Write the core interval recurrence relation used by SM-2 for repetition n ≥ 3.

I(1) = 1 day, I(2) = 6 days, and for n ≥ 3: I(n) = round(I(n - 1) × EF).

What is the 'RMSE (bins)' metric used in the open-source FSRS benchmark?

Root Mean Squared Error across binned predicted Retrievability vs. observed recall rate, measuring how well the scheduler's probability predictions (e.g., R = 85%) match empirical recall percentages.

What is 'Ease Hell' in legacy SM-2 spaced repetition?

A pathological scheduling state where a card's Ease Factor drops to or near the 1.30 floor due to early 'Again' or 'Hard' ratings and remains permanently trapped there because rating 'Good' (+0.00) never restores the Ease Factor.

In SM-2 / legacy Anki, what is the minimum allowed floor for a card's Ease Factor (EF)?

EF_min = 1.30 (130%), meaning intervals grow by only 30% per successful review once a card hits the floor.

Why do conscientious students accidentally push hundreds of cards into SM-2 Ease Hell?

Because students often press 'Hard' when a card requires moderate effort to recall, not realizing that each 'Hard' click permanently subtracts 0.15 from the card's Ease Factor even though recall succeeded.

Who created the SM-2 algorithm, and in what year was it implemented for early computer-assisted spaced repetition?

Dr. Piotr Wozniak in 1987 for SuperMemo 2.0 on MS-DOS computers.

How did legacy SM-2 handle premature 'early' reviews (cramming a card days before its due date)?

SM-2 either applied full or poorly scaled multipliers that could artificially inflate intervals when cards were reviewed too early.

How does FSRS-6 treat that same 365-day card when it lapses once?

FSRS-6 uses S'_f(D, S, R) where prior stability enters as (S + 1)^(w_13) - 1, assigning a multi-day or multi-week re-consolidation interval proportional to its mature history rather than resetting it to a brand-new card.

What is the 'Fuzz Factor' in flashcard schedulers, and how does it interact with FSRS?

A small random jitter (e.g., ±5%) applied to scheduled intervals > 2.5 days so that cards introduced together on the same day do not stay clumped in permanent review spikes ('load balancing').

What was the 'Fixed Relearning Steps' limitation in legacy Anki SM-2 (e.g., 1m 10m 1d)?

New and lapsed cards were locked into rigid, manually configured minute-step queues before graduating to the main algorithm, creating a jarring disconnect between short-term steps and long-term intervals.

Why does Leitner Box scheduling fail catastrophically during exam season when new cards are added daily?

Because fixed short intervals in Boxes 1–3 create massive, unprioritized daily bottlenecks, and every single lapse dumps mature cards right back into Box 1.

Summarize the paradigm shift from Leitner (1972) → SM-2 (1987) → FSRS-6 (2024–2026).

Leitner scheduled cards by box position; SM-2 scheduled cards by a fragile per-card multiplier (EF); FSRS-6 models the underlying psychological state of human memory (D, S, R) using empirical power-law equations.

How does FSRS-6 handle same-day (short-term) reviews differently from legacy SM-2?

FSRS-6 natively models same-day memory stability transitions using dedicated parameters (w_17, w_18, w_19), unifying intra-day learning and multi-day spacing under a single continuous DSR state.

In benchmark evaluations across 100M+ real flashcard review logs (FSRS-Benchmark), how does FSRS-6 compare to SM-2 in prediction accuracy (Log Loss and RMSE)?

FSRS-6 achieves substantially lower Log Loss and calibration RMSE (bins) than SM-2 across nearly all users, meaning its predicted Retrievability R closely matches actual human recall rates.

In side-by-side simulations at 90% retention, how much daily review time does FSRS-6 save compared to SM-2?

Typically 20% to 30% fewer total reviews over a 1-year study horizon to maintain the exact same 90% recall rate.

How does FSRS-6 completely eliminate 'Ease Hell'?

By replacing the static Ease Factor with Difficulty D ∈ [1, 10] that incorporates linear damping near the ceiling and built-in mean reversion (w_7) toward baseline difficulty on every 'Good' rating.

How do the 4 rating buttons (Again, Hard, Good, Easy) modify a card's Ease Factor in legacy Anki SM-2?

Again: EF − 0.20; Hard: EF − 0.15; Good: EF + 0.00 (no change!); Easy: EF + 0.15.

What happens in legacy SM-2 when a card with a 365-day interval lapses (is rated 'Again') under default settings?

By default in classic SM-2 ('New Interval = 0%'), the card's interval is wiped out to 1 day (a 99.7% reduction) AND its Ease Factor drops by 0.20.

