How spaced repetition and FSRS work

If you use flashcards, the most important thing the app does is not showing you cards. It is deciding when to show each one again. That decision is the scheduler, and it is what separates a flashcard app from a stack of paper cards.

Why spacing and self-testing work

Two findings from memory research sit behind almost every flashcard scheduler.

The first is the spacing effect: material reviewed over spread-out sessions is remembered better than the same material reviewed in one block. Researchers have studied this since the late 1800s, starting with Hermann Ebbinghaus’s 1885 experiments on forgetting. A 2006 review by Cepeda and colleagues pulled together 839 assessments of distributed practice from 317 experiments in 184 articles.

The second is the testing effect, also called retrieval practice: trying to recall something strengthens memory more than reading it again. In a 2006 study, Roediger and Karpicke found that on delayed tests, students who had been repeatedly tested remembered more than students who had repeatedly studied, even though repeated studying made the students more confident they would remember.

A flashcard asks you to recall an answer, which is the testing effect. A scheduler spaces your reviews, which is the spacing effect. Spaced repetition is the two combined.

The scheduling question

Spacing leaves a practical question open: how long should the gap be? Too short and you waste time on cards you already know. Too long and you have forgotten them by the time they return. Different cards, and different people, need different gaps.

For many years the common answer was SM-2, an algorithm from the SuperMemo software that Anki used as its default scheduler. It tracks a single “ease” number per card.

What FSRS does differently

FSRS, the Free Spaced Repetition Scheduler, is an open-source algorithm created by Jarrett Ye. It is based on the DSR model, which describes each card’s memory with three values:

• Difficulty: how hard the card is to remember. It affects how much a review strengthens the memory.
• Stability: how durable the memory is. The higher it is, the more slowly the card is forgotten.
• Retrievability: the probability that you can recall the card right now. It falls as time passes since your last review.

The model follows a few rules. Harder material gains less stability from a review. The more stable a memory already is, the less each extra review adds. And a review at a moment when recall was harder, meaning lower retrievability, adds more stability than an easy one. FSRS uses these to work out when a card’s retrievability will fall to the recall level you want, and schedules the review for then.

The algorithm fits its parameters to review histories, so it can adapt to how you actually remember. The Anki project added FSRS as an option in version 23.10 and says it lets you do fewer reviews than Anki’s older algorithm for the same level of retention.

What you do as a learner

You do not need to understand the maths. After each card you rate how it went: Again, Hard, Good or Easy. In FSRS, Again lowers the card’s stability and raises its difficulty, while Easy raises stability the most. Honest ratings are the input that keeps the schedule accurate.

How Mnemi uses it

Mnemi, our flashcard app for iPhone and iPad, schedules reviews with FSRS-5, so your time goes to the cards you are about to forget. You rate each card Again, Hard, Good or Easy, and your decks sync across your devices.

Sources

• Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354–380.
• Roediger, H. L., & Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255.
• Anki documentation: What spaced repetition algorithm does Anki use?
• Free Spaced Repetition Scheduler, project repository