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Rule of the Square

Learn the geometric shortcut to instantly determine whether a king can catch a passed pawn.

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Introdução

The Rule of the Square is a powerful geometric shortcut for king-and-pawn endgames. To use it, draw a diagonal from the pawn to the promotion rank — this forms one side of a square. If the defending king is inside that square (or can step into it on its turn), the king catches the pawn. If the king is outside the square, the pawn promotes. In this position, White has a passed pawn on b2 and the Black king sits on h6 — far from the b-file. The square of the b2-pawn stretches from b2 to b8 (6 ranks), extending rightward to g2–g8. Since the Black king on h6 is outside this square, the pawn can race to promotion without any help from White's king. The key lesson: don't waste time marching your king — just push the pawn!

Conteúdo da lição

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1. b4

Push the pawn immediately! The Rule of the Square tells us the Black king on h6 is outside the pawn's square, so no king escort is needed. The double-push b4 is the fastest start — the pawn is now 4 ranks from promotion. After b4, the new square runs from b4 to b8 to f8 to f4. The Black king on h6 is still outside this square, confirming the pawn will outrun it.

Peão passadoCorrida de peões
Lances alternativos
Ke2 — Wastes a tempo moving the king when the pawn can promote on its own. Every king move lets Black get one step closer.
b3 — Also wins but slower — the double push b4 saves a full move in the race.
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1. ..Kg5

Black's king rushes toward the pawn as fast as possible. Kg5 is the most direct diagonal path toward the b-file. But the king started outside the square — no matter how fast it moves, it cannot catch the pawn.

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2. b5

Keep pushing! The square shrinks with each advance: it now runs from b5 to b8 to e8 to e5. The Black king on g5 is still outside — two files too far to the right. The pawn is unstoppable.

Peão passadoCorrida de peões
Lances alternativos
Kf1 — Draws! Moving the king toward the kingside abandons the pawn. Black catches it after Kf4-Ke5-Kd6-Kc7.
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2. ..Kf5

Black continues the desperate chase, moving diagonally toward the pawn. The king reaches f5, but the square of the b5-pawn only extends to the e-file. The king is still one file too far away.

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3. b6

The pawn advances relentlessly. The square is now b6–b8–d8–d6 — just a 3x3 area. The king on f5 is two files outside the square. Each push shrinks the square faster than the king can close the gap.

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3. ..Ke5

Black's king reaches e5, still heading toward the pawn at maximum speed. But the b6-pawn's square only reaches the d-file — the king needs one more move just to enter the square, and the pawn won't wait.

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4. b7

One square from promotion! The pawn reaches b7. The square is now tiny: b7–b8–c8–c7. The Black king on e5 is three files away — it would need at least two moves to reach c7, but the pawn promotes next move.

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4. ..Kd6

Black makes one final lunge toward the b-file, but the king on d6 is still two squares from b8. The race is over — the pawn promotes next move.

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5. b8=Q+

Promotion with check! The pawn becomes a queen, delivering check from b8 to the king on d6 along the diagonal. With a queen and king against a lone king, the position is trivially won. The entire game was decided before a single move was played — the Rule of the Square told us immediately that the Black king could never catch the pawn.

Peão passadoVitória por tablebases

Pontos-chave

  • Draw a square from the pawn to the promotion rank — if the defending king is outside it, the pawn promotes
  • Remember the double-push: a pawn on its starting rank gets a bonus move, so the square is drawn from one rank ahead
  • Don't waste tempo with king moves when the pawn can promote on its own — every king move gives the opponent a free step closer
  • The square shrinks by one file and one rank with each pawn advance — once the king falls behind, it can never catch up
  • When the king IS inside the square, you'll need your own king to escort the pawn — that's a different technique (opposition/key squares)

Resumo

You've learned the Rule of the Square — a geometric shortcut that instantly tells you whether a king can catch a passed pawn. By drawing a square from the pawn to the promotion rank, you saw that the Black king on h6 was outside the square of the b2-pawn and could never catch it. The key was to push the pawn immediately without wasting time on king moves.

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