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Bähr’s Rule: The Essential Endgame Heuristic

But what is the rule?

But what is the rule?

if there is no clear way to define the exceptions, its exaggerated to call it a rule?

if there is no clear way to define the exceptions, its exaggerated to call it a rule?

白方:666 大初年五接财神啦顺风顺水财顺神Happy New Year "烟火向星辰,所愿皆成真 "GGG

白方:666 大初年五接财神啦顺风顺水财顺神Happy New Year "烟火向星辰,所愿皆成真 "GGG

lichess articles as clickbait. classy.

lichess articles as clickbait. classy.

The written post and the first 7+ minutes of the video don't actually say what the rule is and can be skipped. You need to respect people's time and get to the point way faster if you want to be a successful content creator.

The written post and the first 7+ minutes of the video don't actually say what the rule is and can be skipped. You need to respect people's time and get to the point way faster if you want to be a successful content creator.

Here's my summary of the rule, sorry if I've got this wrong...

Bähr’s rule is useful for the common pawn endgame situation of opposed rooks’ pawns and one side having another passer somewhere else on the board. Can the stronger side win by abandoning the passer?
For example: “8/8/p4k2/P7/4KP2/8/8/8 w - - 0 1” is a win, but why?

The conditions to decide are:

  1. If stronger side’s rook's pawn has passed the middle then it is a win (with some exceptions).
  2. Otherwise, the stronger side’s king must be next to (or ahead of) the passer, supporting it, or be able to get there.
  3. The defender’s king needs to be in front of the passer and/or king to have a chance of a draw.

Once the conditions are satisfied then Bähr's rule says that you draw a line diagonally back from the defender's pawn to the bishop's file and then from there diagonally forward to the opposite side of the board. If the stronger side's pawn is on or behind the line then it is a win, otherwise the defender should be able to draw.

As far as I can tell the exception cases appear either (1) when the defender can simply get to the stronger side's rook's pawn and capture it with a trivial draw (8/8/p7/P7/3k4/8/3KP3/8 w - - 0 1), or (2) when the defender's rook's pawn is on the 7th rank and the stronger side's king will get trapped on, for example, a7-a8 without being able to make progress (8/p2k4/P7/2KP4/8/8/8/8 w - - 0 1). I think the first of these exception cases is easy to recognise but the second one is trickier.

In the winning positions, usually the stronger side can simply get the king next to the passer and then abandon it to grab the defender's rook's pawn and promote their own pawn. Sometimes more technique is needed, first pushing the passer (but not too far) to get to a position where the attacker's king can make a run for the defender's rook's pawn. Sometime's the defender's job is quite tricky even if it is technically drawn but that is a whole different story.

Here's my summary of the rule, sorry if I've got this wrong... Bähr’s rule is useful for the common pawn endgame situation of opposed rooks’ pawns and one side having another passer somewhere else on the board. Can the stronger side win by abandoning the passer? For example: “8/8/p4k2/P7/4KP2/8/8/8 w - - 0 1” is a win, but why? The conditions to decide are: 1. If stronger side’s rook's pawn has passed the middle then it is a win (with some exceptions). 2. Otherwise, the stronger side’s king must be next to (or ahead of) the passer, supporting it, or be able to get there. 3. The defender’s king needs to be in front of the passer and/or king to have a chance of a draw. Once the conditions are satisfied then Bähr's rule says that you draw a line diagonally back from the defender's pawn to the bishop's file and then from there diagonally forward to the opposite side of the board. If the stronger side's pawn is on or _behind_ the line then it is a win, otherwise the defender should be able to draw. As far as I can tell the exception cases appear either (1) when the defender can simply get to the stronger side's rook's pawn and capture it with a trivial draw (8/8/p7/P7/3k4/8/3KP3/8 w - - 0 1), or (2) when the defender's rook's pawn is on the 7th rank and the stronger side's king will get trapped on, for example, a7-a8 without being able to make progress (8/p2k4/P7/2KP4/8/8/8/8 w - - 0 1). I think the first of these exception cases is easy to recognise but the second one is trickier. In the winning positions, usually the stronger side can simply get the king next to the passer and then abandon it to grab the defender's rook's pawn and promote their own pawn. Sometimes more technique is needed, first pushing the passer (but not too far) to get to a position where the attacker's king can make a run for the defender's rook's pawn. Sometime's the defender's job is quite tricky even if it is technically drawn but that is a whole different story.

After clicking around with the board editor a bit there seem to be two obvious exception cases. I'd have to write a script to determine whether there are others.
The first case is simple and can be accounted for by modifying the first condition for Bähr's Rule. If the defending king cannot be prevented from winning the stronger side's rooks pawn while still being "in the square" for the passer, then it is a draw (e.g. "8/8/p7/P7/3k4/8/3KP3/8 w - - 0 1" is drawn). It's a bit more complicated but still relatively easy to see whether it is a potential issue even if you can't quite tell whether it is a draw or not without a bit of counting.
The second case is more complicated. If the defender's pawn is on the 7th rank then sometimes the attacker's king can be trapped in the corner without being able to make progress (e.g. "8/p2k4/P7/2KP4/8/8/8/8 w - - 0 1" is drawn). This messes-up the geometry of Bähr's rule because the defender's king no longer reaches the corner before the attacker but instead draws by trapping the attacker's king on the rook's file.

After clicking around with the board editor a bit there seem to be two obvious exception cases. I'd have to write a script to determine whether there are others. The first case is simple and can be accounted for by modifying the first condition for Bähr's Rule. If the defending king cannot be prevented from winning the stronger side's rooks pawn while still being "in the square" for the passer, then it is a draw (e.g. "8/8/p7/P7/3k4/8/3KP3/8 w - - 0 1" is drawn). It's a bit more complicated but still relatively easy to see whether it is a potential issue even if you can't quite tell whether it is a draw or not without a bit of counting. The second case is more complicated. If the defender's pawn is on the 7th rank then sometimes the attacker's king can be trapped in the corner without being able to make progress (e.g. "8/p2k4/P7/2KP4/8/8/8/8 w - - 0 1" is drawn). This messes-up the geometry of Bähr's rule because the defender's king no longer reaches the corner before the attacker but instead draws by trapping the attacker's king on the rook's file.