Probability of the result of 9 4-sided (pyramidal) dice (faces: 1 -> 4) is greater than the result of 6 6-sided (cubic) dice (faces: 1 -> 6)

PyramidWins.scala

object PyramidWins extends App {
  private def pdf(v: IndexedSeq[Int]) =
    v.groupBy(identity).map { pair =>
      (pair._1, pair._2.size / v.size.toFloat)
    }
  private val pyramids = pdf(for {
    p1 <- 1 to 4
    p2 <- 1 to 4
    p3 <- 1 to 4
    p4 <- 1 to 4
    p5 <- 1 to 4
    p6 <- 1 to 4
    p7 <- 1 to 4
    p8 <- 1 to 4
    p9 <- 1 to 4
  } yield p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9)
  private val cubics = pdf(for {
    c1 <- 1 to 6
    c2 <- 1 to 6
    c3 <- 1 to 6
    c4 <- 1 to 6
    c5 <- 1 to 6
    c6 <- 1 to 6
  } yield c1 + c2 + c3 + c4 + c5 + c6)
  private val pyrWinsPercs = for {
    p <- pyramids
    c <- cubics
  } yield if (p._1 > c._1) p._2 * c._2 else 0
  println(pyrWinsPercs.sum)
}