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@mayonesa
Last active February 4, 2022 17:25
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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)
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)
}
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