About

The Louisa Rule gives cube action for a 3-roll no-miss position on-roll versus 3 or 4 checkers, meaning Black has 5 or 6 checkers stacked on the ace point (so will bear off in exactly three rolls, or two rolls with a doublet), and White has 3 or 4 checkers. For example:

The Louisa Rule is described in Art Benjamin's "Math Overboard: Three Checkers Left and Variations" (PrimeTime Backgammon, Winter 2021). It was named after Louisa, Liesl's younger sibling in The Sound of Music; the Liesl Rule covers the mirror situation (4 checkers on-roll versus a 3-roll no-miss position).

Unlike the Liesl Rule, the cube decision here depends on the opponent's position: Black will always be off in 3 rolls (or 2 if they roll a doublet), so cube action is determined by how close White is to bearing off. The relevant measure is White's Adjusted Pip Count (APC).

How to use

Step 1: Compute White's Adjusted Pip Count (APC)

Start with White's pip count, then add penalties for spare checkers (any checker beyond the first on a given point):

This is the same APC formula used by the Benjamin 3 vs. 3 Checker Rules.

Step 2: Apply the Louisa Rule