How does the scheduler work?

Update

This wiki page describes the execution process of the custom scheduling code, which has been outdated since FSRS was integrated into Anki 23.10+ and AnkiDroid 2.17+.

Requirement

To more deeply understand the working process of the FSRS4Anki scheduler, we recommend you install AnkiWebView Inspector . The following text will use the screenshot with the Inspector window.

And please note, open the inspector before you start the review.

How to see the execution of the scheduler?

Launch the inspector before you clicking Study Now, and then enter into a deck, you will see the following:

The left window shows the running code of custom scheduling.

F10 or the button in the next figure is used to execute the code per line.

Important!: Don't click the show answer before the code run to the end. You can use F8 to execute to the end.

Details about the scheduler

There are three parts of the scheduler's code.

Set parameters

Line 5-18 are setting the parameters for all cards. Line 24-40 are setting the parameters for a specific deck.

Related discussion: [Question] How to workaround with Anki custom scheduling not being "Per Deck"

Check the states of scheduling

Line 142-192 are used to check the scheduling states. In Anki, there are four types of states for card scheduling: New, Learning, Review, and Relearning. Learning and Relearning are the same in scheduling. And there are two types of decks: normal and filtered. In normal decks, all reviews will modify the interval of cards. But in filtered decks, only checking the box Reschedule cards based on my answer in this deck will allow Anki to update the interval of cards. The FSRS4Anki scheduler also supports filtered decks.

Calculate memory states

The FSRS4Anki scheduler will calculate memory states from your rating and the DSR model. The scheduled interval is based on memory states and your custom parameters.

If the memory states are not available during review, the FSRS4Anki scheduler will convert the Anki's built-in scheduling information to the memory states.

The interval and factor of Anki's built-in scheduling, an SM-2 variation, will be automatically converted to the memory states of FSRS.

Interval to Stability

If the card's memory states are empty, FSRS assumes that the $\text{Interval}$ given by Anki is equal to $\text{Stability} \times \text{Interval modifier}$, where $\text{Interval modifier} = 9 \times \left(\frac{1}{\text{RequestRetention}} - 1 \right)$

So, $\text{Stability} = \text{Interval} / \text{Interval modifier}$

Ease Factor to Difficulty

In SM-2, after a recall, the interval (stability) increases by the Ease Factor.

In FSRS, after a recall, the stability increases by a factor of $(1 + e^{w_8} \cdot (11-D) \cdot S^{-w_9} \cdot (e^{w_{10}\cdot(1-R)}-1) \cdot w_{15}(\textrm{if G = 2}) \cdot w_{16}(\textrm{if G = 4}))$.

If we equate these two, the Difficulty can be calculated as:

$$D = 11 - \cfrac{factor - 1}{e^{w_8}\cdot S^{-w_9}\cdot(e^{w_{10}\cdot(1-R)}-1)}.$$

After the stability and difficulty are calculated as above, they are used for the calculation of the next stability and the next difficulty (after the review).