FSRS vs SM-2: Which Spaced Repetition Algorithm Should You Use?

The short answer

That last sentence is the one most comparisons leave out, so it's worth stating first: algorithm choice is a real but second-order optimisation. Someone with a well-curated deck on SM-2 who reviews daily will comprehensively out-learn someone with a bloated deck on perfectly tuned FSRS who reviews twice a week. Fix the habit and the cards first. Then come back to this page.

How SM-2 works

Piotr Woźniak published it as part of SuperMemo 2 in 1987–88. The design constraints were severe — it had to run on an early PC, and it had to work from a handful of numbers per card. Judged against that, it is a remarkable piece of engineering that has held up for the better part of forty years.

The mechanics, in the original formulation:

• The first interval is 1 day; the second is 6 days.
• Thereafter, interval(n) = interval(n−1) × ease.
• You grade recall from 0 to 5. Ease is then adjusted by a small polynomial: a perfect answer raises it by 0.10, a "correct after hesitation" answer leaves it roughly unchanged, and anything worse lowers it — by 0.14 for a difficult recall, and considerably more for a failure.
• Ease is floored at 1.3 and never goes below it.
• Failing a card sends it back to the start of the interval sequence.

Anki's long-standing default scheduler was a modified SM-2. It replaced the 0–5 grades with Again / Hard / Good / Easy, where Good multiplies the interval by the ease and leaves the ease alone, Hard applies a small multiplier and cuts the ease, Easy applies a bonus and raises the ease, and Again counts as a lapse. Same skeleton, friendlier grading.

The four things SM-2 can't see

The limitations aren't bugs. They're consequences of the design, and they're all consequences of the same thing: SM-2 has no model of memory. It has a multiplier.

1. It ignores how long you actually waited

A card is due on day 10. You answer it on day 10; you get the same next interval as if you'd answered it on day 24 after a fortnight away. In the second case you demonstrably knew it after 24 days — that's much stronger evidence of durability — and SM-2 discards that information entirely. It knows the scheduled interval, not the elapsed one.

This is why SM-2 handles backlogs badly. Everything you clear late is evidence the algorithm can't read.

2. It has no notion of probability

Ask SM-2 "what's the chance I remember this card today?" and there's no answer to give. Ease isn't a probability; it's a growth rate. Because there's no predicted recall probability, there's nothing to compare against a target — so there is no way to say "schedule this so I'll remember 90% of what's due", which is the request most people actually want to make.

3. Ease drifts in one direction

Under Anki's variant, Good — the answer you'll press for the overwhelming majority of reviews — leaves ease unchanged. Hard and Again cut it. Only Easy raises it, and pressing Easy on a card you found merely fine is a habit few people have.

So ease is a ratchet that mostly turns one way. A card that gave you trouble in its first fortnight carries the penalty for the rest of its life, even after it has become genuinely easy. This is the failure mode with a name.

4. It can't learn from you

The constants — 2.5, 1.3, 6, the coefficients of the ease polynomial — were chosen by hand in the 1980s. They are identical for a medical student drilling pharmacology and a hobbyist learning Italian. There is no mechanism by which fifty thousand of your own reviews could improve them, because SM-2 has no parameters to fit.

Ease hell, with numbers

The arithmetic makes it vivid. Take two cards, both currently at a 10-day interval, both answered Good every time from here on:

After five more successful reviews the healthy card has effectively left your queue. The ease-hell card is still showing up monthly, and will keep doing so indefinitely. Ten reviews later it reaches about four months while the other is past a decade.

Note what has and hasn't happened here. The ease-hell card was hard once. It is not hard now — you have answered it correctly six times running. SM-2 has no mechanism for noticing that, because ease only rises on Easy, and you're not going to press Easy on a card you've been failing for months out of sheer habit.

Experienced Anki users developed folk remedies for this — periodically resetting ease across a deck, or never pressing Hard. Both are workarounds for a structural gap. FSRS closes the gap by making a card's difficulty regress toward the mean as it accumulates successes, so a card can genuinely recover.

How FSRS works

It grew out of the DSR framework in Woźniak's later work on memory, and was developed as an open-source project — chiefly by Jarrett Ye and contributors — trained on a large public dataset of real review logs.

The three variables

• Retrievability (R) — the probability you'd recall the card right now, between 0 and 1.
• Stability (S) — measured in days, defined as the interval at which R falls to 0.9.
• Difficulty (D) — on a 1–10 scale, how resistant this particular card is to gaining stability.

The forgetting curve, explicitly

FSRS computes retrievability as R(t) = (1 + f · t/S)^−0.5, with t days since the last review and f = 19/81. Put t = S and it evaluates to exactly 0.9, which is stability's definition made concrete. In recent revisions the decay exponent has itself become a fitted parameter rather than a fixed −0.5.

