King and two Knights vs King

 --- --- --- ---
|   |   |   |   |
 --- --- --- ---
|   |WN |WN |   |
 --- --- --- ---
|   |   |WK |   |
 --- --- --- ---
|BK |   |   |   |
 --- --- --- ---  

An end game that is virtually impossible and must be assisted by a moronic opponent (or someone who is ready to lose), otherwise known as a helpmate. The opponent's king must be forced into the corner, BUT must move there on the move just before the knight checks it (the other two pieces already being in position). This, of course, is a royal pain (haha) because you must have the kings on the same file, then check with the knight on the right and HOPE that the king moves down instead of up and avoiding this mate altogether.

ie:

   --- --- --- ---
4 |   |   |   |WN |
   --- --- --- ---
3 |   |   |WN |   | White Knight has just moved to C3. He 
   --- --- --- ---  must now hope that the King will move 
2 |BK |   |WK |   | to A1.  This only happens if the
   --- --- --- ---  opponent is dumb.
1 |   |   |   |   |
   --- --- --- ---  
    A   B   C   D

   --- --- --- ---
4 |   |   |   |WN |
   --- --- --- ---
3 |   |   |WN |   |
   --- --- --- ---  The black king moves and leaves this 
2 |   |   |WK |   | position.  The likelyhood of this is 
   --- --- --- ---  slim to nil.
1 |BK |   |   |   |
   --- --- --- ---  
    A   B   C   D

   --- --- --- ---
4 |   |   |   |   |
   --- --- --- ---
3 |   |WN |WN |   |
   --- --- --- ---  Allowing white's other knight to  
2 |   |   |WK |   | checkmate.
   --- --- --- ---
1 |BK |   |   |   |
   --- --- --- ---  
    A   B   C   D

While this is fun to try and do, it just becomes a bit of a pain in the ass. It is fun to toy with newbies though by drawing the game out as long as possible and this is a damn good way to do it. This endgame becomes far easier if the knights have a helper in the way of a rook or bishop.

King and two Knights vs King Puzzle One: Black to move, helpmate in two

The Knight is the most fascinating piece in all of chess because no other piece in the game shares its movement affinity. The King, Queen, and Rook all traverse the ranks and files, while the Queen and Bishop command the diagonals of the chessboard. The Knight is the only piece to not fall into these categories, instead having the ability to move to the set of all squares which are closest to it while being neither diagonally nor orthogonally related to the square the knight is currently on.

Said another way: the knight moves two squares along a rank or file, and then one square in either direction along the other axis.

I prefer to explain it as the set of all closest squares which are neither diagonal nor orthogonal, but one must play the room.

A King and a single Knight versus a King is a draw due to insufficient material to execute checkmate. Neither King may make a move to put themselves in check, and it isn't possible for the Knight to both deliver check and prevent escape. In the best case scenario, where the stronger side has the opposition, forces the king to the corner, and is able to deliver check by the Knight on the subsequent move, the weaker side King will have 1 free square to move to. Along the edge of the board: there will be at least 2 free squares. Any set of squares near the middle: 4 squares. There is no way to attain checkmate with only one Knight. As you may well observe from your own games, anytime a piece is one square away and diagonal to a Knight, the Knight can attack that piece on its very next turn. However, the inverse is also true. If a piece is one square away and orthogonal to a Knight, the Knight cannot attack that piece on its next turn. In fact, if we limit the example to just a single Knight and King of opposite color, we see that if the King ever closes to an immediately adjacent and orthogonal square of the Knight's, then the Knight will be hard pressed to escape the King!

Now, two Knights, you say? Checkmate is, as an academic exercise, possible.

But it's going to take some help.

A King and any major piece can force checkmate. So to can a King and two Bishops, or a King and a Bishop and Knight. A King and two Knights cannot force checkmate. The two diagrams below show the total board control exhibited by a pair of adjacent Knights. What is, during the midgame, a force to be reckoned, becomes instead by the endgame quite underwhelming. The strongest possible deployment is to have the pair of Knights sharing a rank or file among the middle four squares of the board. Ideally, this position will have forced the weaker side's King to traverse a long edge of the board without being able to approach the middle.

As illustrated in Puzzles One and Two, this is the only position from which checkmate is academically possible (depending upon the stronger side's King placement, either in the corner or along the edge). However: it is important to note and remember that as the stronger side you are hoping for a blunder, preying on a fledgling player, or expecting your opponent to lose intentionally. Not the most sporting options. As the weaker side's player, it is most important to move closer to d5, e5, d4, or e4 whenever possible, and to track exactly how many moves have passed since the last capture or pawn move to claim a draw by the Fifty-move rule.

It does no better to have a space between the Knights. If they share a rank or file, then there are many similar holes in protection as we see in the diagonal-adjacent example above. If they share a diagonal, then there is virtually no support between the pieces (it will take three moves for one Knight to protect the other) due to the lack of cohesion with respect to the consecutive squares the Knights control.

All said, there are only two possible ways to helpmate versus a King and two Knights. By avoiding these precise solutions in a live game, you'll easily be able to avoid checkmate and collect your draw by the fifty-move rule versus even the most obstinate of players.

King and two Knights vs King Puzzle Two: Black to move, helpmate in two

Further instruction

• Chessboard
  
• Chessboard laboratory
  
• Chess notation
  
• Chess Openings
  
• Endgames in Chess
  
• The Opposition, King vs King and single pawn
  

• This chessboard next to my keyboard
  
• Patience