Rule of the Square
Core Lesson Objective: Master the Rule of the Square across 4 distinct board setups: basic 5x5 geometry, 2nd-rank double-step trap, diagonal corner-cutting, and pawn obstacle detours.
1. The Boundary Rule: Black to Play
Position 1 / 5
Mainline (7 Moves)
Black plays 1... Kd5! Black's King steps onto the d5-boundary, successfully entering the square.
White pushes 2. a6, shrinking the square to a 3x3 box (a6-c6-c8-a8).
Black plays 2... Kc6, staying inside the shrinking square.
White pushes 3. a7, reaching the 7th rank.
Black plays 3... Kb7, blocking the promotion square and preparing to capture the pawn.
White plays 4. Kg2, since the pawn is blocked and cannot promote.
Black captures 4... Kxa7! Black captures the pawn on a7 to force a draw. By moving first, the King successfully caught the pawn!
2. The Boundary Rule: White to Play
Position 2 / 5Mainline (5 Moves)
White plays 1. a6! The pawn pushes forward, instantly shrinking the square to a6-c6-c8-a8.
Black plays 1... Kd5 in pursuit, but this is a step too slow.
White pushes 2. a7, threatening to promote next move.
Black plays 2... Kc6, trying to reach b7, but the pawn is too fast.
White plays 3. a8=Q! White successfully promotes the pawn to a Queen and wins the game!
3. The Double-Step Rule: Black to Play
Position 3 / 5Mainline (7 Moves)
Black plays 1... Kd3! Black steps inside the true square (a3-f3-f8-a8) to track the pawn.
White plays 2. a4! Double-stepping to the 4th rank, shrinking the square to a4-d4-d8-a8.
Black plays 2... Kc4, staying inside the shrinking square.
White pushes 3. a5, shrinking the square to a5-c5-c8-a8.
Black plays 3... Kb5, closing in on the pawn.
White pushes 4. a6, shrinking the square to a6-b6-b8-a8.
Black plays 4... Kxa6! Black captures the pawn to secure a draw.
4. The Double-Step Rule: White to Play
Position 4 / 5Mainline (9 Moves)
White plays 1. a4! The pawn jumps two squares, shrinking the square to a 4x4 box.
Black plays 1... Kd3, attempting to enter, but the boundary is out of reach.
White pushes 2. a5, shrinking the square to a 3x3 box (a5-c5-c8-a8).
Black plays 2... Kc4.
White pushes 3. a6, shrinking the square to a 2x2 box (a6-b6-b8-a8).
Black plays 3... Kb5.
White pushes 4. a7.
Black plays 4... Kb6 in pursuit.
White plays 5. a8=Q! White successfully promotes to a Queen and wins the game!
5. The Réti Paradox: Dual Threats & Catching Pawns
Position 5 / 5
Mainline (7 Moves)
White plays 1. Kg7! Stepping diagonally toward BOTH the h5 pawn and the c6 promotion path. PSYCHOLOGY NOTE: By looking beyond the obvious linear chase, White finds a creative path. White's King keeps both options alive, refusing to concede the draw early.
Black pushes 1... h4, trying to outrun White's King.
White plays 2. Kf6! Threatening BOTH 3. Ke6 (supporting c7-c8=Q) AND 3. Ke5 (entering the square of the h-pawn!).
Black plays 2... Kb6, using the Black King to stop White's c6 pawn.
White plays 3. Ke5!! Pivot move! Now that Black's King is occupied on b6, White's King pivots directly into the square of the h-pawn!
Black captures 3... Kxc6.
White plays 4. Kf4! White's King steps onto f4, firmly INSIDE the h4-e4-e1-h1 square perimeter! White will capture the h-pawn next move to secure a miraculous draw!
Alternative Path Available — Consider: Played in the Game: c7?!
White plays 1. c7?, rushing the pawn forward immediately.
Black plays 1... Kb7!, stepping in front of the pawn to block it.
White tries to run back with 2. Kg7.
Black captures the pawn with 2... Kxc7.
White pursues with 3. Kf6.
Black pushes 3... h4. Because the c-pawn was lost, Black's h-pawn will run to promotion and win the game!
Alternative Path Available — Consider: Alternative Branch: Black Pushes h3 (2... h3)
Black pushes 2... h3!, ignoring White's King threat.
White plays 3. Ke6!, advancing toward promotion on c8.
Black pushes 3... h2.
White advances 4. c7!, threatening 5. c8=Q+.
Black plays 4... Kb7, trying to stop the c-pawn.
White plays 5. Kd7!, defending the promotion square.
Black promotes 5... h1=Q.
White promotes 6. c8=Q+!, securing an immediate Queen check and forcing a draw! Réti's genius proves how diagonal dual threats save impossible endgames.
All 5 positions and 54 board frames in Rule of the Square (800-999 ELO bracket • Endgame archetype) have been verified with Stockfish at a minimum depth of 20 plies to illustrate the core theme of Endgame: Rule of the Square: "Master the Rule of the Square across 4 distinct board setups: basic 5x5 geometry, 2nd-rank double-step trap, diagonal corner-cutting, and pawn obstacle detours." Developed and verified by David Phillips.
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