What is 'Log Loss' (Binary Cross-Entropy) in evaluating spaced repetition algorithms?

Log Loss = -1/N ∑ [y_i ln(R_i) + (1 - y_i) ln(1 - R_i)], where y_i ∈ {0, 1} is the actual recall outcome and R_i is the algorithm's predicted Retrievability prior to the review.

In the original SM-2 algorithm, what variable controls how fast a card's interval grows, and what is its starting value?

The Ease Factor (EF, or E-Factor), which starts at 2.50 (250%) for every new card.

Who invented the physical flashcard box system in 1972, and how does its core promotion/demotion rule work?

German science journalist Sebastian Leitner (in his 1972 book 'So lernt man lernen'): correctly answered cards move up one box (with longer review intervals), while any incorrectly answered card is demoted all the way back to Box 1.

What are the two biggest structural flaws of the classic 5-Box Leitner System?

1. Coarse quantization (every card in Box k gets the exact same interval regardless of item difficulty); 2. Catastrophic reset penalty (a single lapse on a Box 5 card erases months of progress by sending it back to Box 1).

If you migrate an existing deck with review history from SM-2 to FSRS-6, how does FSRS-6 reconstruct each card's DSR state?

FSRS-6 replays the card's chronological review log (timestamps and ratings G_1, G_2, ...) through the FSRS-6 state transition equations from the first review to compute its exact current Difficulty (D) and Stability (S).

How did Piotr Wozniak's own algorithms evolve after SM-2 (e.g., SM-15 through SM-18)?

Wozniak himself abandoned SM-2's Ease Factor in the 1990s in favor of the Two-Component / Three-Component (DSR) model in proprietary SuperMemo releases, which FSRS later brought to the open-source ecosystem via modern machine-learning optimization.

Calculate the 5-review interval trajectory of a card at EF = 2.50 vs. a card trapped in Ease Hell at EF = 1.30 (starting from a 10-day interval, rated 'Good' 5 times).

At EF = 2.50: 10 → 25 → 63 → 156 → 391 → 977 days (~2.7 years). At EF = 1.30: 10 → 13 → 17 → 22 → 29 → 37 days (~1.2 months)—a 26× difference in interval length despite 5 consecutive 'Good' ratings!

Why is a neural network (like RNN/LSTM or Transformer) not always superior to FSRS-6's 21-parameter analytical equations for on-device flashcard scheduling?

FSRS-6's interpretable analytical formulas match or beat heavyweight recurrent neural networks on benchmark accuracy while running instantaneously on any device, guaranteeing monotonic behavior, and requiring far fewer reviews to personalize.

How did legacy SM-2 handle a card that was reviewed late (overdue) and successfully recalled?

Original SM-2 ignored overdue days completely; modified Anki SM-2 added a rough linear fraction (e.g., +50% of overdue days for Good), which fails to match the true non-linear memory reconsolidation curve.

What if a card is imported without full review logs (only its last interval and ease factor are known)?

FSRS-6 can initialize Stability (S) from the current interval and map the legacy Ease Factor inversely onto the Difficulty scale D ∈ [1, 10].

Can legacy SM-2 let a user directly set a target retention percentage (like 90% or 85%)?

No. SM-2 has no explicit variable for Retrievability (R); users had to guess an arbitrary 'Interval Modifier' percentage by trial and error.

How does FSRS-6 handle an early review when elapsed time t is very small (so R is close to 1.0)?

Because 1 - R ≈ 0 when reviewed early, the stability growth term exp(w_10 · (1 - R)) - 1 is very small, preventing premature reviews from inflating long-term intervals.

Why does SM-2 assume an exponential memory growth curve (I_n = I_1 × EF^(n-1)), and why does that fail at long horizons?

A constant multiplier EF assumes that memory stability grows exponentially without bound, ignoring the empirical stabilization decay (S^(-w_9)) where mature memories grow at a decelerating multiplicative rate.

How does FSRS-6 mathematically handle an overdue review when you successfully recall the card?

FSRS-6 computes the exact lowered Retrievability R(t, S) at the overdue elapsed time t and plugs it into exp(w_10 · (1 - R)) - 1, giving a scientifically calibrated Stability jump proportional to how unlikely the recall was.

FSRS-6 & Spaced Repetition — FSRS-6 vs. Legacy SM-2, Ease Hell & Leitner Box Systems

Comparative analysis of Sebastian Leitner's 1972 Box System, SuperMemo SM-2 (1987), Anki's modified SM-2, and FSRS-6, including mathematical proof of why Ease Hell occurs and how FSRS eliminates it.

