my current understanding of Anki's spacing algorithm

anki_algorithm.js

// https://gist.github.com/riceissa/1ead1b9881ffbb48793565ce69d7dbdd

// "New cards" tab
const NEW_STEPS = [15, 25, 35]  // in minutes
const GRADUATING_INTERVAL = 15  // in days
const EASY_INTERVAL = 4  // in days
const STARTING_EASE = 2.50  // in percent

//  "Reviews" tab
const EASY_BONUS = 1.30
const INTERVAL_MODIFIER = 1
const MAXIMUM_INTERVAL = 36500  // in days

// "Lapses" tab
const LAPSES_STEPS = [20]  // in minutes
const NEW_INTERVAL = 0.70
const MINIMUM_INTERVAL = 2  // in days

class Card {
    constructor() {
        this.status = 'learning' // can be 'learning', 'learned', or 'relearning'
        this.steps_index = 0
        this.ease_factor = STARTING_EASE
        this.interval = null
        this.history = []

        this.repr = this.repr.bind(this);
        this.choice = this.choice.bind(this);
        this.minutes_to_days = this.minutes_to_days.bind(this);
        this.prompt = this.prompt.bind(this);
    }

    repr() {
        return `Card[${this.status}; steps_idx=${this.steps_index}; ease=${this.ease_factor}; interval=${this.interval}]`
    }

    choice(button) {
        //button is one of "wrong", "hard", "good", or "easy"
        // returns a result in days
        this.history.push(button)

        if (this.status === 'learning') {
            // for learning cards, there is no "hard" response possible
            if (button === 'wrong') {
                this.steps_index = 0
                return this.minutes_to_days(NEW_STEPS[this.steps_index])
            }
            else if (button === 'good') {
                this.steps_index += 1
                if (this.steps_index < NEW_STEPS.length) {
                    return this.minutes_to_days(NEW_STEPS[this.steps_index])
                } else {
                    // we have graduated!
                    this.status = 'learned'
                    this.interval = GRADUATING_INTERVAL
                    return this.interval
                }
            }
            else if (button === 'easy') {
                this.status = 'learned'
                this.interval = EASY_INTERVAL
                return EASY_INTERVAL
            }
            else {
                // raise ValueError("you can't press this button / we don't know how to deal with this case")
            }
        }
        else if (this.status === 'learned') {
            if (button === "wrong") {
                this.status = 'relearning'
                this.steps_index = 0
                this.ease_factor = Math.max(1.30, this.ease_factor - 0.20)
                // the anki manual says "the current interval is multiplied by the
                // value of new interval", but I have no idea what the "new
                // interval" is
                return this.minutes_to_days(LAPSES_STEPS[0])
            }
            else if (button === 'hard') {
                this.ease_factor = Math.max(1.30, this.ease_factor - 0.15)
                this.interval = this.interval * 1.2 * INTERVAL_MODIFIER
                return Math.min(MAXIMUM_INTERVAL, this.interval)
            }
            else if (button === 'good') {
                this.interval = (this.interval * this.ease_factor
                    * INTERVAL_MODIFIER)
                return Math.min(MAXIMUM_INTERVAL, this.interval)
            }
            else if (button === 'easy') {
                this.ease_factor += 0.15
                this.interval = (this.interval * this.ease_factor
                    * INTERVAL_MODIFIER * EASY_BONUS)
                return Math.min(MAXIMUM_INTERVAL, this.interval)
            }
            else {
                // raise ValueError("you can't press this button / we don't know how to deal with this case")
            }

        }
        else if (this.status === 'relearning') {
            if (button === "wrong") {
                this.steps_index = 0
                return this.minutes_to_days(LAPSES_STEPS[0])
            }
            else if (button === "good") {
                this.steps_index += 1
                if (this.steps_index < LAPSES_STEPS.length) {
                    return this.minutes_to_days(LAPSES_STEPS[this.steps_index])
                }
                else {
                    // we have re-graduated!
                    this.status = 'learned'
                    this.interval = Math.max(MINIMUM_INTERVAL, this.interval * NEW_INTERVAL)
                    return this.interval
                }
            } else {
                // raise ValueError("you can't press this button / we don't know how to deal with this case")
            }
        }
    }

    minutes_to_days(minutes) {
        return minutes / (60 * 24)
    }

    prompt() {
        const promt_pp = (ivl, s) => {
            if (ivl) {
                if (ivl <= 1)
                    return `${s} ${ivl*1440}m`
                 else
                     return `${s} ${ivl.toFixed(2)}d`
            }
        }
        let c = new Card()
        let wrong_ivl =  [...this.history, 'wrong'].map(x => c.choice(x)).pop()
        c = new Card()
        let hard_ivl =  [...this.history, 'hard'].map(x => c.choice(x)).pop()
        c = new Card()
        let good_ivl =  [...this.history, 'good'].map(x => c.choice(x)).pop()
        c = new Card()
        let easy_ivl =  [...this.history, 'easy'].map(x => c.choice(x)).pop()
        const s = [
            promt_pp(wrong_ivl, "wrong"),
            promt_pp(hard_ivl, "hard"),
            promt_pp(good_ivl, "good"),
            promt_pp(easy_ivl, "easy")
        ].filter(x => x !== undefined).join(" | ")
        return s
    }

