From the instructor side, "blank days" are basically reserve days. I haven't NOT been used on a blank day thus far. Someone needs at least a non-fly, if not teaching a lesson.

On the line side, reserves are viewed as insurance. Every month there is an exchange while lines are being created over reserve numbers (headcount). The company wants as many as possible, the folks in PBS (pilots), want the fewest. The contract gives planned guidance (bid pack) to a min/max so it becomes an discussion over needed/wanted/warranted. 20% and above is a problem for the pilots, 10% or less is a problem for the company. 15% is a good spot (nominally, depending on the base size), but if the line average isn't high, the company stands on 20% without a contractual aspect to say no. The schedulers love to have reserves, some pilots on reserve don't want to be used (the few that live in base). Most pilots either want a line, or want to fly with an early release time on the last day.

All known, and in most cases, apply to common sense. Ending the day with a bunch of reserve folks unused isn't efficient, as is ending the day with canceled flights due to lack of reserves. It's the balance that needs to be found, and contractual positions to protect the bad end for the pilots. A compromise doesn't exist at the moment.

Guess what, few have it. Whether it's other regionals, majors, or cargo operators, the line is always moving and is not able to be a simple mathematical probability on any realistic level.