AZB Osmium Member
Here's an update on this rule of thumb since Dr. Dave actually did the analysis........
Throw When Balls Are Close – Bob Jewett
If the balls are a quarter-inch apart, there is no throw or cut, no matter how you hit them.
The actual distance is exactly 3/8 of an inch (and not 2/8 or 1/4).
Surprisingly the rule does not depend on how dirty the balls are at least for fairly full hits into the back ball because the balls will be gearing before the end of the shot.
Here is the related page on Dr. Dave's site: https://billiards.colostate.edu/FAQ/combination/small-gap/