How do the study schedules work in detail?
The details of the learning schedules are complex, and we deliberately don't go into great detail in the help pages. We want the tool to be accessible to everyone, not just people who know a lot about flashcard systems.
But if you are into flashcard systems, here are some details about what we are doing behind the scenes...
The 'Cram' schedule is based on the Leitner system, which uses a series of boxes. There are 5 boxes. Cards start in the first box. If you get them right, they move to the next box. Get one wrong and it goes back to the first box. The system makes the notes due that are in the lowest occupied box.
Cram is the only system that is not time based. You can just keep refreshing your due notes to make more due when you finish a slideshow. This schedule is best when you are in the last days before a test or exam and you just have to keep going over your notes until they stick.
The other systems all have a time element. The standard 'Long Term Learning' schedule is based on one of Supermemo's algorithms. The schedule begins with a sequence of increasing time intervals. Assuming you keep grading a note correct, the note will first become due again after 1 day, then 6 days later, 16 days later, and so forth. Get the note wrong, and the note starts the schedule again.
(Even this is a simplification of the actual algorithm, because the intervals are also adjusted based on how well you answer a particular note. Answer wrong a few times, and the intervals for that note shorten to help you out.)
The 'Date-Targeted Schedule' is unique to Mental Case. It is basically the Supermemo algorithm, but it dynamically adapts to try to ensure a certain likelihood of recall on the day you target (eg exam). The intervals are increasing just like the long-term schedule, but can be dynamically contracted or extended to try to ensure you know the information on the day you need it. The schedule thus combines the efficiency of the long-term schedule, with the pragmatic need to pass an exam. It works best when your target date is a few months away.
Studies for macOS and iOS
Mental Case for Mac OS X
Mental Case for iOS