Skip to content

Chapter 3 of 8

Spaced Repetition Systems and Algorithms

Spaced repetition is the operational form of distributed practice applied to individual facts. After each successful review the next review is pushed further into the future, ideally timed so that recall would have just begun to fail. This produces expanding rehearsal, with intervals of roughly one day, then a few days, then weeks, mirroring how memories stabilize over time. Longer gaps between study and test (the lag effect) generally lead to better long-term retention, provided each study session ends with successful retrieval rather than passive re-exposure. A recommended spacing curve for newly learned facts begins with a first review after about one day, then two or three days, then seven, twenty-one, and sixty days, scaling roughly with the SM-2 algorithm's default behavior for an average card. The strongest form of distributed practice, the distributed lag schedule, uses multiple sessions separated by increasing gaps and outperforms cramming by wide margins.

SM-2, the SuperMemo-2 algorithm devised by Piotr Woźniak in the mid-1980s, is the foundation of most modern spaced repetition software. Each review is scored on a six-point quality scale: 0 for total blackout, 1 for incorrect but familiar, 2 for incorrect but easy once seen, 3 for correct with serious difficulty, 4 for correct after hesitation, and 5 for perfect recall. After the first successful repetition the next interval is one day; after the second, six days; from the third repetition onward, the next interval equals the previous interval multiplied by the card's ease factor, a per-card multiplier (default 2.5, floor 1.3) that grows with successful reviews and shrinks with failures. A quality below 3 is treated as a fail: the repetition counter resets, the interval drops back to one day, and the ease factor is reduced toward the floor, forcing the card into heavy short-term review.

The Leitner system implements spacing more crudely with discrete boxes (typically five), moving cards up a box on successful recall and down on failure. Anki's default algorithm is a modified SM-2, adding "easy bonus" and "hard interval" modifiers that deck authors can tune per deck. Anki distinguishes learning cards (short review intervals during initial acquisition), young cards (intervals below twenty-one days), and mature cards (intervals of twenty-one days or more, considered reliably learned but still needing periodic review). Each card has learning steps (short review intervals during the learning phase, e.g., one minute then ten minutes) and a graduating interval (the longer interval applied once the card passes into the review queue, typically one day, then four days for the second graduation). Settings such as the minimum interval (the smallest gap between reviews, often one day), the maximum interval (a cap, e.g., 365 days), the starting ease (default 2.5), and the fuzz factor (a small random jitter, typically plus or minus five percent, that prevents many cards from coming due on the same day) shape how each deck behaves. Anki's review queue orders due cards by interval so that urgent reviews come first, with a small learning queue of new and lapsed cards running alongside.

The Again, Hard, Good, and Easy buttons in Anki map onto SM-2 logic: Again fails the card and restarts learning, reducing the ease factor; Hard repeats the card sooner with reduced ease; Good applies the standard SM-2 multiplier; Easy awards a bonus that lengthens the next interval. A leech, a card flagged after many lapses (Anki's default threshold is eight), signals a bad card rather than a bad memory, and the right response is usually to rewrite, split, or delete it. Expansion, a small multiplier added to long-interval cards, slows accumulation of overdue cards and trims the daily review load. Good card design follows the minimum information principle: each card tests exactly one fact or idea, and cards longer than about twenty to thirty words on the front tend to punish skim-reading. Cloze deletion (fill-in-the-blank cards where words are masked) and image occlusion (hiding parts of an image to be revealed on click) are efficient special-purpose formats. The "20-card rule" advises testing the first twenty cards of a new topic before generating more, because difficulty phrasing them as clean questions usually means the material is not yet understood well enough to encode. Reverse cards add the back-to-front direction for paired facts such as country and capital, doubling deck size in exchange for bidirectional recall. Most learners should also cap new cards at ten to thirty per day per deck, since more than that compounds review backlogs quickly.

All chapters
  1. 1Foundations of Memory and Learning
  2. 2Cognitive Strategies for Deeper Learning
  3. 3Spaced Repetition Systems and Algorithms
  4. 4Metacognition, Self-Explanation, and the Teaching Mindset
  5. 5Generation, Errorful Learning, and the Testing Family
  6. 6Practice Design, Skill Acquisition, and Transfer
  7. 7Sleep, Consolidation, and Long-Term Memory
  8. 8Putting It All Together

Drill it

Reading is not remembering. These come from the Learning Strategies deck:

Q

What is spaced repetition?

A learning technique where material is reviewed at gradually increasing intervals. Each successful recall pushes the next review further into the future, optimi...

Q

What is the forgetting curve (Ebbinghaus)?

Hermann Ebbinghaus's finding that memory decays exponentially over time without reinforcement — we forget ~50% within an hour and ~70% within 24 hours of learni...

Q

How does spaced repetition counteract the forgetting curve?

By timing reviews just before you would forget, each review resets and strengthens the memory trace, making the forgetting curve shallower with each repetition.

Q

What is retrieval practice (the testing effect)?

The act of recalling information from memory — rather than re-reading — strengthens memory far more than passive review. Tests are not just assessments; they ar...