Two names come up whenever people talk about how a flashcard app decides what to show you next: SM-2 and FSRS. They are both spaced-repetition schedulers, and they are often described as "old" and "new". That is true as far as it goes, but it hides the interesting part: they start from different ideas about what memory is and what a scheduler should know about it.
In short
- SM-2 is a rule-based algorithm. Each card gets an "ease" number, and the next gap is the previous gap multiplied by it.
- FSRS is a model-based algorithm. It estimates, for each card, how stable your memory is and how likely you are to recall it right now.
- SM-2's rules are fixed and identical for everyone. FSRS has parameters that can be fit to your own review history.
- SM-2 doesn't use how late or early you were when you reviewed. FSRS does, because its estimates are tied to elapsed time.
- The FSRS project reports, from simulations, that it needs roughly 20 to 30 percent fewer reviews to reach the same retention. Treat that as the project's own claim, not a promise for any one person.
What SM-2 is
SM-2 is a published algorithm from Piotr Wozniak, a researcher in the field, and is described in his own write-up (the SM-2 algorithm). It is simple enough to fit on a page, which is a large part of why so many tools adopted it or a close variant. Here is how it works.
Every item has an E-Factor, an ease number, which starts at 2.5 and is never allowed to drop below 1.3. After each review you give a quality grade from 0 to 5, where 5 is a perfect response, 3 is correct but recalled with serious difficulty, and 0 is a complete blackout.
The schedule then follows three rules:
- The first interval is 1 day and the second is 6 days.
- After that, each interval is the previous interval multiplied by the E-Factor, rounded up to a whole number of days.
- If a grade is below 3, the repetition sequence restarts from the beginning, as if the item were new.
After each review, the E-Factor itself is nudged up or down by a formula that depends on the grade. A grade of 4 leaves it unchanged; better grades raise it a little, worse grades lower it.
A worked example
Take a card that you answer with a grade of 4 every time, so its E-Factor stays at 2.5. The gaps run 1 day, then 6, then 15 (6 times 2.5), then about 38 (15 times 2.5, rounded up), then roughly 95. Within five reviews the card is on a gap of about three months. Now suppose on the fourth review you blank and give a 2. The sequence restarts: 1 day, then 6, and so on again from the beginning.
That is a neat, predictable ladder. It is also where its limits show.
Where SM-2's design gets stuck
None of these are bugs. They are consequences of building a scheduler from a few fixed rules.
- The interval ignores when you actually reviewed. SM-2 multiplies the planned gap by the ease value. If you reviewed a card a week late and still got it right, that is evidence your memory is stronger than expected. If you reviewed it early, the review gave less information. The rules do not treat those cases differently.
- One number carries two ideas. The E-Factor stands in for both "this card is hard" and "my memory of this card is durable". Those are related but distinct.
- A lapse is harsh. Resetting the sequence after one failed recall throws away everything the system had learned about how well you knew the item.
- The constants are universal. The first two intervals, the starting ease and the update formula are the same for every learner and every kind of material.
What FSRS is
FSRS, the Free Spaced Repetition Scheduler, is an open-source algorithm developed by Jarrett Ye and a community of contributors (the ABC of FSRS). Instead of a rule that multiplies intervals, it keeps a memory state for each card with three parts:
- Difficulty - how inherently hard the card is for you.
- Stability - how long the memory lasts, defined as the number of days for the chance of recall to fall from 100 percent to 90 percent.
- Retrievability - the probability that you can recall the card at this moment.
After each review, the model updates difficulty and stability. Retrievability is derived from stability and elapsed time, so it falls naturally as days pass. FSRS-6, the current version, has 21 parameters that shape these formulas (more in what is FSRS).
The scheduler's job then becomes a question of prediction: given what the model believes about this card, when will the chance of recall drop to the level you want? That level is called desired retention, and it has its own explainer: desired retention in FSRS.
The differences that matter
Rules versus a fitted model
SM-2 is a recipe. FSRS is a model with parameters that can be trained on review data. Defaults come from many learners; you can fit them to one learner. Cirello does this fitting automatically each night (inside the pipeline).
What the review time means
In FSRS, how long it had been since the last review is part of the calculation. A successful recall at low retrievability raises stability more than an easy one at high retrievability. SM-2 has no such notion: the interval was planned, the grade comes in, the next interval is computed.
Target-driven scheduling
An SM-2 user gets whatever retention the ladder happens to produce. An FSRS user can choose a retention target and the scheduler works toward it, trading workload for recall deliberately.
How lapses are handled
When a card fails, FSRS reduces stability but does not erase its history. The card comes back soon, but the model remembers it was once well known, so its recovery can be quicker than a true restart.
Does the difference show up in practice?
According to the FSRS project's own simulations, FSRS needs roughly 20 to 30 percent fewer reviews than SM-2 to reach the same retention, and even FSRS with default parameters beats SM-2 in those comparisons. Those are simulations by the people who built the tool, so they are best read as a strong signal about the design, not a guaranteed number for you.
What you are likely to feel is less dramatic and more steady. Cards you know well drift to long gaps sooner. Cards you struggle with come back sooner and stay in view. A heavy week produces a backlog that resolves instead of cascading, which is part of why this kind of scheduling suits calmer study of dense material.
Is SM-2 bad?
No. For its time it was a clear advance on fixed ladders such as the Leitner system, where cards simply move between boxes. A large number of people have learned a great deal with it. It is predictable, easy to implement and easy to reason about. If you are using a tool built on it and your reviews feel fine, there is no emergency.
The case for FSRS is narrower: if you are going to spend months or years reviewing, a scheduler that fits your own memory and aims at a chosen retention level can save a meaningful number of reviews and make workloads easier to plan.
What this means for Cirello
Cirello schedules with FSRS-6 and retrains its parameters nightly. You do not pick an algorithm or tune weights. The scheduler is meant to disappear into the background so what you notice is a short daily queue. If you want the app-level view, see the FSRS app page, or start from what spaced repetition is if the underlying idea is new to you.