Makes me wonder -- does it make any economic sense for a theater to have screenings before 2pm on a Tuesday? I get that some people can afford the leisure, but I'm almost certain the theater loses money on that
For the first few weeks of a film's release, all of the ticket sales goes to the studio. Pretty much the only revenue for the theatre is popcorn, candy and soda.
Since most theatres have gone full digital, the "projector" won't show the film if there have been no tickets sold. That eliminated the game of buying one ticket and then sneaking in to see a few more movies.
Why do you have projector in scare quotes? And what makes you think they don't screen the movie? Exhibitors have a contractual obligation to show movies a certain number of times a week, and the media players that run them show receipts to the studios ... it would be surprising if they didn't actually do that simply because nobody bought a ticket.
Probably just showing that it's not a film projector, but in actuality, it is still a projector. It may be assumed that digital movies are shown on a giant display, but that's cost prohibitive at that size; it's still a blank screen with light projected onto it.
How much extra does it cost to show an extra movie that nobody shows up to? It seems like the majority of the cost is rent of the building and salary. If employees are already working to operate the few movies that are expected to have people and the building is already being paid for then they may as well use up all their theaters just in case since the extra cost would be low.
Especially since you may have someone walk-up and willing to buy-in to the movie even though it started ten minutes ago, so I think I've answered my question above - they just show everything no matter what the sales look like.