Monty Hall Problem in Scala

Montyhall.scala

import scala.util.Random

sealed trait Prize
case object Car extends Prize
case object Goat extends Prize

object Montyhall {
  def main(args: Array[String]) {
    val runs = 10000000
    val (cars,_) =
      1.to(runs).map(_ => play()).partition(_ == Car)
    val percentCarChosen: Double = cars.length.toDouble / runs
    println(f"Car selected $percentCarChosen of the time.") //This will be 0.6667'sh or so
  }

  def play(): Prize = {
    //Create three doors and assign car to a single random door
    val doors = List(Goat,Goat,Goat).updated(selection(),Car)

    //Allow user to pick a random door as selection
    val firstPickIndex = selection()

    //Take away a door that 1) contains a goat 2) is not a door the user picked
    val doorsNotEligibleToReveal = Set(firstPickIndex,doors.indexOf(Car))
    val takeAwayIndex = selection(filter = doorsNotEligibleToReveal.toList)

    //Return the door that remains that the user did not select
    doors(selection(List(firstPickIndex,takeAwayIndex)))
  }

  def selection(filter: List[Int] = Nil): Int = {
    val indices: List[Int] = List(0,1,2).diff(filter)
    indices(Random.nextInt(indices.size))
  }
}