This is a power curve rather than an exponential one, matching what the retention literature found decades ago — forgetting decelerates, so long-interval cards decay more slowly than a constant-rate model predicts. See the forgetting curve for that background.

How stability updates

This is where FSRS earns its keep. When you answer a card successfully, the increase in stability depends on three things:

• Current stability — the higher it already is, the smaller the proportional gain. Diminishing returns are built in, which is why a card doesn't run away to a hundred years.
• Difficulty — harder cards gain less per review.
• Retrievability at the moment of review — and this is the interesting one: the lower R was, the bigger the gain. Recalling something you had nearly forgotten increases stability more than recalling something still fresh.

That third rule is Bjork's desirable-difficulties principle expressed as arithmetic. SM-2 has no equivalent; it cannot distinguish an easy success from a hard-won one except through your button press.

Failing a card doesn't reset stability to zero either. A separate post-lapse formula computes a reduced stability that still reflects what the card had accumulated, so a single bad day doesn't undo a year.

Fitting it to you

FSRS has a set of numeric parameters — seventeen in FSRS-4.5, more in later revisions — governing these updates. The optimiser fits them to your own review log by minimising prediction error against what you actually remembered. Until you have enough history, it uses defaults derived from a large public dataset, which already outperform SM-2.

This is the genuinely new capability. Not "better constants" — the ability to have your constants.

Side by side

What the benchmark shows

The methodology is the right one: rather than arguing about which schedule "feels" better, it treats scheduling as a prediction problem. Given a card's history and the elapsed interval, what's the probability the user recalls it? Score every algorithm's predictions against what actually happened. Better calibration means the scheduler can hit your retention target with fewer reviews, because it isn't wasting reviews on cards you'd have remembered anyway.

Three caveats an honest comparison has to make:

• The benchmark is run by FSRS's own developers. It is open source, reproducible, and includes SM-2 and several alternatives as baselines, which is close to best practice for this kind of thing. It is still not independent evaluation, and you should read it that way.
• The corpus is self-selected. It is drawn from Anki users who opted to share review logs — heavily weighted toward language learning and medicine, and toward people committed enough to run Anki for years. Your material may behave differently.
• "20–30% fewer reviews" is a headline, not a promise. The realised saving depends on your retention target, your deck, and how good your cards are. Someone whose deck is full of compound cards will see less benefit, because their problem isn't scheduling.

FSRS has shipped inside Anki since version 23.10, initially as an opt-in setting, and has since become the recommended scheduler there. That is a meaningful signal on its own: the project with the most to lose from a bad scheduler adopted it.

The dial SM-2 never had

The shape of the trade-off is worth internalising:

There's a real optimum in here, and it's usually a little below 0.90 rather than above it. Every failed card has to be relearned, which costs reviews; every unnecessarily early review also costs reviews. Push the target too high and you drown in premature reviews, too low and you drown in relearning. The minimum sits in a broad valley somewhere around 0.85–0.90 for most decks, which is why the default is where it is.

If your queue is unmanageable, lowering this is a far better response than skipping days.

When SM-2 is still fine

Cases where switching isn't worth the effort:

• Small or young decks. Under a few hundred cards, or in your first month, the schedulers barely diverge. There isn't enough interval growth yet for the difference to compound.
• Short, fixed horizons. Studying for something six weeks away, after which the deck is retired? Almost all the difference between the algorithms shows up over months and years.
• You want to reason about the schedule by hand. SM-2 is arithmetic you can do on paper; FSRS is a fitted model. If predictability matters more than efficiency, that's a legitimate preference.
• Your app doesn't support it. Migrating apps to change scheduler is a large cost for a second-order gain. Improve your cards instead.

Switching without breaking your deck

1. Understand that nothing is destroyed. FSRS reads your existing review history and computes new intervals from it. Your cards, decks and logs are untouched, and the change is reversible.
2. Expect movement in both directions in the first fortnight. Cards stuck at the ease floor typically jump a long way out — that's the correction working. A few mature cards may come back sooner.
3. Leave the retention target at 0.90 initially. Change one thing at a time, or you won't know what caused what.
4. Don't optimise immediately. Defaults are good. Fitting to your own history becomes worthwhile once you have a substantial log — on the order of a thousand reviews — and improves from there. Re-optimising every day is pointless.
5. Grade honestly, and use all four buttons. FSRS extracts more signal from your ratings than SM-2 did, which means sloppy grading now costs you more. In particular, Hard means "I got it, but barely" — not "I failed".
6. Judge after a month. Compare daily review count and your true retention rate against where you were. One week tells you nothing.

Frequently asked questions

Where this comes from