Monty Hall paradox simulation (probability puzzle) / published by https://github.com/dacr/code-examples-manager #57afcd4b-a9bc-4204-82f8-d28a8338ee69/6e4d429ef956c63bdc615daa16fafe017f9232a3

simu-monty-hall-paradox.sc

// summary : Monty Hall paradox simulation (probability puzzle)
// keywords : scala, math, probability, puzzle, paradox, simulation, monty-hall, @testable
// publish : gist
// authors : David Crosson
// license : Apache NON-AI License Version 2.0 (https://raw.githubusercontent.com/non-ai-licenses/non-ai-licenses/main/NON-AI-APACHE2)
// id : 57afcd4b-a9bc-4204-82f8-d28a8338ee69
// created-on : 2020-12-29T21:01:25Z
// managed-by : https://github.com/dacr/code-examples-manager
// run-with : scala-cli $file

// ---------------------
//> using scala  "3.3.0"
//> using dep "org.scalatest::scalatest:3.2.16"
//> using objectWrapper
// ---------------------

/*
  Monty Hall paradox wikipedia : https://en.wikipedia.org/wiki/Monty_Hall_problem
*/

import org.scalatest._
import flatspec._
import matchers._

import scala.annotation.tailrec
import scala.math._
import scala.util.Random


object MontyHall {
  type Door = Int
  sealed trait BehindDoor
  object Goat extends BehindDoor
  object NewCar extends BehindDoor

  object Game {
    def apply(doorsCount: Int = 3): Game = {
      val state =
        1.to(doorsCount)
          .map(n => n -> Goat)
          .toMap
          .updated(Random.nextInt(doorsCount) + 1, NewCar)
      new Game(state,None)
    }
  }

  case class Game(state: Map[Door, BehindDoor], played:Option[Door]) {
    val doors = state.keys.toSet

    def chooseDoor(door:Door):Game = this.copy(played=Some(door))

    def play(door:Door):Boolean = state.get(door).exists(_ == NewCar)

    def revealDoor(): Door = {
      val doors = state.collect{case (door,Goat) if played.isEmpty || played.get != door => door}.toArray
      doors(Random.nextInt(doors.size))
    }

  }


  def simulate(rounds:Int=100_000)(strategy: (Door,Door,Set[Door])=>Door):Double = {
    @tailrec
    def play(round:Int, winCount:Int):Int = {
      if (round==0) winCount else {
        val gameInitialState = Game()
        val doors = gameInitialState.doors
        val firstChosenDoor = doors.to(Array)(Random.nextInt(doors.size))
        val gameAfterGivenChoice = gameInitialState.chooseDoor(firstChosenDoor)
        val revealedDoor = gameAfterGivenChoice.revealDoor()
        val finalChoice = strategy(firstChosenDoor, revealedDoor, doors)
        val result = gameAfterGivenChoice.play(finalChoice)
        play(round-1, winCount + (if (result) 1 else 0))
      }
    }
    play(rounds,0).toDouble/rounds
  }


  def simulateChangeMind(rounds:Int=100_000):Double = simulate(rounds) {
    (firstChosenDoor, revealedDoor, doors) =>
      (doors - firstChosenDoor - revealedDoor).head
  }

  def simulateKeepChoice(rounds:Int=100_000):Double = simulate(rounds) {
    (firstChosenDoor, revealedDoor, doors) => firstChosenDoor
  }

}


class MontyHallTest extends AnyFlatSpec with should.Matchers {
  override def suiteName: String = "MontyHallTest"
  import MontyHall._
  "Monty Hall paradox" should "give 33% of win chance if I keep my initial choice" in {
    simulateKeepChoice(500_000) shouldBe 0.33d +- 0.01d
  }
  it should "give 66% of win chance if I change my mind" in {
    simulateChangeMind(500_000) shouldBe 0.66d +- 0.01d
  }
}

org.scalatest.tools.Runner.main(Array("-oDF", "-s", classOf[MontyHallTest].getName))