Lasker's Manoeuvre: The Stepladder
Win Emanuel Lasker's 1890 study: your king hides from the rook checks behind the enemy king, your rook checks along the rank, and each cycle pushes the black king one rank down the a-file — until the capture on h2 pins the black rook and the c-pawn queens.
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Your king blocks its own pawn. Step out on the side where the rook checks will run out.
♔︎b8 clears the queening square, so c8=♕︎ is a threat and Black has to start checking. The side matters. Towards the d-file the checks would never stop. Towards the a-file there is a shelter one step away: the corner square a8, where Black's own king on a6 blocks the file. It is the only winning move in the position.
Alternative Moves
♖︎b2+ is forced: without a check the pawn queens. Taking it does not help either — after ♖︎xc7 your king recaptures, and rook against the h-pawn is a win for White. So Black checks and hopes to push your king back in front of its pawn.
Only one square ends the checks and keeps the win. Use the black king as a shield.
♔︎a8 looks like a dead end, but it is the shelter. The rook cannot check on the a-file because the black king stands on it, and it cannot check on the eighth rank without being taken. With the checks over, the threat to queen the pawn is back. Notice where the two kings stand: yours two ranks above Black's, on the same file. That formation is the core of the study.
Alternative Moves
♖︎c2 is forced again: with no check left, only a rook on the c-file stops the pawn from queening. Black has rebuilt the starting set-up with one difference — your king is on a8, not c8. From the corner it no longer protects the pawn; only your rook does, along the seventh rank. If the rook leaves that rank without a check, Black takes on c7 and draws.
Your king guards the squares above the black king. Use the rook to send that king one rank down.
♖︎h6+ is the second half of the cycle. Your king covers a7 and b7, the rook covers the whole sixth rank, so the black king has to step down to the fifth. Because it is a check, Black has no time to take the pawn the rook has just stopped guarding. One cycle is now complete: king out, king to the a-file, rook check.
Alternative Moves
♔︎a5 is the only square that lets Black go on defending. On b5 the king would stand in front of its own rook: your king steps to b7, there is no check on the b-file, and the pawn queens at the cost of Black's rook. Blocking the check on c6 simply loses the rook. So the king stays on the a-file, one rank lower — that single rank is all the cycle has won, and it will be enough.
The pawn has lost its guard and the black rook attacks it. Protect it with a move that also threatens to queen.
♔︎b7 does two things. It guards the pawn, which the rook left unprotected when it gave check, and it renews the threat to queen. The king is also heading for a7, to stand two ranks above the black king again. The tablebase rates the same step on the eighth rank as exactly equal — from either square your king reaches a7 next.
Alternative Moves
♖︎b2+ — the same forced check as on move one. Queening the h-pawn with check changes nothing: your rook takes the new queen, and the cycle runs on without the pawn, only faster. Black can do no better than follow the pattern.
Hide behind the black king again — one rank lower than before.
♔︎a7 is the shelter again, one rank lower than last time. The black king on a5 shields you from a check on the a-file, and your king covers a6 and b6 — the squares the black king would need to climb back. Compare with move two: kings on a8 and a6 then, a7 and a5 now.
Alternative Moves
♖︎c2 — forced, as before, to stop the pawn from queening. Everything on the left side of the board has moved down one rank: your king, Black's king, and your rook, now on h6 instead of h7. Only the black rook and the two pawns stand where they stood.
Same formation, one rank lower. Push the king down again.
♖︎h5+ sends the black king to the fourth rank. The squares above it belong to your king, the fifth rank to your rook. As in the first cycle, the check is what makes it safe for the rook to stop guarding the pawn: Black must answer the check first, and next move your king will guard c7.
Alternative Moves
♔︎a4 — down the a-file once more, for the same reason: on b4 the king would block its own rook's check, your king would step to b7, and the pawn would queen. Black's king is now two ranks from the second rank, where its rook stands.
Guard the pawn and threaten to queen, on the way to your next shelter.
♔︎b7 guards the pawn and threatens to queen. Your king is on its way to a6, and two squares both guard the pawn and touch a6 — the tablebase rates b6 as exactly equal. What matters is that the king first protects the pawn and only then returns to the a-file.
