《西瓜遊戲得分裡的數學》(https://blog.cruciferslab.net/?p=1535) 的模擬程式

tally.js

function randomFruit()
{
	return Math.floor(Math.random() * 5);
}

const FruitInfo = [
	{apple: 1/32, point: 3.09375}, // 櫻桃
	{apple: 1/16, point: 5.1875}, // 草莓
	{apple: 1/8, point: 7.375}, // 葡萄
	{apple: 1/4, point: 8.75}, // 柑橘
	{apple: 1/2, point: 7.5}, // 柿子
];

function applePoints(draws)
{
	let appleEquiv = 0, extraPoint = 0;
	for(let i = 0; i < draws; i++)
	{
		let fruit = randomFruit();
		appleEquiv += FruitInfo[fruit].apple;
		extraPoint += FruitInfo[fruit].point;
	}
	return extraPoint / appleEquiv;
}

const RUNS = 10_000_000;
let sum = 0, sqsum = 0;
for(let i = 0; i < RUNS; i++)
{
	let result = applePoints(250);
	sum += result;
	sqsum += result * result;
	if((i+1) % 100_000 == 0)
	{
		let avg = sum / (i+1);
		let sqavg = sqsum / (i+1);
		let stddev = (sqavg - avg ** 2) ** 0.5;
		console.log((i+1), //局數
			avg.toFixed(4), //平均蘋果值
			stddev.toFixed(4), //蘋果值標準差
			(avg * 32 + 849).toFixed(4), //換算成的平均西瓜值
			(stddev * 2 * 32).toFixed(4)); //兩個標準差 (95%) 對應的西瓜值差距
	}
}