This is the same quantitative model of the contextual interference effect from educational psychology (Battig 1979; Shea & Morris 1979) as the 3D version: practicing several skills in interleaved order (ABCABC…) feels harder and produces lower scores during training than blocked order (AAABBBCCC), yet interleaving usually produces better long-term retention and transfer.
Each rep of skill k adds to a short-term strength Sk, boosted when the same skill repeats consecutively (a priming/fluency bonus that inflates in-session performance during blocked runs):
gain = g0 · (1 + p · min(consecutive_same − 1, 5))
S_k += gain
Immediate accuracy: P_acq(k) = 1 − exp(−S_k / K)
Every time the schedule switches to a different skill, a global discrimination index D increases — this represents the extra retrieval effort and inter-skill contrast that comes from comparing skills against each other in memory:
D = switch_count / (total_reps − 1) (0 = pure blocked, → 1 = fully interleaved)
tau_k = tau0 · (1 + β · D) (memory persistence, in days)
Retention(k, delay) = P_acq(k) · exp(−delay / tau_k)
Because D stays near zero for blocked practice, its retention decays fast (small τ); because D climbs toward 1 for interleaved practice, its retention decays slowly (large τ). The top chart shows immediate in-practice accuracy rising trial-by-trial — blocked rises faster because of the consecutive-rep priming bonus. The bottom chart shows the full retention-vs-delay curve computed from the accumulated strength and discrimination — drag the delay slider and watch the crossover: blocked starts ahead right after training, but interleaved decays more slowly and overtakes it at longer delays, the classic "desirable difficulty" finding. The comparison boxes above run both schedules to completion (same reps and delay) so the reversal is visible without switching back and forth.
- Blocked / Interleaved — choose the practice order, then resets the trial sequence.
- Reps per skill — how many practice trials each of the 3 skills gets in total.
- Practice pace — how fast auto-play advances through the trial sequence.
- Start practice / Step ×1 — run all trials automatically, or advance one at a time.
- Delay slider — simulated days between the end of practice and a recall test; recomputes retention instantly, no need to re-practice.