Gacha of Monte Carlo (Genshin Impact ver.)

montecarlo.js

/*
 * MIT No Attribution
 * 
 * Copyright 2022 perillamint
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a copy of this
 * software and associated documentation files (the "Software"), to deal in the Software
 * without restriction, including without limitation the rights to use, copy, modify,
 * merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
 * INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
 * PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

// This code simulates and calculate Genshin Impact Gacha probability.
// I'm too lazy to analyze Discrete Cumulative Distribution Function by myself
// So this code just simulates and analyze it using Monte Carlo method.

function prob_distribution_func(n) {
    if (n < 75 && n >= 1) return 0.006;
    if (n <= 89) return 0.33;
    if (n == 90) return 1;
    throw new Error("Undefined!")
}

function do_gacha(n, m) {
    if (Math.random() <= prob_distribution_func(n, m)) {
        // Simulate prize
        if (m == 1) {
            return {
                ur: true,
                pickup: true,
            };
        } else {
            return {
                ur: true,
                pickup: Math.random() <= 0.5,
            };
        }
    }
    return {
        ur: false,
        pickup: false,
    }
}

function montecarlo_cnt() {
    let n = 1; m = 0;
    let cnt = 1;

    for(;;) {
        let res = do_gacha(n, m);
        if (res.pickup) {
            return cnt;
        } else if (res.ur) {
            m += 1;
            n = 0;
        }

        cnt += 1;
        n += 1;
    }
}

const iter = 1000000;

const gachaMap = [];

for (let i = 0; i <= 90*2; i++) {
    gachaMap[i] = 0;
}

let sum = 0;
for (let i = 0; i < iter; i++) {
    let cnt = montecarlo_cnt();
    sum += cnt;
    gachaMap[cnt] += 1;
}

console.log(`Avg try: ${sum / iter}`);
console.log("Gacha histogram");
for (let i = 0; i <= 90*2; i++) {
    let msg = `${i}: `.padStart(6);
    for (let j = 0; j <= Math.ceil(gachaMap[i] / 200); j++) {
        msg += "*";
    }
    console.log(msg);
}
for (let i = 0; i <= 90*2; i++) {
    let msg = `${i}: `.padStart(6);
    msg += `${gachaMap[i] / iter * 100}%`;
    console.log(msg);
}