app.js

// source: https://stackoverflow.com/a/49434653
function randn_bm() {
  let u = 0, v = 0;
  while(u === 0) u = Math.random(); //Converting [0,1) to (0,1)
  while(v === 0) v = Math.random();
  let num = Math.sqrt( -2.0 * Math.log( u ) ) * Math.cos( 2.0 * Math.PI * v );
  num = num / 10.0 + 0.5; // Translate to 0 -> 1
  if (num > 1 || num < 0) return randn_bm() // resample between 0 and 1
  return num
}

// source: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/random
function getRandomIntInclusive(min, max) {
  min = Math.ceil(min);
  max = Math.floor(max);
  return Math.floor(Math.random() * (max - min + 1) + min); //The maximum is inclusive and the minimum is inclusive
}

function getRandomIntInclusiveNormal(min, max) {
    min = Math.ceil(min);
    max = Math.floor(max);
    return Math.floor(randn_bm() * (max - min + 1) + min); //The maximum is inclusive and the minimum is inclusive
}

// random game time in minutes [min, max] uniform distribution
function gameTimeMins(min, max) {
    var minMin = Math.round(min) * 60;
    var maxMin = Math.round(max) * 60;
    var gameTimeSeconds = getRandomIntInclusive(minMin, maxMin);
    return gameTimeSeconds / 60;
}

// random game time in minutes [min, max] normal distribution
function gameTimeMinsNormal(min, max) {
    var minMin = Math.round(min) * 60;
    var maxMin = Math.round(max) * 60;
    var gameTimeSeconds = getRandomIntInclusiveNormal(minMin, maxMin);
    return gameTimeSeconds / 60;
}

// wr: win rate [0,1]
function game(wr) {
    if (Math.random() < wr) {
        return 1;
    }
    return 0;
}

// points: mission points
function completeBasicMission(points) {
    var games = 0;
    while (points > 0) {
        points -= 2 + 3 * game(0.5);
        games ++;
    }
    return games;
}

// target: misison points
// win: points rate for win
// loss: points rate for loss
// avg: average game length
// (un)comment the different length generation and rounding types to change the simulation
function completePoints(target, win, loss, avg) {
    var games = 0;
    var points = 0;
    var length = avg;

    while (points < target) {

        // uniform
        length = gameTimeMins(avg * 0.5, avg * 1.5);
        // normal
        // length = gameTimeMinsNormal(avg * 0.5, avg * 1.5);

        // different rounding methods
        length = Math.round(length);
        // length = Math.ceil(length);
        // length = Math.floor(length);

        if (game(0.5)) {
            points += win * length;
        }
        else {
            points += loss * length;
        }
        games ++;
    }

    return games;
}

// tries: iterations to run
// mission: mission points
// avg: average game length
function sim(tries, mission, avg){
    var totalGames = 0;
    for (var i = 0; i < tries; i ++) {
        totalGames += completePoints(mission, 6, 4, avg);
    }
    return totalGames/tries;
}

// tries: iterations to run
// mission: mission points
// avg: average game length
// reward: tokens for completing mission
function simTokens(tries, mission, avg, reward) {
    var gamesPerTokens = 0;
    for (var i = 0; i < tries; i ++) {
        gamesPerTokens += completePoints(mission, 6, 4, avg);
    }
    gamesPerTokens /= tries;
    return reward / gamesPerTokens;
}

// tries: iterations to run
// mission: mission points
function simOld(tries, mission){
    var totalGames = 0;
    for (var i = 0; i < tries; i ++) {
        totalGames += completeBasicMission(mission);
    }
    return totalGames / tries;
}

// tries: iterations to run
// win: tokens for win
// loss: tokens for loss
function tokensOld(tries, win, loss) {
    var total = 0;
    for (var i = 0; i < tries; i ++) {
        if (game(0.5)) {
            total += win;
        } else {
            total += loss;
        }
    }
    return total / tries;
}

console.log("Old Weekly: ", simOld(25000000, 40));
console.log("New Weekly ARAM: ", sim(25000000, 1650, 20));
console.log("New Weekly SR: ", sim(25000000, 1650, 30));

console.log("Old Orb Mission: 30");
console.log("New Orb Mission ARAM: ", sim(25000000, 4500, 20));
console.log("New Orb Mission SR: ", sim(25000000, 4500, 30));

console.log("Old Tokens EV ARAM: ", tokensOld(25000000, 6, 3));
console.log("New Tokens EV ARAM: ", simTokens(25000000, 400, 20, 20));

console.log("Old Tokens EV SR: ", tokensOld(25000000, 10, 5));
console.log("New Tokens EV SR: ", simTokens(25000000, 400, 30, 20));