How to checkmate with bishop and knight

The hard one. It is a forced win, it takes up to 33 moves against the fifty you are allowed, and plenty of strong club players cannot do it. Here is what it actually involves.

Worst case, perfect play: 33 moves
You are allowed 50
Every trainer position a proven forced win
Free practice, no account

Practise this against a king that defends A fresh position every time, generated and verified. The defending king takes anything you hang and will not step into mate in one, so the only thing that finishes the game is your technique. Open the trainer

What the mate looks like

Start at the end. Every basic mate happens on an edge or in a corner, and it is worth knowing the finished picture before learning the moves that produce it.

Checkmate. The black king on a8 is in check from the bishop on f3. It has three squares to try and none of them work: a7 and b7 are covered by the king on b6; b8 is covered by the knight on a6.

Where it started, 28 moves earlier. The shaded squares are the box: everywhere the black king could still walk to if White stood still. There are 43 of them. Making that number fall is the entire ending.

The idea

Start with the honest part. This ending is difficult in a way the other four are not. It cannot be worked out at the board from first principles inside the time you have, the worst case is 33 moves out of fifty, and a first phase played badly really does run the clock out. If you decide it is not worth your evening, that is a defensible decision and a great many good players have made it.

The reason it is hard is one fact: the mate only exists in a corner your bishop can attack. A bishop sees one colour of square forever. Two of the four corners are the wrong colour and no amount of technique produces a mate in them. So the ending is not one problem, it is two -- drive the king to the edge, and then walk it along the edge from the wrong corner to the right one while it is trying to go the other way.

The method

Know which corner you are aiming for before you start. A light-squared bishop mates on a light corner: a8 or h1. A dark-squared bishop mates on a8's opposite pair: a1 or h8. Get this wrong and the whole first phase is wasted.
Phase one: drive the king to any edge. King, bishop and knight all pushing together, exactly like the other endings -- take squares away, bring your king, do not let the box grow. This part is ordinary.
Phase two: walk it along the edge. If it is in the wrong corner it will not leave willingly, and this is the part that has to be learned. The bishop cuts the diagonal, your king takes the squares in front, and the knight jumps around the edge covering the squares the bishop cannot see.
The knight's route is the thing to memorise. It traces a shape commonly described as a W across the board as it hands the king from one square to the next along the edge. Learn one version of this properly rather than three partially.
Mate. Enemy king in the right corner, your king two squares away facing it, bishop checking along the long diagonal into the corner, knight covering the last square beside it.

A worked example, move by move

The position on the right above, played out. This is not a line somebody typed in: it is the shortest forced mate that exists from that position, taken from a tablebase built for this page, with Black defending as well as it is possible to defend.

The box columns are the squares the black king could still walk to if White stood still. It starts at 43 and the mate is played when it is one. It does not fall smoothly: nine of White's 28 moves here leave the king more room than it had, not less. That is real and it is worth understanding. A tablebase plays the shortest mate it can find rather than the most teachable one, and it can afford a move that opens the box because it can already see the finish. You cannot, which is why the method above trades a few moves for a box that mostly only shrinks. This ending is the extreme case, and it is worth being blunt about it: for most of the line above the box barely moves at all, because a bishop and a knight never build the standing wall a rook does. The confinement is dynamic -- it exists only in what White can play next -- and it collapses right at the end. That is a large part of why this mate has to be learned as a procedure. Feeling your way through it by watching the king's room does not work here, and on the other four endings it does.

After 13 moves. The box is 41 squares, down from 43. Nothing dramatic has happened; the king simply has less room than it did.

Mate on move 28. The box is one square, the king is standing on it, and it is in check.

