Julia count RPS combinations

countRPSwins.jl

using IterTools
using Test
# This script counts the amount of 'winning' combinations for a n-player game of Rock, Paper Scissors (RPS).
# To test the mycount function I calculated I wanted to generate all possible combinations and programatically count them.
# That's what the actualcount function does.


x = [2,3,5]
#x = ['R','P','S']

#Generates a tuple as argument input for the product function.
function genArg(n)
  Tuple(fill(x,n))
end
@show genArg(2)
@show genArg(3)


#Caclulates whether the combination t is a ty based on modulo calculus.
function isTie(t,n)
  prod = reduce(*,t)
  if prod % (2*3*5) == 0
    return true
  elseif prod % 2 ^ n == 0
    return true
  elseif prod % 3 ^ n == 0
    return true
  elseif prod % 5 ^ n == 0
    return true
  end
  return false
end

#Some testing of the product function.
#for p in Iterators.product(genArg(n)...)
#  @show p
#end

#Generates all possible outcomes for n-player RPS 
function actualcount(n)
  totalcount = 3^n
  tiecount = count(x -> isTie(x,n), Iterators.product(genArg(n)...))
  wincount = totalcount - tiecount
  #winrate = wincount / totalcount
end           


# Hand calculated function for my blogpost
function mycount(g)
  3 * 2 * (2^(g-1) -1)
end

#Test the function up to n=15
@testset "test my count" begin
  for t in Array(3:15)
     @test mycount(t) == actualcount(t)
  end     
end;

@time actualcount(15)
@time actualcount(16)