Monty Hall problem

MontyHallProblem.scala

// http://en.wikipedia.org/wiki/Monty_Hall_problem
// http://d.hatena.ne.jp/hiratara/20120330/1333122309

import scala.util.Random._

case class Door(index: Int, isCar: Boolean)
def chooseDoor(doors: Seq[Door]): Door = doors(nextInt(doors.size))

object MontyHall {
  val NUM_OF_DOORS = 3
  def prepareDoors(): Seq[Door] = {
    val doorToCar = nextInt(NUM_OF_DOORS)
    (0 until NUM_OF_DOORS) map { x => Door(x, x == doorToCar) }
  }
  def choose(doors: Seq[Door], chosen: Door): Door = chooseDoor(doors) match {
    case choice if choice != chosen && ! choice.isCar => choice
    case _ => choose(doors, chosen)
  }
}

case class Player(doors: Seq[Door]) {
  lazy val firstChoice: Door = doors(nextInt(doors.size))
  def choose(): Door = firstChoice
  def reChoose(montyChoice: Door): Door = doors.find { door  => 
    door != firstChoice && door != montyChoice 
  }.get
}

def game(change: Boolean): Boolean = {
  val doors: Seq[Door] = MontyHall.prepareDoors()
  val player = new Player(doors)
  val firstChoice = player.choose()
  val montyChoice = MontyHall.choose(doors, firstChoice)
  val finalChoice = if (change) player.reChoose(montyChoice) else firstChoice
  finalChoice.isCar
}

def calculateWinRate(times: Int, change: Boolean): Double = {
  val winCount = (1 to times) map { _ => game(change) } count (win => win)
  winCount.toDouble / times.toDouble * 100
}

val times = 10000
println("first choice : %.2f %%".format(calculateWinRate(times, false)))
println("changed      : %.2f %%".format(calculateWinRate(times, true)))

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