Show the whole line

	White	Box	Black	Box
1.	Kc6	43	Kd4	43
2.	Kd6	43	Kc4	43
3.	Ne2	18	Kb4	18
4.	Kd5	42	Kb3	42
5.	Kd4	44	Kb2	44
6.	Kc4	43	Ka1	43
7.	Nc1	45	Kb2	45
8.	Nb3	4	Ka3	4
9.	Kc3	44	Ka2	44
10.	Bc2	45	Ka3	45
11.	Bb1	45	Ka4	45
12.	Nd4	45	Ka5	45
13.	Be4	41	Ka4	41
14.	Bd5	41	Ka3	41
15.	Nc2+	41	Ka4	40
16.	Kc4	41	Ka5	41
17.	Bc6	42	Kb6	42
18.	Nd4	41	Ka6	41
19.	Kc5	41	Ka5	41
20.	Nb3+	43	Ka6	42
21.	Bg2	44	Ka7	44
22.	Kc6	45	Ka6	45
23.	Bh3	4	Ka7	4
24.	Nc5	3	Kb8	3
25.	Kb6	2	Ka8	2
26.	Bg4	2	Kb8	2
27.	Na6+	2	Ka8	1
28.	Bf3#	1	—	—

Replayed through the same rules engine the app runs on. The final position is called checkmate because isCheckmate() says it is.

What goes wrong

Driving the king to the wrong corner. The commonest disaster, and it costs the whole first phase. Decide the target corner from your bishop's colour before your first move.
Trying to improvise phase two. It does not improvise. The squares the knight has to visit are specific and the order matters.
Running the fifty-move counter down in phase one. Nothing is captured in this ending, so the counter starts the moment it begins. Perfect play needs 33 of those fifty from the worst starting position.
Stalemating on the edge. With three attackers covering a king on the rim it is easy to leave it no square and no check.

How long you actually have

Fifty moves. Under the fifty-move rule a game is drawn on request once fifty moves pass with no capture and no pawn move, and in an ending like this one nothing is ever captured, so the count runs from the moment the last piece came off the board.

Working backwards from every checkmate position that exists with these pieces until every position has an exact answer gives the real worst case: 33 moves with perfect play on both sides from the least convenient starting position there is. That is two thirds of the allowance gone before you have made a single inaccuracy, which is why this ending is lost on the clock more often than it is lost to defence.

Practise it

Reading the method is the easy half. The trainer below the fold on the practice page gives you a fresh generated position, a defending king that does not help you, a live count of the box, and a move budget of 55 for this ending -- 22 more than perfect play would need.

How to checkmate with bishop and knight, for real Free, no sign-up, works offline. It warns you before you stalemate and explains it if you do. Practise bishop and knight

Questions people ask

How do you checkmate with bishop and knight?

In two phases. First drive the enemy king to the edge of the board with all three pieces working together. Then walk it along the edge into a corner your bishop can attack, with the bishop cutting the diagonal, your king taking the squares in front of it and the knight covering the squares the bishop cannot see. The mate is king opposite, bishop checking into the corner, knight covering the last square.

Why can't you mate in any corner with bishop and knight?

Because a bishop only ever attacks one colour of square. The mating position needs the corner square itself to be attacked by the bishop, so two of the four corners are impossible. Which two depends on which colour your bishop started on.

Is bishop and knight checkmate worth learning?

It is rare, it is hard, and it is a forced win you will throw away if you do not know it. That combination is why it splits opinion. The honest answer is to learn the first four basic mates until they are automatic first, because they come up far more often, and to come back to this one only if you want it.

How many moves does bishop and knight checkmate take?

Up to 33 with perfect play from the worst starting position, against the fifty the rules allow. That figure was computed for this page by building a complete tablebase for the ending. It is the reason a poorly played first phase can lose a won game to the clock rather than to the opponent.

Can you checkmate with two knights?

Not by force. Two knights against a lone king can produce a mate only if the defender cooperates, because the move that takes away the last square also relieves the stalemate. Bishop and knight is a forced win; two knights is not.

The other basic mates

Five endings, one page each, all of them forced wins.

Elsewhere on the site: endgame tactics from real games, mate in one for seeing a mate before forcing one, stalemate and the opposition in the glossary, and free printable worksheets for clubs and classrooms.