Alternative Moves
♖︎b2+ is the only move that stops the pawn from queening, for the third time. Black's rook is doing all it can — check, return, check, return — but it cannot stop its king from being pushed down.
Back behind the black king, another rank lower.
♔︎a6 — the shelter is now on the sixth rank, two above the black king on a4. Your king covers a5 and b5, so the next rook check will again leave Black only the way down.
Alternative Moves
♖︎c2 stops the pawn from queening, and the formation is complete again: kings on a6 and a4, your rook ready on the h-file. Black has not made a single mistake, and the position keeps sliding down the board.
Third cycle, same move. Send the king down.
♖︎h4+ pushes the black king to the third rank. One more cycle and it will be on the second, next to its own rook — keep that in mind, because it changes what the capture on h2 does.
Alternative Moves
♔︎a3 is forced by the same logic: a king on b3 blocks the b-file, your king goes to b7, and the pawn queens. The black king has been driven from a6 to a3 without ever being given a choice.
Guard the pawn from the square that leads to your next shelter.
♔︎b6 is the one precise step this time. Your king wants a5 next, two ranks above the black king, and b6 is the only square that guards the pawn and touches a5. In the earlier cycles two squares on the b-file did the job; here there is a single fastest one.
Alternative Moves
♖︎b2+ — the last of the forced checks that keep the pawn from queening. Stepping down to the second rank voluntarily would only bring the finish forward, so Black keeps to the pattern.
Take your shelter behind the black king one last time.
♔︎a5 completes the formation for the fourth time: kings on a5 and a3. Your king has come down the a-file from the eighth rank to the fifth, always two ranks above Black's.
Alternative Moves
♖︎c2 stops the pawn from queening once more. Look at the black king on a3: it is one rank above its rook. The next check will put the two on the same rank.
One more rank. Put the black king on the same rank as its rook.
♖︎h3+ is the last check of the ladder. The black king has to step onto the second rank, where its rook stands — or block on c3 and lose the rook at once. Everything so far was preparation for this: a king and a rook on one rank, with your rook about to arrive on that rank too.
Alternative Moves
♔︎b2 is the square that resists longest according to the tablebase; Lasker's own solution gives the step to a2, which loses sooner in the same way. On either square the king stands on the second rank, in line with its own rook and the pawn on h2. Black still stops your pawn and still has a pawn one step from queening — and is lost.
The black king and rook share a rank. Now the pawn you could never take is yours.
♖︎xh2 — the capture that only drew earlier now wins. The black rook is pinned against its king along the second rank, so it cannot take your pawn; it can only move along the rank. If Black takes your rook, the c-file is open and the pawn queens. If the king moves instead, you exchange rooks on c2 and the pawn queens with no rook left to stop it.
Alternative Moves
♖︎xh2 leaves Black a rook up for one move, but the rook has had to leave the c-file — the file it returned to four times to stop your pawn. Nothing stands behind the pawn any more, so it queens, and queen against rook is winning.
The c-file is clear. Finish.
c8=♕︎, and the study is solved: queen against rook is a theoretical win. Look back at the route. Your king went a8, a7, a6, a5; Black's was driven a6, a5, a4, a3 and onto the second rank; your rook checked from h6, h5, h4 and h3. Four identical cycles, and the last one put the black king on the rank of its own rook, where the h-pawn could finally be taken.
Alternative Moves
Key Takeaways
- A king can hide from rook checks behind the enemy king: on the same file, the enemy king blocks the check
- With your king two ranks above the enemy king, a rook check along the rank leaves that king only the way down
- Keep the order: the king guards the pawn, then hides, then the rook checks — two rook checks in a row let the black king climb back up
- Black cannot leave the pattern — a king on the b-file blocks its own rook, and a rook that leaves the c-file lets the pawn queen
- The capture on h2 draws while the black rook can take on c7, and wins once that rook is pinned on its own rank
Now play it through
Step through every move on a real board, try the wrong ones, and ask Knighty why they fail.
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