SM-2 Algorithm

SM-2 is a spaced-repetition scheduling algorithm, published by Piotr Wozniak in 1987 for SuperMemo, that computes when to next review each item based on your self-graded recall — easy items drift out to long intervals, hard items snap back to short ones.

It is the algorithm behind the explosion of spaced-repetition software: Anki's scheduler descends from it, and countless learning systems implement it outright. Its endurance comes from a rare combination — it captures the essential dynamics of the forgetting curve in a handful of arithmetic operations anyone can implement in an afternoon.

How it works

Each item carries three values: an ease factor (EF, starting at 2.5), the current interval in days, and a repetition count. After every review you grade your recall from 0 to 5, and SM-2 updates the item:

• Grade 3 or higher (successful recall): the interval grows. First success: 1 day. Second: 6 days. After that, new interval = previous interval times EF — so a mature item with EF 2.5 goes 1, 6, 15, 38, 94 days.
• Grade below 3 (failed recall): repetitions reset and the item returns tomorrow, though EF is retained.
• The ease factor itself adjusts with every grade: perfect 5s nudge it up, hesitant 3s pull it down, with a floor of 1.3 so no item's growth stalls entirely.

The elegance is per-item adaptivity. Vocabulary you find trivial stretches toward multi-month gaps; the concept that keeps slipping stays on a tight leash. No global schedule could do both.

Why it matters

SM-2 operationalizes the spacing effect — it is the difference between knowing that distributed review beats cramming and actually running distributed review across two thousand items without a spreadsheet meltdown. It also embodies an honest principle: the schedule is driven by demonstrated recall, not by time spent or pages turned. You cannot negotiate with it; you either retrieved the answer or you did not. Newer algorithms (SM-18, FSRS) model memory more finely, but SM-2 remains the reference implementation of the idea and more than good enough in practice.

A worked example

You add the item: "What does an ease factor floor of 1.3 prevent?" — EF starts at 2.5.

Review 1 (day 0): grade 4. Next interval: 1 day.

Review 2 (day 1): grade 5. Next interval: 6 days. EF rises to ~2.6.

Review 3 (day 7): grade 3. Next interval: 6 x 2.6 = ~16 days.

EF dips to ~2.46 — the hesitation cost you.

Review 4 (day 23): grade 2. Failed. Repetition resets;

see it again tomorrow, EF ~2.14.

Four reviews, and the algorithm has already learned this item is harder for you than average — and scheduled accordingly.

How miatz uses it

SM-2 is the scheduler inside the miatz daily training loop: every concept a learner touches becomes a reviewable item, graded on recall, with due dates computed by the algorithm. Learners also implement SM-2 themselves as an early coding rep — a tidy exercise in state, arithmetic, and edge cases — so the tool that schedules their memory is one they have built with their own hands.