Two students study the exact same amount. One crams it all into one night; the other spreads it over a week. At the test a month later, the spacer remembers far more — same effort, different SCHEDULE. The most robust, most ignored finding in the science of learning. Slide the spacing and watch cramming lose.
Same four reviews, two schedules. A review boosts stability S by more when the memory has FADED (a ‘desirable difficulty’): S ← S·(1 + k(1−R)) where R = e^(−gap/S). Cramming reviews at R≈1 (no fade → tiny gain); spacing reviews at lower R → big gains. At a fixed later test the spaced learner’s S is higher, so retention is higher. A fail-loud self-check throws unless, at a day-20 test, the spaced schedule beats the massed one — more remembered from identical effort, purely by timing.
A stability-boost model of one memory trace; the exact numbers depend on k and the gaps, but that spaced > massed for long-term retention is one of the most replicated results in learning science (Cepeda et al. 2006). The comparison here is exact.