How SM-2 Works in SmartRecall

SM-2 is the spaced-repetition algorithm Piotr Wozniak published in his 1987 SuperMemo paper. It's also the algorithm behind Anki and Mnemosyne. This page documents exactly how SmartRecall implements it — every constant, every transition, with a worked example.

The 60-second summary

After every review, you rate how the recall felt:

• Again (0) — failed, didn't recall
• Hard (3) — recalled, but with serious effort
• Good (4) — recalled with normal effort
• Easy (5) — trivial recall

SM-2 uses that rating to update two numbers per card:

1. Interval (I) — days until the next review
2. Ease factor (EF) — a multiplier that controls how fast the interval grows

Higher ratings → bigger EF → faster-growing intervals. Lower ratings → smaller EF → tighter intervals. A failure resets the interval but only nudges EF down.

The exact rules SmartRecall uses

Initial values for a new card:
  I  = 0       (will be set on first review)
  EF = 2.5
  reps = 0     (consecutive successful reviews)

On review with quality q (0–5):

  if q < 3:                  // lapse
    reps = 0
    I    = 1                 // back to 1 day
    // EF still updates below

  else:                      // success
    if reps == 0: I = 1
    elif reps == 1: I = 6
    else:          I = round(I_prev * EF)
    reps = reps + 1

  EF = max(1.3, EF + (0.1 - (5 - q) * (0.08 + (5 - q) * 0.02)))

The EF formula collapses to friendly numbers at each rating:

EF is clamped at a minimum of 1.3 — we never let a card grow exponentially slower than that, no matter how many lapses.

A worked example

A new card on "What is the spacing effect?":

A few things to notice:

• The first two intervals (1 d → 6 d) are fixed, not multiplied. SM-2 hard-codes them so brand-new cards don't immediately fly out to 30 days because of a high EF.
• After review 4, the interval is round(16 * EF) = round(16 * 2.46) = 39.
• Review 5 is a lapse — reps resets to 0, I resets to 1, but EF only drops by 0.80 (not back to 2.5). The card is "wounded," not erased.
• After the lapse, the schedule does not repeat the 1 → 6 ramp; it continues from reps = 1 after review 6 because review 6 was successful.

What SmartRecall changes

SM-2 is the floor, not the ceiling. We make three pragmatic adjustments:

1. Soft-lapse on Hard ratings. If you rate Hard three times in a row, we cap the next interval at I_prev — so a card you keep struggling with stops growing until you flip to Good. Pure SM-2 would keep multiplying by EF and surface it less often.
2. Leech detection. If a card lapses 8 times total, we tag it as a leech and surface it on your dashboard so you can rewrite it. A bad card is a workflow problem, not an algorithm problem.
3. Deterministic seeding from generation time. When the AI emits a 200-card deck, we don't drop them all on day one — we spread the initial I = 1 reviews across the next 5 days using a deterministic hash of the card ID. That keeps the daily review queue flat.

Everything else — EF formula, the 1/6 day ramp, the 1.3 floor, the lapse semantics — is exactly the 1987 paper.

Why not FSRS?

FSRS is a more recent scheduler that learns per-user retention curves from review history. It's measurably better than SM-2 once you have ~1000 reviews. We're working on it as an opt-in scheduler — track Updates for the rollout.

Further reading

• Wozniak, P. (1990). Optimization of learning. The original SM-2 specification.
• Cepeda, N. J., et al. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin. Meta-analysis of the spacing effect across 317 experiments.
• Karpicke, J. D., & Roediger, H. L. (2008). The critical importance of retrieval for learning. Science. The testing-effect paper SM-2 implicitly depends on.