}


// a = new Card()
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
//
//
// console.log()
// a = new Card()
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("good")
// console.log(a.repr())
// console.log(a.prompt())
// a.choice("wrong")
// console.log(a.repr())

// ```bash
//node anki_algorithm.js
//```

anki_algorithm.py

"""
https://gist.github.com/riceissa/1ead1b9881ffbb48793565ce69d7dbdd
"""


# "New Cards" tab
NEW_STEPS = [15, 25, 35]  # in minutes
GRADUATING_INTERVAL = 15  # in days
EASY_INTERVAL = 4  # in days
STARTING_EASE = 2.50  # in percent

# "Reviews" tab
EASY_BONUS = 1.30
INTERVAL_MODIFIER = 1
MAXIMUM_INTERVAL = 36500  # in days

# "Lapses" tab
LAPSES_STEPS = [20]  # in minutes
NEW_INTERVAL = 0.70
MINIMUM_INTERVAL = 2  # in days

class Card:
    def __init__(self):
        self.status = 'learning'  # can be 'learning', 'learned', or 'relearning'
        self.steps_index = 0
        self.ease_factor = STARTING_EASE
        self.interval = None

        self.history = []

    def __repr__(self):
        return "Card[%s; steps_idx=%s; ease=%s; interval=%s]" % (self.status,
                                                                 self.steps_index,
                                                                 self.ease_factor,
                                                                 str(self.interval))


    def choice(self, button: str):
        '''button is one of "wrong", "hard", "good", or "easy"
        returns a result in days'''
        self.history.append(button)

        if self.status == 'learning':
            # for learning cards, there is no "hard" response possible
            if button == "wrong":
                self.steps_index = 0
                return self.minutes_to_days(NEW_STEPS[self.steps_index])
            elif button == "good":
                self.steps_index += 1
                if self.steps_index < len(NEW_STEPS):
                    return self.minutes_to_days(NEW_STEPS[self.steps_index])
                else:
                    # we have graduated!
                    self.status = 'learned'
                    self.interval = GRADUATING_INTERVAL
                    return self.interval
            elif button == "easy":
                self.status = 'learned'
                self.interval = EASY_INTERVAL
                return EASY_INTERVAL
            else:
                # raise ValueError("you can't press this button / we don't know how to deal with this case")
                return
        elif self.status == 'learned':
            if button == "wrong":
                self.status = 'relearning'
                self.steps_index = 0
                self.ease_factor = max(1.30, self.ease_factor - 0.20)
                # the anki manual says "the current interval is multiplied by the
                # value of new interval", but I have no idea what the "new
                # interval" is
                return self.minutes_to_days(LAPSES_STEPS[0])
            elif button == "hard":
                self.ease_factor = max(1.30, self.ease_factor - 0.15)
                self.interval = self.interval * 1.2 * INTERVAL_MODIFIER
                return min(MAXIMUM_INTERVAL, self.interval)
            elif button == "good":
                self.interval = (self.interval * self.ease_factor
                                 * INTERVAL_MODIFIER)
                return min(MAXIMUM_INTERVAL, self.interval)
            elif button == "easy":
                self.ease_factor += 0.15
                self.interval = (self.interval * self.ease_factor
                                 * INTERVAL_MODIFIER * EASY_BONUS)
                return min(MAXIMUM_INTERVAL, self.interval)
            else:
                # raise ValueError("you can't press this button / we don't know how to deal with this case")
                return
        elif self.status == 'relearning':
            if button == "wrong":
                self.steps_index = 0
                return self.minutes_to_days(LAPSES_STEPS[0])
            elif button == "good":
                self.steps_index += 1
                if self.steps_index < len(LAPSES_STEPS):
                    return self.minutes_to_days(LAPSES_STEPS[self.steps_index])
                else:
                    # we have re-graduated!
                    self.status = 'learned'
                    self.interval = max(MINIMUM_INTERVAL, self.interval * NEW_INTERVAL)
                    return self.interval
            else:
                # raise ValueError("you can't press this button / we don't know how to deal with this case")
                return


    def minutes_to_days(self, minutes):
        return minutes / (60 * 24)



    @property
    def prompt(self):
        c = Card()
        wrong_ivl = [c.choice(b) for b in self.history + ["wrong"]][-1]
        c = Card()
        hard_ivl = [c.choice(b) for b in self.history + ["hard"]][-1]
        c = Card()
        good_ivl = [c.choice(b) for b in self.history + ["good"]][-1]
        c = Card()
        easy_ivl = [c.choice(b) for b in self.history + ["easy"]][-1]
        def prompt_pp(ivl, s: str):
            if ivl:
                if ivl <= 1:
                    return f'{s} {ivl * 1440}m'
                else:
                    return f'{s} {round(ivl, 2)}d'
        s = " | ".join(filter(None,
        [
            prompt_pp(wrong_ivl, "wrong"),
            prompt_pp(hard_ivl, "hard"),
            prompt_pp(good_ivl, "good"),
            prompt_pp(easy_ivl, "easy")
         ]))

        return s




# python
# >>> from anki_algorithm import *
# >>> a = Card()
# >>> a.prompt
# >>> a.choice("good")
# >>> a.choice("good")
# >>> a.prompt