Spaced repetition is O(log n) sustainable

Wednesday September 8, 2021

If you use spaced repetition software like Anki for a long time, will you have to spend more and more time studying every day? Yes, but the increase is logarithmic with time, which is a very slow increase. If you add ten cards a day, then after a year you do 85 reviews per day. After ten years, that goes to 118 reviews per day, and even after 100 years, it's 152 reviews per day—still only half an hour or so each day.

The major simplifying assumption here is that review delays double, so that after n days, the number of days that are contributing their cards to today's review is log₂(n).

Your review delays won't be exactly that, and you won't add cards evenly across days. For me, the estimate is close but slightly high after 336 days of using Anki.

The average number of cards added per day is an important multiplicative factor; my average is currently 11.3 cards per day and trending lower. It might be higher for full-time students, but I'd be surprised if many people stayed much above ten cards per day over multiple years. When you stop adding so many cards, daily reviews decrease rapidly.

I think spaced repetition study could reasonably be a lifelong practice, like daily exercise.