Bähr's rule

Bähr's rule helps determine whether a very specific pawn ending is won or drawn. On one edge of the board, two rook pawns block each other, and the stronger side also has a distant passed pawn. A rook pawn stands on the a- or h-file. It is blocked when it cannot advance because another pawn occupies the next square. A passed pawn has no enemy pawn ahead of it on its own or either neighboring file.

The stronger side usually plans to sacrifice the passed pawn to lure the defending king away from the edge. While that king chases or captures it, the attacking king tries to reach the blocking pawn, capture it, and free its rook pawn to reach the last rank and turn into another piece. The defender tries to eliminate the passed pawn and return to the promotion corner in time.

When the rule applies

• The stronger side's rook pawn has not advanced beyond its fourth rank. If it has reached the fifth rank or farther, the standard setup is winning for the attacker and this rule is no longer the needed test.
• The attacking king stands beside the passed pawn and can support its advance.
• The defending king stands in front of the passed pawn or the attacking king, so it still has a chance to contain them.

Once those conditions hold, a two-segment diagonal boundary is constructed. The first segment runs from the defending rook pawn toward that side's back rank, the rank nearest its own edge of the board. When it reaches a bishop file, c or f, named for the bishops' starting files, the second segment continues along the opposite diagonal. The passed pawn's position relative to this boundary normally classifies the ending: on the line or on the attacker's favorable side indicates a win; beyond it on the defender's side indicates a draw. The transition square on the bishop file itself is a special case, so it should not be judged only by words such as above or below. The orientation also changes with the edge and color, which is why the construction is best learned with a diagram.

This is an evaluation shortcut, not a law that replaces calculation. The exact king positions, the side to move, and documented exceptions can alter the result. When a concrete line conflicts with the rule, exact analysis of the pawn race, the move-by-move comparison of which side promotes or arrives first, takes priority.