Learning science

FSRS vs SM-2: why the algorithm most apps still use is wrong

SM-2 is the algorithm that made spaced repetition practical, it shipped in SuperMemo in 1987, and versions of it still schedule a large fraction of the world's flashcards. It is also, we now know, wrong in a specific and correctable way — and FSRS is what correcting it looks like.

9 min readLearning science

What SM-2 does

SM-2 keeps one number per card, the ease factor, starting around 2.5. Recall the card and the next interval is the last one multiplied by the ease. Fail it and the card resets to the beginning and the ease drops. That is essentially the whole algorithm, and its elegance is precisely why it survived: it is a few lines of arithmetic and it works well enough to be transformative compared with no scheduling at all.

The three things it gets wrong

1. It collapses memory into one variable

"How hard is this card for me" and "how well do I currently know it" are different quantities, and SM-2 stores them in the same number. A card can be intrinsically difficult *and* currently well-remembered. SM-2 has no way to represent that, so it mis-schedules it.

2. Its forgetting curve is the wrong shape

SM-2's intervals imply exponential decay. Human forgetting is closer to a power law: it drops fast early, then develops a long, flat tail. The practical consequence is that SM-2 systematically under-schedules well-known cards — it brings them back long before you were going to forget them. Every one of those reviews is a review you did not need to do.

3. It cannot learn from you

SM-2's constants were chosen by hand, in the 1980s, and they are the same for everybody. Your memory is not the same as everybody's, and neither is your material.

What FSRS does instead

FSRS — the Free Spaced Repetition Scheduler — models memory with three separate variables, an idea drawn from the DSR (difficulty–stability–retrievability) framework:

  • Stability — how long this memory will last before recall probability decays to the target. Grows each time you successfully retrieve.
  • Difficulty — how intrinsically hard *you* find *this* card. Separate from how well you currently know it.
  • Retrievability — the probability you could recall it right now, which falls with time since the last review, along a power-law curve.

The scheduler computes the interval at which retrievability will have decayed to your target retention — 90%, say — and shows you the card then. Its weights were fitted against many millions of real reviews rather than chosen by intuition, and the model can be optimised further against your own history.

What that's worth in practice

SM-2FSRS
Memory modelOne number (ease factor)Stability, difficulty, retrievability
Forgetting curveImplicitly exponentialPower law — fits real data far better
ParametersHand-chosen, 1987, fixedFitted on millions of reviews; optimisable per user
Target retentionNot directly controllableExplicit, and you can set it
Typical outcomeMore reviews than necessaryFewer reviews for the same retention

The headline claim you will see quoted is that FSRS reaches the same retention with substantially fewer reviews — often cited in the range of 20–30% fewer, though the honest answer is that it depends heavily on your material, your ratings and your target retention. Take any single number with salt. The direction, however, is not in serious dispute, and the Anki community's adoption of FSRS as its default was the practical verdict.

Does any of this matter to you?

If you're doing twenty reviews a day: not much. Both algorithms will get you there and the difference is noise.

If you're a medical student with four thousand cards and two hundred reviews a day, a 25% reduction is an hour of your life back, every day, for years. That is who this is for, and it is why medics adopted it first.

Common questions

Is FSRS better than SM-2?

For nearly everyone, yes — it models memory with three variables instead of one and fits the forgetting curve with a power law, which generally means meaningfully fewer reviews for the same retention. SM-2's advantage is simplicity, which no longer buys much.

Does Anki use FSRS?

Anki has supported FSRS for some time and the community drove much of its development. Check Anki's current documentation for how it's configured in the version you're running.

What FSRS version does Thaxas use?

FSRS-4.5, with the published seventeen weights and a power-law forgetting curve, computed server-side from your stored review history and verified against reference values in our tests.

Can I set my own target retention?

FSRS is built around an explicit target — that is one of its main advantages over SM-2, where retention is an emergent property of the ease factor rather than something you choose.

Try it on your own material

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