Level: intermediate
Languages: en → en
Cards: 32
Markdown: FSRS-6 & Spaced Repetition — FSRS-6 vs. Legacy SM-2, Ease Hell & Leitner Box Systems (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	Write the core interval recurrence relation used by SM-2 for repetition n ≥ 3.	I(1) = 1 day, I(2) = 6 days, and for n ≥ 3: I(n) = round(I(n - 1) × EF).
2	What is the 'RMSE (bins)' metric used in the open-source FSRS benchmark?	Root Mean Squared Error across binned predicted Retrievability vs. observed recall rate, measuring how well the scheduler's probability predictions (e.g., R = 85%) match empirical recall percentages.
3	What is 'Ease Hell' in legacy SM-2 spaced repetition?	A pathological scheduling state where a card's Ease Factor drops to or near the 1.30 floor due to early 'Again' or 'Hard' ratings and remains permanently trapped there because rating 'Good' (+0.00) never restores the Ease Factor.
4	In SM-2 / legacy Anki, what is the minimum allowed floor for a card's Ease Factor (EF)?	EF_min = 1.30 (130%), meaning intervals grow by only 30% per successful review once a card hits the floor.
5	Why do conscientious students accidentally push hundreds of cards into SM-2 Ease Hell?	Because students often press 'Hard' when a card requires moderate effort to recall, not realizing that each 'Hard' click permanently subtracts 0.15 from the card's Ease Factor even though recall succeeded.
6	Who created the SM-2 algorithm, and in what year was it implemented for early computer-assisted spaced repetition?	Dr. Piotr Wozniak in 1987 for SuperMemo 2.0 on MS-DOS computers.
7	How did legacy SM-2 handle premature 'early' reviews (cramming a card days before its due date)?	SM-2 either applied full or poorly scaled multipliers that could artificially inflate intervals when cards were reviewed too early.
8	How does FSRS-6 treat that same 365-day card when it lapses once?	FSRS-6 uses S'_f(D, S, R) where prior stability enters as (S + 1)^(w_13) - 1, assigning a multi-day or multi-week re-consolidation interval proportional to its mature history rather than resetting it to a brand-new card.
9	What is the 'Fuzz Factor' in flashcard schedulers, and how does it interact with FSRS?	A small random jitter (e.g., ±5%) applied to scheduled intervals > 2.5 days so that cards introduced together on the same day do not stay clumped in permanent review spikes ('load balancing').
10	What was the 'Fixed Relearning Steps' limitation in legacy Anki SM-2 (e.g., 1m 10m 1d)?	New and lapsed cards were locked into rigid, manually configured minute-step queues before graduating to the main algorithm, creating a jarring disconnect between short-term steps and long-term intervals.
11	Why does Leitner Box scheduling fail catastrophically during exam season when new cards are added daily?	Because fixed short intervals in Boxes 1–3 create massive, unprioritized daily bottlenecks, and every single lapse dumps mature cards right back into Box 1.
12	Summarize the paradigm shift from Leitner (1972) → SM-2 (1987) → FSRS-6 (2024–2026).	Leitner scheduled cards by box position; SM-2 scheduled cards by a fragile per-card multiplier (EF); FSRS-6 models the underlying psychological state of human memory (D, S, R) using empirical power-law equations.
13	How does FSRS-6 handle same-day (short-term) reviews differently from legacy SM-2?	FSRS-6 natively models same-day memory stability transitions using dedicated parameters (w_17, w_18, w_19), unifying intra-day learning and multi-day spacing under a single continuous DSR state.
14	In benchmark evaluations across 100M+ real flashcard review logs (FSRS-Benchmark), how does FSRS-6 compare to SM-2 in prediction accuracy (Log Loss and RMSE)?	FSRS-6 achieves substantially lower Log Loss and calibration RMSE (bins) than SM-2 across nearly all users, meaning its predicted Retrievability R closely matches actual human recall rates.
15	In side-by-side simulations at 90% retention, how much daily review time does FSRS-6 save compared to SM-2?	Typically 20% to 30% fewer total reviews over a 1-year study horizon to maintain the exact same 90% recall rate.
16	How does FSRS-6 completely eliminate 'Ease Hell'?	By replacing the static Ease Factor with Difficulty D ∈ [1, 10] that incorporates linear damping near the ceiling and built-in mean reversion (w_7) toward baseline difficulty on every 'Good' rating.
17	How do the 4 rating buttons (Again, Hard, Good, Easy) modify a card's Ease Factor in legacy Anki SM-2?	Again: EF − 0.20; Hard: EF − 0.15; Good: EF + 0.00 (no change!); Easy: EF + 0.15.
