Simulation of the Monty Hall problem

monty.js

/*
  There are a certain number of doors (usually 3). Behind one is a prize. Behind the others are goats.
  The contestant picks a door, and then the host removes one of the non-selected choices that did contain
  the prize. The contestant is given the option to either keep their original choice, or switch to one of
  the remaining doors. What should they do?

  Let's simulate their potential decisions to find out!
*/

const doors = [1, 2, 3]

const numberOfTrials = 100000

const resultsForSwitching = {
  WIN: 0,
  LOSE: 0
}

const resultsForStaying = {
  WIN: 0,
  LOSE: 0
}

console.log(`Running ${numberOfTrials} simulations of Monty Hall problem with ${doors.length} doors\n`)

for (let i = 0; i < numberOfTrials; i++) {
  resultsForStaying[playGameWithStrategy('STAY')]++
  resultsForSwitching[playGameWithStrategy('SWITCH')]++
}

console.log(`Results when switching: ${formatResults(resultsForSwitching)}`)
console.log(`Results when keeping original choice: ${formatResults(resultsForStaying)}`)

function playGameWithStrategy (strategy) {
  const prizeBehind = pick(...doors) // Hide the prize behind a door
  const firstChoice = pick(...doors) // Contestant picks a door

  // host removes one of the doors the contestant did not select that does not contain the prize
  const removed = pick(...doors.filter(choice => choice !== firstChoice && choice !== prizeBehind))

  // based on selected strategy, the contestant will either keep their original choice, or pick the remaining door
  const finalChoice = strategy === 'SWITCH'
    ? pick(...doors.filter(choice => choice !== firstChoice && choice !== removed))
    : firstChoice
  
  return finalChoice === prizeBehind ? 'WIN' : 'LOSE'
}

function pick (...choices) {
  const numberOfChoices = choices.length
  const choiceIndex = Math.floor(Math.random() * numberOfChoices)

  return choices[choiceIndex]
}

function formatResults (results) {
  return `

  Wins: ${results.WIN}
  Loses: ${results.LOSE}

  Winning percentage: ${100 * results.WIN / (results.WIN + results.LOSE)}%
`
}