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A blog featuring in-depth articles about spaced repetition, FSRS algorithm, Anki optimization, and...
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### FSRS Retrievability Function Examples

Source: https://expertium.github.io/Algorithm

Demonstrates different retrievability (R) curves used in FSRS versions, including exponential and power functions. It shows how the curves approximate data and how a superposition of exponential functions is better fitted by a power function.

```mathematics
R_1=0.9^(t/0.2)
```

```mathematics
R_1=0.9^(t/3)
```

```mathematics
R=0.5*(0.9^(t/0.2)+0.9^(t/3))
```

--------------------------------

### Match Pairs Syntax Example

Source: https://expertium.github.io/Avoid_Pattern_Matching

Demonstrates the basic syntax for creating 'Match Pairs' cards in Anki. The '|' character is used as a separator between items. Leading/trailing spaces are ignored.

```text
Answer1 | Answer2
```

--------------------------------

### City Coordinates for TSP Example

Source: https://expertium.github.io/TSP_NN_worst

Defines the coordinates for the four cities used in the Traveling Salesman Problem example. These coordinates are crucial for calculating distances and evaluating different routes.

```python
cities = [(0, 0), (200, 0), (101.002500, -173.780019), (398.997500, -28.301855)]
```

--------------------------------

### Randomized Cloze Syntax Example

Source: https://expertium.github.io/Avoid_Pattern_Matching

Illustrates how to create 'Randomized Cloze' cards, including multiple cloze deletions within a single card. The numbers in curly brackets (e.g., {c1::text}) must be consistent across all cloze selections for a single card.

```text
Just some {c1::random} {c2::text}| Also just some {c1::random} {c2::text} | And this is some {c1::random} {c2::text}, too
```

--------------------------------

### FSRS Initial Difficulty (D) Calculation

Source: https://expertium.github.io/Algorithm

Details the formula for calculating the initial difficulty (D) after the first review. It uses the grade (G) as input, with specific values assigned to each grade (Again=1, Hard=2, Good=3, Easy=4). The output is clamped to ensure D0 is between 1 and 10.

```plaintext
D0 = (G / 4) * 9 + 1
```

--------------------------------

### FSRS Difficulty (D) Update Formula

Source: https://expertium.github.io/Algorithm

Explains the multi-step process for updating the difficulty (D) after subsequent reviews. It involves an initial grade-dependent change, followed by 'linear damping' to asymptotically approach a maximum value, and finally 'mean reversion' towards a default value.

```plaintext
change_in_D_based_on_grade = grade_factor(G)
```

```plaintext
D_after_damping = D_prev - (D_prev - 10) * damping_factor
```

```plaintext
D_final = D_after_damping * (1 - mean_reversion_rate) + default_D * mean_reversion_rate
```

--------------------------------

### Sort Cards Format

Source: https://expertium.github.io/Avoid_Pattern_Matching

Defines the complex format for the 'Sort Cards' note type, which categorizes items. It uses brackets for items within categories and commas as separators for both items and categories. This format also supports images and audio, although image embedding can be inconvenient.

```text
category1[item1, item2, item2], category2[item3, item4, item5]
```

--------------------------------

### Sequence Note Type Separator

Source: https://expertium.github.io/Avoid_Pattern_Matching

Illustrates the separator used in the 'Sequence' note type for ordered elements. The double pipe symbol '||' is used to separate individual events or items within the sequence, suitable for memorizing historical events or chemical reactions.

```text
||
```

--------------------------------

### FSRS-6 Interval Calculation Formula

Source: https://expertium.github.io/Algorithm

Presents the formula used in FSRS-6 to calculate the interval length (I) based on memory stability (S) and desired retention (DR). It notes that when DR is 90%, the interval equals stability before Anki's fuzz factor.

```mathematics
I = S * DR
```

--------------------------------

### FSRS Short-term Memory (S) Calculation in FSRS-6

Source: https://expertium.github.io/Algorithm

Describes the calculation of the 'S' value in FSRS-6 after a same-day review. It highlights the role of specific parameters (w17, w18, w19) in influencing how grades affect S and the impact of previous S values. It also notes a condition where S cannot decrease if the grade is Good or Easy (G >= 3).

```plaintext
S_new = S_prev + (w17 * (1 - S_prev)) - (w18 * S_prev * (1 - S_prev))
```
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