First checkmates

White has a king on a1 and a rook on b2. Black has a lone king, right in the centre, on e5. White wins, but not quickly: even with the best play, mate comes only on move 16. It cannot take longer. Among the positions of king and rook against king, this is one of the longest.

How can we be so exact? The part of the game when few pieces are left on the board is called the endgame, or the ending. There are comparatively few positions with three or four pieces, so they can all be worked out in advance, every one of them. The engine of this course has done exactly that. It has endgame tablebases for thirteen such endings: for every position they record how it ends with best play from both sides and in how many moves. Queen against king and rook against king are among them.

Sixteen moves is not many. The fifty-move rule allows more than three times that, because the count starts again after the last capture. But a tablebase knows the move, and a person needs a plan. Without one, the opponent's king runs about the board and the fifty moves melt away. Two chapters ended on this promise, the one on mate and stalemate and the one on piece values: to learn to give checkmate to a lone king by a plan, without hoping for a mistake and without stalemating.

We go from the strong to the weak: two rooks, then a queen, then one rook. Each time there are fewer pieces and more work for the White king. Two rooks do not need it at all, the queen needs it only at the very end, and with one rook it works from almost the first move. At the end of each section you give the mate yourself. The engine defends. With the queen and with one rook it plays from the tablebases, so better than any human, and against two rooks it calculates the lines itself, at the level of a strong grandmaster.

Two rooks: the king rests

Let's start with something you have already seen. In the second chapter two rooks built a ladder: one holds a rank, the other checks on the next one, and the king retreats step by step towards the edge until some check turns out to be mate. The white king took no part, and that is no accident. Each rook shuts off a whole line, and together they take one rank away from the king with every move.

The ladder breaks in only one case: when the black king walks towards the rooks. A king attacks the squares next to it, and an unprotected rook beside it is lost. But a king moves one square and a rook moves across the whole board. If the king comes up to a rook, take the rook to the other end of the same line. It still holds the line, and the king again needs several moves to reach it.

Where should you drive the king? A check along its rank leaves the choice to the king itself: it can retreat both up and down. If you want to choose the side yourself, first use one rook to shut off the rank on the side where the king must not go, and then check with the other. Usually you drive the king to the nearer edge: the fewer ranks between the king and the edge, the fewer checks you need.

Now it is your turn. Imagine that all the other pieces have been traded and the rooks stand where they did at the start of the game, on a1 and h1. The black king has gone to the centre. Two rooks do not need any help from the king, so you can forget about the white king.

The queen: a knight's move from the king

By value two rooks are stronger than a queen: ten points against nine. But for mate something else matters. There is only one queen, and one piece cannot hold a line and check on the next one at once. Without its own king, the queen cannot mate a lone king at all. We have been through all 364 positions in which a king and a queen mate a lone king, and in every one the white king stands two steps from the black one: it either defends the queen or takes squares from the king itself. So the king is needed. But not at once.

First the queen alone shuts the king in. Everything depends on where you put it: a knight's move away from the black king. From such a square the queen gives no check, because a knight's move is not along any line the queen attacks. And the king cannot take it, because the square is two steps away. Yet of the eight squares around a king in the middle of the board, the queen takes five and cuts off a whole part of the board.

The part of the board where the king is shut in, let's call it the box. The king retreats, the queen follows and again stands a knight's move away, and the box gets smaller with every move. You need no checks for this: a check forces the king to move but does not say where, and the king picks the roomier side itself.

Here is how it looks. Black defends as stubbornly as possible: all their moves are the best by the tablebase. The white king stays on b1 for now.

Now comes the most dangerous place in the whole queen mate. A box of two squares at the edge is very nearly stalemate. One more queen move like that, and the king has no squares at all while there is no check. You saw such a position at the very start of chapter 5: queen on g6 against king on h8.

The rule is simple: once the box has shrunk to two squares at the edge, the queen stops moving. The opponent's king can only go back and forth, since it has to move, and meanwhile your king comes to help.

The king took the shortest road to the opponent, and you remember from chapter 3 that going diagonally is no longer for a king than going straight. Five steps with the king, one queen move, and it is mate.

