Monty Hall Problem (Paradox)

simulate.js

const percent = (a, b) => {
  return (a / b * 100).toFixed(2);
}

const getRandomIndex = (n) => {
  return Math.floor(Math.random() * n);
};

const getRandomNumbers = (n) => {
  const arr = new Array(n);
  const index = getRandomIndex(n);

  arr[index] = 1;

  return arr;
};

const chooseRandom = (skipIndexes, n) => {
  const rand = getRandomIndex(n - skipIndexes.length);

  for (let i = 0, c = 0; i < n; i++) {
    if (skipIndexes.indexOf(i) !== -1) continue;
    if (c === rand) return i;

    c++;
  }
};

const revealRandChangeRand = (question, answer, N) => {
  const rightAnswer = question.indexOf(1);
  const reveal = chooseRandom([rightAnswer, answer], N);

  return chooseRandom([answer, reveal], N);
};


const revealRandChangeNext = (question, answer, N) => {
  const rightAnswer = question.indexOf(1);
  const reveal = chooseRandom([rightAnswer, answer], N);

  return question.findIndex((_, i) => i !== answer && i !== reveal);
};

const revealNextChangeNext = (question, answer, N) => {
  const rightAnswer = question.indexOf(1);
  const reveal = question.findIndex((_, i) => i !== rightAnswer && i !== answer);

  return question.findIndex((_, i) => i !== answer && i !== reveal);
};

const revealNextChangeRand = (question, answer, N) => {
  const rightAnswer = question.indexOf(1);
  const reveal = question.findIndex((_, i) => i !== rightAnswer && i !== answer);

  return chooseRandom([answer, reveal], N);
};

const TESTS = 1000000;
const N = 3;
let statsRandRand = 0;
let statsRandNext = 0;
let statsNextNext = 0;
let statsNextRand = 0;

for (let i = 0; i < TESTS; i++) {
  const question = getRandomNumbers(N);
  const answer = getRandomIndex(N);
  const rightAnswer = question.indexOf(1);

  const changeRandRand = revealRandChangeRand(question, answer, N);
  const changeRandNext = revealRandChangeNext(question, answer, N);
  const changeNextNext = revealNextChangeNext(question, answer, N);
  const changeNextRand = revealNextChangeRand(question, answer, N);

  if (changeRandRand === rightAnswer) statsRandRand++;
  if (changeRandNext === rightAnswer) statsRandNext++;
  if (changeNextNext === rightAnswer) statsNextNext++;
  if (changeNextRand === rightAnswer) statsNextRand++;
}

const original = percent(1, N);
const printResult = (name, win) => {
  const loose = TESTS - win;
  const winP = percent(win, TESTS);
  const looseP = percent(loose, TESTS);

  console.log(`${name}:`);
  console.log(`Won: ${win} (${winP} %), Lost: ${loose} (${looseP} %)`);
  console.log('-----');
  console.log('');
};

console.log('Expected %:', original)
console.log('-----');
console.log('');

printResult('RandRand', statsRandRand);
printResult('RandNext', statsRandNext);
printResult('NextNext', statsNextNext);
printResult('NextRand', statsNextNext);