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Updated August 4, 2026

FSRS vs SM-2, and what Moji actually runs

Moji - Learn Japanese Daily for iPhone schedules every card with official FSRS-6, the Free Spaced Repetition Scheduler, using all 21 parameters (w0 through w20) at their FSRS-6 default values and a target retention of 90%. It is not an SM-2 derivative, and it is not a hand-tuned interval ladder with an FSRS label on it. The one deliberate adaptation is the input: you answer with two grades instead of four, swiping left for again and right for good. There is no daily cap on reviews, so the app shows you everything the scheduler says is due. If you have used FSRS in Anki, this is the same algorithm family, set up for you rather than by you.

What FSRS actually models

SM-2, published by Piotr Wozniak in 1987 and still the engine inside most flashcard apps, keeps one number per card, an ease factor. Answer well and the next interval is the last interval times that ease. Answer badly and the ease drops. The card’s history lives in a single multiplier, and the algorithm has no notion of how likely you are to remember the card today.

FSRS keeps three, and they map to things you can actually reason about:

Retrievability decays along a curve, and FSRS-6 makes the flatness of that curve a fitted parameter rather than a constant. In Moji’s implementation the curve is R = (1 + factor · t / S)^(-w20), with the factor chosen so that retrievability is exactly 90% when elapsed time equals stability. Scheduling then becomes a question with an actual answer: given this card’s stability, how many days until retrievability falls to the target? That is the next interval. We show the same math back to you as memory bands in the app, which is its own page.

Why FSRS beats SM-2

The claim is measurable, and the measurement is public. The srs-benchmark project evaluates spaced repetition algorithms on 9,999 anonymized Anki collections totalling 349,923,850 reviews, scoring how well each one predicts whether a given review will be recalled. On the maintainers’ published results, FSRS-6 posts a log loss of 0.4821 against Anki SM-2’s 0.5967, and an AUC of 0.7580 against 0.6390. The summary line is the one worth keeping: FSRS-6 has “a 99.6% superiority over Anki SM-2, meaning that for 99.6% of users, log loss will be lower with FSRS-6 than with SM-2.”

The benchmark authors are careful, and so are we: SM-2 was never designed to output probabilities, so scoring it as a predictor is slightly unfair to it, and they say so outright. What the numbers support is the modest version of the claim, which is the true one. A scheduler that predicts your forgetting well puts reviews closer to where they belong, so fewer of them are wasted on cards you clearly still know and fewer arrive after the memory has already gone.

The parameters Moji ships

All 21, at the FSRS-6 defaults, no per-user optimizer:

0.212,  1.2931, 2.3065, 8.2956, 6.4133, 0.8334, 3.0194,
0.001,  1.8722, 0.1666, 0.796,  1.4835, 0.0614, 0.2629,
1.6483, 0.6014, 1.8729, 0.5425, 0.0912, 0.0658, 0.1542

They are not decoration. w0 through w3 set a card’s initial stability from your first answer, so a word you fail on entry starts at 0.212 days of stability and one you get starts at 2.3065. w4 and w5 set initial difficulty, w6 and w7 update it with mean reversion, w8 through w10 govern how much stability grows on a successful review, and w11 through w14 govern how far it falls after a lapse, with a cap so a failed card’s stability always drops. w19 damps stability growth for cards reviewed twice in the same day, which is what stops a quick second look from inflating a memory that has not actually been tested by time. w20 is the decay of the forgetting curve.

Two of the 21, w15 and w16, are the hard penalty and easy bonus. In a two-button app they never fire. We keep them at their defaults rather than quietly repurposing them.

What 90% target retention means for you

Target retention is the only number in the whole system a learner needs to have an opinion about, and it has a plain reading: it is the chance the scheduler is aiming for that you still know a card at the moment it comes back. At 90%, roughly one card in ten should feel gone when you see it. That is not the algorithm failing. That is the algorithm working, because a card you were certain of taught you nothing.

The trade runs in both directions. Push the target up and intervals shrink, recall gets more comfortable, and your daily review count climbs steeply, because holding the last few percent costs far more reviews than holding the first ninety. Push it down and you get fewer reviews per day and more genuine forgetting. Moji ships 90%, the same default Anki’s manual recommends as “a good balance of retention and workload,” and the engine accepts anything from 80% to 97%. Most people should leave it alone.

Why two buttons instead of four

FSRS is specified for four grades: again, hard, good, easy. Moji collects two. Swipe left is again (grade 1), swipe right is good (grade 3), and the FSRS-6 formulas run unchanged on those inputs.

This costs something, and it is worth being straight about it. Four grades give the model more signal per review, and a user who grades honestly and consistently will get slightly better-fitted intervals from a four-button app. The reason we still chose two: the middle grades ask you to rate your own confidence, which is a second, harder question layered on top of the one you were actually answering, and people are not good at it. Hard gets used as a soft again, easy gets used as a victory lap, and both push the model around in ways that are noise rather than data. Two grades ask one question with an honest answer, and a review takes a swipe rather than a decision. On a phone, held one-handed, at whatever time of day you actually study, that difference compounds into sessions you finish.

Around the FSRS core, Moji adds short learning steps of its own: a missed card returns after 60 seconds, and learning and relearning cards step at 10 minutes before graduating into day-scale intervals. Graduated cards become due at the start of their day rather than at the exact minute of the last review, so a morning routine stays a morning routine instead of drifting later every day.

Why there is no daily review cap

Moji used to cap daily reviews, on the reasonable-sounding theory that a smaller number is kinder after a few days away. It is not. A cap does not delete the work, it hides it, and it hides it precisely when the backlog means the scheduler most needs to catch up: every due card it withholds is one whose retrievability keeps falling while you are told you are done. You end up studying cards you know at the expense of cards you are actively losing, which is the exact failure FSRS exists to prevent. We removed the cap in August 2026, and the scheduler now serves everything that is due, with the full story in why we removed the review cap. How many new words you take on per day stays your choice, because that is a genuine pace decision rather than a filter over work the algorithm has already scheduled.

Anki has FSRS too, and that is fine

The honest comparison, because you will find this out in five minutes anyway: FSRS is not a Moji feature. It is a free, open algorithm, and Anki has shipped support for it since version 23.10, where you enable it in deck options and can run an optimizer over your own review history to fit the parameters to you. Anki’s version is more configurable than ours and always will be, and per-user optimized parameters beat defaults.

What Moji sells is not the algorithm, it is not having to assemble anything around it. FSRS-6 is on from the first card, with a curated 7,435-word Japanese catalog behind it, example sentences on every entry, and no deck hunting, add-on installing, or optimizer runs. If you want the tuning knobs, take Anki, genuinely. We wrote out where each tool wins in the Anki alternative comparison.

If a scheduler with real math behind it and nothing to configure sounds like the trade you want, Moji is on the App Store.

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