How do flashcard apps decide when to show you a card again?

They use a rule of thumb that fits in a few lines: every time you get a card right, wait longer before showing it again, and when you get it wrong, start over. Spaced-repetition programs such as SuperMemo and Anki show new and hard cards more often and older, easier ones less often, to exploit the spacing effect.

SuperMemo's scheduler was written by a student. Piotr Woźniak began developing his software after struggling to retain course material at the Poznań University of Technology in the 1980s, and its original computer algorithm, called SM-2, was released in 1987; Anki's scheduler is still derived from it.

Here is how it works. After you see a card, you grade your recall from 0, the hardest, to 5, the easiest. The first success sets the next review one day away, the second six days away, and from then on each gap is the previous gap multiplied by an easiness factor that starts at 2.5. A failed card goes back to one day. A card you always answered with some hesitation would come back after 1, 6, 15, 38 and 95 days.

Why growing gaps? As early as 1932, C. A. Mace proposed revising at gradually increasing intervals, roughly one day, two days, four days, eight days. Later work found that the best gap depends on how long you want to remember. In a study of more than 1,350 people, the best gap was about 20 to 40% of the time to the test when the test came a week later, but only about 5 to 10% when it came a year later.

Whether the growth itself matters is unsettled. Some papers favour expanding intervals, while other meta-analyses find that expanding and even gaps give similar results. Little evidence supports the common explanation that growing gaps help by gradually making recall harder, and the best schedule may depend on the learner.