gamblers_falacy.jl

###### test 1

function gamblers_falacy_1(n)

   h,t = 0,0; c=0; r=0
   
   for i=1:n
      p = t>h ? :h : (h>t ? :t : nothing)

      o = rand((:h,:t))

      c = p==nothing ? c : c+1
      r = p==o ? r+1 : r

      o==:h ? (h+=1) : (t+=1)
      
      println("i=$i  t=$t h=$h  c=$c  r=$r  rr=$(r/c)")
   end
end

##

gamblers_falacy_1(1000)


######## test 2

function gamblers_falacy_2(n)
   last = :none
   number = 0
   guesses = Dict{Int,NamedTuple{(:tries, :rights),Tuple{Int64,Int64}}}()

   for i=1:n
      if number > 1
         guess = last==:h ? :t : :h
      else
         guess = nothing
      end
      
      outcome = rand((:h,:t))

      if guess != nothing
         guesstries, guessrigths = get(guesses, number, (0,0))
         guesstries += 1
         if guess == outcome
            guessrigths += 1
         end
         guesses[number] = (tries=guesstries, rights=guessrigths)
      end

      #println("$last"^number, " $outcome")

      if outcome == last
         number += 1
      else
         last = outcome
         number = 1
      end
   end

   guesses
end

##

println()
guesses = gamblers_falacy_2(1000000)
guessesarr = sort([(n, g[:tries], g[:rights], round(g[:rights]/g[:tries], digits=3)) for (n,g) in guesses])
for g in guessesarr
   println(g)
end