Triangulation in King and Pawn Endgames
White to play and win, after Triangulation
PlayYou have the winning position, but it is your move, and it should be his. The rule: when the kings are on the right squares but the wrong side is to move, walk your king round a triangle. Three moves bring back the same position, and now he has to move.
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Triangulation: Losing a Move to Win
White to play and win · Win against perfect defense
Waking the engine…
The theory
Watch the method: press play to see the winning idea run, or step through it move by move.
Your king on d5 against his on d7: with Black to move, he would have to give way. It is your move, so you need to lose a move. Breaking now with c6+ only draws: Kc8, and after Kd6 Kb8 Kd7 bxc6 nothing is left.
Triangulation is a way to lose exactly one move on purpose, so that the same position comes back with your opponent to move.
Find the corresponding pair. Here it is d5 and d7. Kings on those squares with Black to move is a zugzwang he cannot survive. With White to move it is nothing at all.
Walk the triangle. Your king goes d5-c4-d4-d5. Three moves, an odd number, so the obligation to move passes to the other side. The black king has no matching detour: the b6 pawn takes a7 and c7 away from it, and your king takes c6, d6 and e6.
Then break through. Forced off d7, the defender lets your king in, and the c5-c6 break comes only once he has been pushed back for good. Play c6 a move early and the win is gone.
In this drill the defense never cracks. Trace the triangle, restore the position with Black to move, and win.
Keep going
Corresponding Squares Behind the Passed Pawn
White to play and win
The Stalemate That Saves
Black to play and draw
Corresponding Squares: Dedrle's Draw
Black to play and draw
All 68 king & pawn positionsFollow the full curriculum (free)