18	What happens in legacy SM-2 when a card with a 365-day interval lapses (is rated 'Again') under default settings?	By default in classic SM-2 ('New Interval = 0%'), the card's interval is wiped out to 1 day (a 99.7% reduction) AND its Ease Factor drops by 0.20.
19	What is 'Log Loss' (Binary Cross-Entropy) in evaluating spaced repetition algorithms?	Log Loss = -1/N ∑ [y_i ln(R_i) + (1 - y_i) ln(1 - R_i)], where y_i ∈ {0, 1} is the actual recall outcome and R_i is the algorithm's predicted Retrievability prior to the review.
20	In the original SM-2 algorithm, what variable controls how fast a card's interval grows, and what is its starting value?	The Ease Factor (EF, or E-Factor), which starts at 2.50 (250%) for every new card.
21	Who invented the physical flashcard box system in 1972, and how does its core promotion/demotion rule work?	German science journalist Sebastian Leitner (in his 1972 book 'So lernt man lernen'): correctly answered cards move up one box (with longer review intervals), while any incorrectly answered card is demoted all the way back to Box 1.
22	What are the two biggest structural flaws of the classic 5-Box Leitner System?	1. Coarse quantization (every card in Box k gets the exact same interval regardless of item difficulty); 2. Catastrophic reset penalty (a single lapse on a Box 5 card erases months of progress by sending it back to Box 1).
23	If you migrate an existing deck with review history from SM-2 to FSRS-6, how does FSRS-6 reconstruct each card's DSR state?	FSRS-6 replays the card's chronological review log (timestamps and ratings G_1, G_2, ...) through the FSRS-6 state transition equations from the first review to compute its exact current Difficulty (D) and Stability (S).
24	How did Piotr Wozniak's own algorithms evolve after SM-2 (e.g., SM-15 through SM-18)?	Wozniak himself abandoned SM-2's Ease Factor in the 1990s in favor of the Two-Component / Three-Component (DSR) model in proprietary SuperMemo releases, which FSRS later brought to the open-source ecosystem via modern machine-learning optimization.
25	Calculate the 5-review interval trajectory of a card at EF = 2.50 vs. a card trapped in Ease Hell at EF = 1.30 (starting from a 10-day interval, rated 'Good' 5 times).	At EF = 2.50: 10 → 25 → 63 → 156 → 391 → 977 days (~2.7 years). At EF = 1.30: 10 → 13 → 17 → 22 → 29 → 37 days (~1.2 months)—a 26× difference in interval length despite 5 consecutive 'Good' ratings!
26	Why is a neural network (like RNN/LSTM or Transformer) not always superior to FSRS-6's 21-parameter analytical equations for on-device flashcard scheduling?	FSRS-6's interpretable analytical formulas match or beat heavyweight recurrent neural networks on benchmark accuracy while running instantaneously on any device, guaranteeing monotonic behavior, and requiring far fewer reviews to personalize.
27	How did legacy SM-2 handle a card that was reviewed late (overdue) and successfully recalled?	Original SM-2 ignored overdue days completely; modified Anki SM-2 added a rough linear fraction (e.g., +50% of overdue days for Good), which fails to match the true non-linear memory reconsolidation curve.
28	What if a card is imported without full review logs (only its last interval and ease factor are known)?	FSRS-6 can initialize Stability (S) from the current interval and map the legacy Ease Factor inversely onto the Difficulty scale D ∈ [1, 10].
29	Can legacy SM-2 let a user directly set a target retention percentage (like 90% or 85%)?	No. SM-2 has no explicit variable for Retrievability (R); users had to guess an arbitrary 'Interval Modifier' percentage by trial and error.
30	How does FSRS-6 handle an early review when elapsed time t is very small (so R is close to 1.0)?	Because 1 - R ≈ 0 when reviewed early, the stability growth term exp(w_10 · (1 - R)) - 1 is very small, preventing premature reviews from inflating long-term intervals.
31	Why does SM-2 assume an exponential memory growth curve (I_n = I_1 × EF^(n-1)), and why does that fail at long horizons?	A constant multiplier EF assumes that memory stability grows exponentially without bound, ignoring the empirical stabilization decay (S^(-w_9)) where mature memories grow at a decelerating multiplicative rate.
32	How does FSRS-6 mathematically handle an overdue review when you successfully recall the card?	FSRS-6 computes the exact lowered Retrievability R(t, S) at the overdue elapsed time t and plugs it into exp(w_10 · (1 - R)) - 1, giving a scientifically calibrated Stability jump proportional to how unlikely the recall was.