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October 8, 2023 14:56
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《西瓜遊戲得分裡的數學》(https://blog.cruciferslab.net/?p=1535) 的模擬程式
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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 | |
} | |
} |
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