# Checkmate with two knights?

Is it really possible to checkmate with two knights and king against a king?

There is a mating position with this but no extra tempo to do it in real game.

What are the explanations, why knights cannot create an extra tempo around 64 squares on the board?

• I don't have the reputation to answer, but I discovered the position can be forced by a queen sacrifice. – Joshua Oct 20 '15 at 3:28
• A very short answer would be because Knights cannot triangulate. All other pieces, except pawns, can do so. – DrZ214 Dec 26 '15 at 10:32
• To force mate you need two knights PLUS they need a pawn properly placed so one knight can block it while the king and other knight maneuver the hunted king into position where it is trapped, then the blockade knight can move to give the pawn a chance to move while the king is mated in the meantine. See BCE by Fine. – edwina oliver Dec 4 '19 at 19:46

Is it really possible to checkmate with two knights and king against a king?

Theoretically, the checkmate is possible, but you can not do it in practice unless the weaker side allows you to. This is related to a drawback in the way knight moves.

There is a mating position with this but no extra tempo to do it in real game.

What are the explanations, why knights cannot create an extra tempo around 64 squares on the board?

There are two reasons:

They can not do it because they can not move to another square while keeping the previous one in control ( like bishop and many other pieces can ) and because they need too much time to position themselves properly.

DEMONSTRATING KNIGHT'S INABILITY TO "LOSE TEMPO" :

Take the following position as an example:

``````[Title "This position is won with a bishop"]
[fen "8/8/8/8/4B3/8/P7/K1k5 w - - 0 1"]
``````

This position is won for White because he can play with bishop and retain control over `c2` square ( `1.Bh7`for example ), which will create zugzwang. As you say in your question, White will "lose tempo" and force Black to move his king away.

Now analyze this position with a knight instead of a bishop:

``````[Title "If it is White to move this is a draw"]
[fen "8/8/8/8/3N4/8/P7/K1k5 w - - 0 1"]
``````

Why is this endgame only a draw? Because White can not move and keep control over `c2` square. This means that he can not create zugzwang, or as you say he can not "lose tempo" to force Black king away.

Without the ability to create zugzwang you are just not able to corner the opposing king.

DEMONSTRATING KNIGHT'S INABILITY TO POSITION ITSELF PROPERLY :

As for the positioning problem, we shall take a look at the below diagrams:

``````[Title "Agile and swift bishop"]
[fen "8/8/8/8/8/1K1N4/3B4/1k6 w - - 0 1"]

1.Nb4 Ka1 2.Nc2+ Kb1 3.Na3+ Ka1 4.Bc3#
``````

Here, bishop needed 1 move to reach the mating square. Notice that the endgame would be drawn, just as the one with two knights, if bishop was not able to reach `c3` in one move.

In the following diagram you will see that knight needs more moves to reach the mating square, which enables the weaker side to draw:

``````[Title "Clumsy knight"]
[fen "8/8/8/8/8/1K1N4/4N3/1k6 w - - 0 1"]

1.Nb4  Ka1 2.Nc2+ Kb1 3.Na3+ Ka1
``````

and here `Ne2` needs 2 moves to reach `c2` and deliver checkmate.

Remember this: Knights experience great difficulties when they need to reposition themselves between short distant squares in a short notice. This is often impossible task for them. The following example demonstrates clearly what I mean:

``````[Title "Slow knight"]
[fen "8/8/8/8/8/1K5p/6N1/1k6 w - - 0 1"]
``````

In this position we can see how hard it is for the knight to position himself fast to a square nearby like `f3` or `g4`. Again he needs 2 moves to do this and thus he fails to save the game.

## SUMMARY:

Knight's way of moving gives him ability to "do the impossible". He can "jump over" obstacles, his attacks can not be stopped, his line of fire can not be covered or intercepted, but all these beautiful features come with a price. He is slow and clumsy when he needs to reposition himself to a square in its proximity, and if player can not "buy" him enough time to do that then knight fails to accomplish this task.

Best regards.

• In your two first diagrams, you seem to assume that the white pawn promotes on a1 instead of a8... – Evargalo Nov 27 '17 at 16:42
• @Evargalo Indeed, nice catch! – AlwaysLearningNewStuff Nov 27 '17 at 17:36
• I see no zugzwang in your 1st example (KBPk). Your 2nd example (KNPk) is not a draw: 1 a4 wins in 14. (Checked with Nalimov.) – Rosie F Dec 6 '19 at 11:22
• @RosieF: Table is flipped in both examples, pawn is on 'h7', not on 'a2', Bishop on 'd5' etc... – AlwaysLearningNewStuff Dec 6 '19 at 18:33

Is it really possible to checkmate with two knights and king against a king?

It is possible, but it is not forced unless the position or a mistake from the opponent allows it.

There is a mating position with this but no extra tempo to do it in real game. What are the explanations, why knights cannot create an extra tempo around 64 squares on the board?

Very Simple Reason -

A knight always moves to a square of the opposite color. If the knight is on a white square it moves to a black square and if it is on a black square it moves to a white square.

Thus, knight on white square moves to -

``````1. Black square
2. White square
3. Black square
4. White square
...forever
``````

In order to create an extra tempo, you would need the capability for a knight to move to a square of the same color twice in a row, but that is not possible. Thus, you cannot create an extra tempo with a knight.

Wikipedia has a long article on this topic.

Unlike some other theoretically drawn endgames, such as a rook and bishop versus rook, the defender has an easy task in all endings with two knights versus a lone king. The player simply has to avoid moving into a position in which he or she can be checkmated on the next move, and always has another move available in such situations

Not only it is showing a lot of explanatory examples, but also speaks about really strange paradox Troitzky line which explains how the material advantage for the weaker size can cost him a game. Having one pawn against 2 knights can give white a chance to win.