Learning Science
Spacing and Interleaving: What the Optimal Gap Actually Is
The gap between study sessions is not a matter of taste. It has a measured optimum, and that optimum is a function of how long the material needs to be remembered — not a fixed number of days.
The optimal gap is a function of the retention interval
Cepeda, Pashler, Vul, Wixted & Rohrer (2006, Psychological Bulletin, 839 assessments across 317 experiments) established that the ideal spacing gap between study sessions is not a constant — it scales with how long the material needs to be remembered. Cepeda, Vul, Rohrer, Wixted & Pashler (2008, Psychological Science, N = 1,354) measured the relationship directly: the optimal gap is approximately 20% of the test delay at a few weeks out, falling to 5–7% at a one-year retention interval.
At a 70-day retention interval, the optimal 21-day gap between study sessions produced a 111% increase in recall over massed (unspaced) study — the largest measured gain in that dataset.
Two-session design
Cepeda et al. (2008) is a two-session design: study, one review, then test. Any spacing schedule with three or more review touches — which describes essentially every spaced-repetition product on the market — extends beyond what this data directly measured. The two-session optima are the best-measured anchors that exist, but longer ladders built from them are extrapolation, not direct measurement.
Delaying the first review matters more than people assume
Karpicke & Roediger (2007) found that what matters is delaying the first retrieval attempt — reviewing material again on the same day it was studied adds little. Mawson & Kang (2025, applied and classroom settings, 22 studies) report d = 0.54, 95% CI [0.31, 0.77], for fixed 7-day lags between reviews, while 1-day lags produced smaller and more variable effects.
More reviews is not more learning
Diminishing and reversing returns
Mawson & Kang (2025) found three exposures produced moderate-to-large effects, but more than three exposures produced smaller effects. Rawson & Dunlosky (2011, Journal of Experimental Psychology: General, N = 533) found the optimum within a session is practicing to 3 correct recalls, then stopping — one-week recall rose from roughly 20% to roughly 80% with relearning to 1 correct across 3 spaced sessions, at a relearning cost of under 2 minutes per concept. Drilling past 3 correct recalls is overlearning and does not survive a delay.
Interleaving helps only when material is confusable
Brunmair & Richter (2019, Psychological Bulletin, 59 studies, 238 effect sizes) meta-analyzed interleaving versus blocked practice:
The direction of the effect flips for word lists, and disappears for expository text and taste judgments. Interleaving is a discrimination intervention for confusable categories, not a general-purpose shuffling philosophy.
The strongest field evidence for interleaving comes from Rohrer, Dedrick, Hartwig & Cheung (2019): a preregistered cluster RCT across 54 seventh-grade math classes, with an unannounced test one month later. Interleaved practice produced 61% correct vs. 38% for blocked practice — d = 0.83, 95% CI [0.68, 0.97] — and the effect was positive for all 15 participating teachers.
It feels worse while it works
Kornell & Bjork (2008) found participants preferred blocked practice immediately after a session, even in conditions where interleaving had just outperformed it on a later test. The subjective sense of fluency during blocked practice does not track the retention outcome — a direct extension of the fluency illusion described on the self-assessment page.
What the evidence does not support
Expanding intervals
Rejected
Latimier, Peyre & Ramus (2021) meta-analyzed expanding intervals directly against uniform (equal-gap) spacing: g = 0.034— no meaningful difference. Karpicke & Roediger (2007) found expanding schedules won at an immediate test but lost at a 2-day delay. Expanding schedules can be defended on review-count efficiency, not on retention.
SM-2's constants
Rejected
The specific numbers underlying the classic SuperMemo SM-2 algorithm — a 2.5 initial ease factor, a 1.3 floor, a 6-day second interval, and an 8-lapse leech threshold — have no experimental provenance in the memory literature. Piotr Woźniak, the algorithm's author, himself characterized SM-2's interval function as having an "arbitrary shape" that "could not claim scientifically proved validity," and described the algorithm as "dumb." The constants are one person's curve-fit to his own review log, propagated by copying.
FSRS's optimal-retention setting
Circular reasoning
The optimal-retention parameter in the FSRS algorithm is computed by simulating FSRS's own memory model and minimizing its predicted workload — circular with respect to the model, with no randomized human trial behind the scheduling policy itself. What the underlying FSRS benchmark does legitimately establish is that its DSR model predicts recall probability better than SM-2 on very large observational review datasets (500 million-plus reviews). That is real; the scheduling policy built on top of it is still an engineering choice awaiting its own evidence.
The "85% rule"
Category error
A widely circulated claim holds that flashcard systems should target an 85% success rate as the optimal difficulty level. The number traces to Wilson, Shenhav, Straccia & Cohen (2019, Nature Communications), who derived a 15.87% optimal error rate for stochastic-gradient-descent training and perceptual-classification models — not a study of human declarative memory. Applying it to flashcard scheduling is a category error. Separately, both Rowland (2014, see the testing-effect page) and Pan & Rickard (2018) — whose transfer moderator shows +0.0058 d per percentage point of initial accuracy, Δd = 0.46 across the full range — both point toward "higher success rate is better," which is not the same claim shape as "there is a specific optimum near 85%."