Queen mates are usually of two kinds. The first you have just seen: the queen stands right next to the king, and your own king protects the queen. In the second the queen checks from far away, along the edge of the board, while the white king stands opposite the black one with one square between them and takes three squares of the next line. Find a mate of the second kind, but remember stalemate.

It is worth recognising the final blow in these mates at once, without counting. For that there is the "Mate in one" trainer from chapter 5: its first level is a queen and rooks against a lone king, and it is also on the "Practice" page.

And now all of it, from start to finish. The queen and king are on their starting squares again, and the black king is in the centre. First the queen a knight's move away and the box squeezed, then the king, then mate. And until the queen is in place, check every move for stalemate.

One rook: the king does the work

One rook is the hardest. The queen alone shut the king in by standing a knight's move away, but a rook does not attack along diagonals. If it stands next to the king without protection, the king takes it. But a rook has two lines, a rank and a file. With the edges of the board they form a rectangular box, and while the rook holds both lines the king cannot get out: books say that the rook has cut the king off. The plan is the same as with the queen: squeeze the box. But the rook cannot squeeze it all the way.

The rook has squeezed the box to two ranks and can go no further: the king stands right against the wall, and any attempt to rise lets it out downwards. To push it back one more line, you need a check after which it cannot go down. That is possible when the kings face each other on one file, with one square between them. This position is called the opposition. You saw it back in the chapter on the king, only without the name: neither king can enter the square between them.

If it is White's move in the opposition, the rook checks along the black king's rank. The king cannot go down: the white king attacks the three squares below it. It can only retreat to the edge, to the next rank, and the box becomes a whole rank lower.

Black, of course, will not walk into the opposition by choice. Usually its king stands diagonally from the white one, a knight's move away. A check is then useless: the king goes down, round the white king. You can put your own king opposite, but then it is Black's move, and they simply step aside. The rook helps: it makes a move along its own wall, away from the king, and changes nothing except whose turn it is: now Black has to move. This is a waiting move. The black king must move: either into the opposition, and then comes the check, or sideways, and then the white king follows. Let's go on from a similar position.

Look at the last move once more. This is how a rook mate on the edge of the board looks: the kings stand in the opposition, and the rook checks along the edge. If the opponent's king does not walk into the opposition itself, you can force it to.

The danger is the same as with two rooks: the king attacks the rook. In a corner this happens especially often.

Now give the mate yourself, starting from the edge. The rook already holds the seventh rank, and the opponent's king is on the eighth. Bring up your king, catch the opposition, and when there is none, make a waiting move.

It remains to put it all together. First the rook builds the box and squeezes it until the opponent's king stands right against the wall or attacks the rook itself. Then your king comes up and stands under the wall. If the rook is attacked, it goes to the other end of its line. If the kings face each other, the rook checks, and the box becomes a rank lower. If the kings are a knight's move apart, the rook makes a waiting move. In this way the opponent's king is driven to the edge, and there a check in the opposition turns out to be mate.

By the tablebase, a rook and king mate a lone king in 16 moves at most, as in the position at the start of the chapter. This plan takes a few moves more than the tablebase, but fifty is a long way off. The last position of the chapter is set up as it was for two rooks and for the queen: pieces on their starting squares, the opponent's king in the centre.

What's next

Now you can bring a won ending to mate when you have a queen, a rook or two rooks against a bare king. Against the best defence two rooks mate in five moves from the centre, a queen in seven and a single rook in fourteen, and with the plan you will fit into fifty moves with plenty to spare. There are harder mates. A bishop and a knight can also mate a lone king, but it may take 33 moves and needs a special technique. It is covered in chapter 37. The opposition returns in the chapter on pawn endings: there it decides whose king gets through. And mates where many pieces are still on the board, with names and patterns of their own, are collected in chapter 18.

But first you have to reach a bare king. A game starts on a full board, and mistakes in the first moves cost the most: you can be mated before you have brought out your pieces. Chapter 10 tells how to start a game: why to fight for the centre, bring out your pieces and castle. And how not to fall for Scholar's Mate.