Spaced Repetition Interval Planner

Spaced repetition schedules reviews so that each one lands shortly before the item would have been forgotten, because retrieval that is effortful but still successful produces the largest gain in memory stability. The SM-2 interval rule used here fixes the first interval at 1 day and the second at 6 days, then multiplies each subsequent interval by an easiness factor. That factor starts at 2.5 and is bounded below at 1.3 in the original algorithm; at 2.5 the schedule runs 1, 6, 15, 38, 94 days and so on, which is why a card reviewed correctly five times may not return for three months. Retention is modelled as exponential decay, R equals 2 raised to the power of minus t over S, where t is days since the last review and S is stability expressed as the half-life at which recall probability falls to 50 percent. Workload, not the algorithm, is what usually breaks a deck. Steady-state daily reviews scale with deck size rather than with new cards, so a 100-card deck at 20 new cards per day settles into roughly 15 reviews per day on top of the new ones; at 5,000 cards the review load alone dominates the session. Raising the target retention above about 90 percent multiplies review counts steeply for a small accuracy gain, which is why later scheduler research settled near 85 to 90 percent as the efficient region. Caveats: SM-2 treats each card independently and ignores interference between similar items, the easiness factor is inferred from self-rated recall difficulty and is therefore noisy, and poorly written cards testing several facts at once break the model regardless of scheduling.

The spacing effect was first documented by Hermann Ebbinghaus in Ueber das Gedaechtnis in 1885, where he found that repetitions distributed over several days were far more economical than the same number massed into one sitting. Practical scheduling schemes appeared much later. Cecil Alec Mace described spaced rehearsal in his 1932 book The Psychology of Study, and the German science journalist Sebastian Leitner popularized the physical implementation in his 1972 book So lernt man lernen - a box of numbered compartments in which a correctly answered card advances to a compartment reviewed less often and a failed card returns to the first. Computerized scheduling was created by Piotr Wozniak in Poland. He began recording his own review intervals in 1985, formulated the SM-0 paper algorithm, and released SuperMemo for DOS in 1987; SM-2, published with his 1990 work and later described in his 1995 doctoral thesis at the Wroclaw University of Economics, introduced the easiness factor and the quality-of-recall grading that this planner reproduces. Because Wozniak published the SM-2 specification openly, it became the default engine for the open-source generation of tools - Mnemosyne, and Damien Elmes's Anki, released in 2006. Anki replaced SM-2 with the FSRS scheduler in 2023, a model developed by Jarrett Ye that fits three components of memory - difficulty, stability and retrievability - to a user's own review logs rather than relying on the fixed SM-2 constants.