Bähr rule easily explained.

Mastering Bähr’s Rule

In chess endgames, the Rook Pawn (a-file or h-file) is a draw's best friend. Even with an extra pawn, the attacking side often struggles because the defending King can hide in the corner. Bähr’s Rule is a geometric shortcut to determine if the attacking King can force the defending King out of the way or if the game is a dead draw.

1. How to Construct the Bähr Triangle

To apply the rule, you must find the key diagonal:

1. Identify the passed Rook Pawn.
2. Find the square one file over (toward the center) on the same rank.
3. Draw a diagonal line from that square down to the edge of the board.

The Verdict:

• Winning: If the defending King is outside this triangle, the attacking King can successfully "shoulder" the defender away and promote.
• Drawing: If the defending King is inside (or can move into) this triangle, they can reach the critical squares to force a stalemate or capture the pawn
• .Play Stockfish level 8 • lichess.org

2. Essential Exceptions

The rule is powerful, but it isn't "magic." You must account for these three exceptions:

• The Borderline Case: If the defending King is exactly on the diagonal boundary, the result depends on whose turn it is. Usually, if the defender can reach the "Drawing Zone" (the b1/b2 or g1/g2 squares) before being cut off, they secure the draw.
• The 6th Rank Threshold: Once the pawn reaches the 6th rank (a6 or h6), Bähr’s Rule becomes less relevant. At this point, if the defending King can simply touch the corner square (a8/h8), the game is a draw regardless of the starting geometry.
• Interference (Obstruction): The rule assumes a "clean" board. If the attacking King's path is blocked by other pieces or if they are forced to take a longer route around the pawn, the geometric count fails.