn moves forward, there is no stalemate, and mate follows.
Exactly where that pawn has to stand was worked out by the Russian endgame study composer Alexey Troitsky - with pencil and paper, long before computers. His boundary runs along the squares a4, b6, c5, d4, e4, f5, g6, h4: if the pawn is securely blockaded on this line or behind it, the two knights win regardless of where the other pieces stand.
The practical value of this knowledge is, honestly, small. The win can take up to one hundred and fifteen moves, and the fifty-move rule kicks in sooner - so over the board such a position usually ends in a draw anyway. Modern computer tablebases have checked Troitsky's analysis square by square and confirmed it: for hand analysis a century old, it turned out to be remarkably accurate.
Two practical conclusions, which are the reason all this is worth knowing.
The mates you really do need to know are with the queen, two rooks and a rook. All six, with interactive boards - how to checkmate a lone king. How the knight itself moves and why it is so awkward here - how the knight moves.
The mating position exists, but it cannot be forced. With correct defence a lone king always escapes: as soon as the stronger side takes away all its squares, it is stalemate. Mate with two knights only happens if the defender walks into the corner by itself and stays there.
Bishops strike along diagonals at any distance and control squares continuously, so the net around the king can be tightened step by step. A knight controls squares by jumping, and when it moves to a new post it stops covering the old ones for a couple of moves - that is exactly the pause in which the king leaves the corner.
No. Unlike a single bishop or a single knight, mate is theoretically possible here, so the position is not considered dead and the draw is not declared at once. Play goes on until the fifty-move rule, or the players agree a draw.
A boundary along the squares a4, b6, c5, d4, e4, f5, g6, h4, worked out by the composer Alexey Troitsky. If the weaker side has a pawn and it is securely blockaded on this line or behind it, the two knights win: the pawn deprives the defender of the stalemate defence.
Because stalemate is only possible when there is no legal move at all. With a pawn the defender always has a move, and the defence's main weapon - stalemate - disappears. The stronger side blockades the pawn with one knight, builds the mating net and releases the blockade at the right moment.
Up to one hundred and fifteen. The fifty-move rule kicks in sooner, so over the board such a position usually ends in a draw even when it is theoretically won.
There is no technique to learn - it does not exist. It is enough to know the fact itself: two knights against a bare king do not win. The practical value lies elsewhere - do not trade down to two knights, and do not hand your opponent an extra pawn if they have the two knights.
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The six basic mates - how to checkmate a lone king. What stalemate is - stalemate in chess. All the ways to draw - draws in chess. How the knight moves - knight moves. Endgames from scratch - endgames for beginners.
At the board since childhood: hazy about his rating, precise about every rook he has blundered. Counts an evening as a good one if the opponent stayed to talk afterwards instead of rushing off to check with an engine. Message →
