Basic checkmate practice

Being a rook up is not the same as winning. Here are the five endings where you have just enough to force mate, against a king that defends instead of walking into it.

• 5 endings
• Positions generated, never repeated
• Budgets from an exact tablebase
• Free, no account

The five endings, and what each one costs

Every ending below is a forced win from any legal position: with correct play there is no defence, only a delay. The middle column is that delay -- the longest a perfectly defending king can survive from the worst starting position it can find, with White playing perfectly too. Those figures are not quoted from anywhere. They were computed for this page by building a complete retrograde tablebase for each ending, which is to say by working backwards from every checkmate position that exists until every position with those pieces has an exact answer.

Read the last row before you start it. Bishop and knight is genuinely hard. It needs a specific technique that has to be learned rather than worked out at the board, it can take two thirds of the fifty moves you are allowed even played well, and plenty of strong club players cannot do it. Anybody telling a beginner it is easy is describing a page they have not tested. The first four are all learnable in an evening.

Why this is the gap

Tactics training teaches you to win material. Almost nothing teaches you to cash it in, and those are different skills that fail at different times. The pattern is familiar to anyone who has watched beginner games: a player wins a rook on move twenty, plays on for another sixty moves, shuffles until the fifty-move rule or their own clock takes the point away, and never finds out what they did wrong.

These endings are also the cheapest points in chess to buy. There are five of them, they never change, they cannot be prepared against, and they come up in a real proportion of decided games. Learn them once and they are yours permanently -- which is the opposite of opening theory.

The one thing that ruins all of them

Stalemate. A king with no legal move that is not in check is a draw, whatever else is on the board. It is the reason "how to checkmate with queen and king without stalemate" is one of the phrases people actually type, and the queen is the worst offender because it takes away so many squares at once that removing the last one is easy to do by accident.

The trainer above is built around this. It counts the defending king's remaining squares after every move you make, and when there is only one left it says so, on the board, before you can throw the game away. If you stalemate anyway it names the squares your move took away, states that the king was not in check, and hands you the move back to play again. That is the whole lesson in one interaction, and it is worth more than any amount of prose about it.

The habit that replaces it is short. Before any quiet move, count the enemy king's squares. If the answer is one, your move has to be a check.

The box, and why the trainer draws it

Shade the box in the trainer and you can see the only thing that matters in these endings. The shaded region is every square the defending king could still walk to if you stood completely still -- not the squares it can reach this move, but everywhere it could eventually get to. That number is technique made visible.

It is a trend, not a rule, and it is worth being straight about that. Perfect play does not shrink the box on every move: a rook stepping off the line it was cutting on opens the king's room for exactly one move before closing it a rank nearer, and a tablebase will happily do that because it can already see the finish. What matters is the floor. Beginners driving a king with a rook will spend six moves checking it around the board while the number never gets below where it started, and watching it not fall is the fastest way to understand why the checks were not the technique.

One ending is different, and the guide pages say so where it applies: bishop and knight barely confines the king statically at all until the very end, because two minor pieces never build the standing wall a rook does. That is one of the reasons it has to be learned rather than felt out.

Two things follow from it that are worth saying plainly. The first is that your king is not a spectator. In four of the five endings the mate is impossible without it, and a rook or a queen on its own can shrink the box only so far before it needs the king to come and take the last squares. The second is that mate happens on an edge or in a corner in every one of these endings, because the edge is where the box runs out of room.

How to practise these properly

1. Start with two rooks. It teaches cutting the king off in the purest form, because your own king never has to take a single step. If the ladder is clear, the idea behind rook and king is already half learned.
2. Then rook and king, until it is boring. This is the one that decides real games. Do it until you can do it without thinking about it, because in a game you will be doing it tired and short of time.
3. Then the queen, watching the square count. The technique is quicker than the rook. The discipline is the whole exercise.
4. Two bishops when the first three are automatic. A rarer ending, but the idea -- two pieces making a wall the king cannot cross -- transfers to a lot of other positions.
5. Bishop and knight last, or never. It is a genuinely different problem and it is fine to decide it is not worth your evening. If you do want it, learn one method properly rather than three partially.

Use the move budget as the test rather than the clock. Getting there in forty moves is not the same skill as getting there in fifteen, and only one of them survives a real game with a real opponent and a real fifty-move counter.

Questions people ask

Where this fits in the course

• Rook and kingThe one that decides real games
• Queen and kingFastest to learn, easiest to draw by accident
• Two rooksThe ladder. Start here
• Two bishopsTwo pieces making a wall
• Bishop and knightThe hard one. Told honestly
• Endgame tacticsPositions from real games, in the course
• Mate in oneSeeing the mate, before forcing one
• StalemateWhat it is and how to stop causing it
• OppositionThe king move that does the pushing
• Coordinates trainerName every square without counting
• Free rating testTwelve positions, an honest range
• Printable worksheetsFree PDFs with answer keys

What the trainer does and does not do

The positions are generated at random and then checked before you see one. Each candidate is parsed by the same rules engine the app's lessons run on, and it is thrown away unless the material is exactly right, the position is legal, it is not already checkmate or stalemate or a dead draw, and nothing of White's is standing next to the black king undefended. The defending king always starts in the middle sixteen squares, because a lone king that starts on the edge is already half mated and would hand you the first two thirds of the technique for free.

The defending king is not perfect and is not pretending to be. It takes any piece you leave hanging, it refuses to step into mate in one when it has any alternative, and otherwise it runs for the middle, keeps away from your king and keeps as many squares as it can. Perfect defence would need the full tablebase, which is tens of megabytes and belongs in a build script rather than on your phone. What this defender guarantees is the thing that matters: it will not walk into your mate, so every move it survives is a move your technique failed to take away from it.

It also has no stalemate avoidance, deliberately. If you take away its last square without giving check, it will happily accept the draw -- because hiding that would remove the most useful thing on this page.