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Guided lesson · Improver · Endgames

The rule of the square

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A pawn is racing toward queening and your king is far away: does it catch it or not? You can calculate it move by move, counting on your fingers and praying you don't get it wrong… or you can use the rule of the square: mentally draw a square from the pawn to its queening square, with that same side facing your king. If your king is inside the square — or can step into it with its move — it catches the pawn. If it's outside, there's nothing to be done. One glance, exact answer.

The key idea

Draw the pawn's square all the way to queening. King inside: it catches it. King outside: the pawn queens. And watch out — the square shrinks with every advance.

Example 1 · Outside the square

The black king chases the white pawn… but starts outside the square. Count and you'll see: it arrives one move too late.

  1. g5 The pawn is on g5 and queens on g8: its square runs from g5 to g8 and from d8 to d5. The black king, on a5, is clearly outside. We already know the result; watch it play out.
  2. Kb5 The king runs as fast as it can.
  3. g6 The square shrinks: now it runs from the e-file to the g-file. Even further for the king.
  4. Kc6 Keeps running, but the distance is what it is.
  5. g7 Second-to-last step. The black king would need to fly.
  6. Kd7 One move too late, exactly what the square predicted.
  7. g8=Q Queens. The rule saved you all the calculation: at first glance you already knew this pawn was unstoppable.

Example 2 · Inside the square

Same race, but the black king starts one file closer: inside the square. Watch the difference.

  1. g5 The pawn's square now runs from g5-g8 to d8-d5, and the black king on c5 can STEP INTO it with its next move. That means it catches the pawn. Check it yourself.
  2. Kd6 Inside the square. From here on it's pure routine.
  3. g6 The pawn keeps its race and the square shrinks…
  4. Ke7 …but the king stays inside the new square. Always inside.
  5. g7 The pawn's last attempt.
  6. Kf7 And the king arrives just in time: it controls g8 and the pawn falls next move. One file of difference at the start, and the result changes completely. That's what the square measures. (By the way, white would have been better off not racing and bringing its own king closer earlier — but that's the lesson on king and pawn.)

Practice

Now YOU play black, and your opponent has just launched their pawn toward queening. Draw the square and step inside it. Every move outside the square is the pawn queening.

  1. Inside the square. That's it: if you don't step out, that pawn is yours. The pawn is on g5 and queens on g8: its square reaches all the way to the d-file. Move your king toward the pawn, to the d-file.
  2. The square shrank and you shrank with it. Perfect. The pawn advanced and its square now starts on the e-file. Stay inside: king to e6.
  3. You made it: your king controls the queening square and the pawn is doomed. Caught on the run, without counting a single move on your fingers. Last stride: bring the king to f7, touching the queening square.

The rule of the square, tested from the chasing side. Next time you see a pawn race against a king — yours or your opponent's — you'll have the answer at a glance.