/* 

  Innocent monkey in Picat.

  https://brainstellar.com/puzzles/probability/115
  """
  A very innocent monkey throws a fair die. The monkey will eat as many 
  bananas as are shown on the die, from 1 to 5. But if the die shows '6', 
  the monkey will eat 5 bananas and throw the die again. This may continue 
  indefinitely. What is the expected number of bananas the monkey will eat?

  Answer: 4
  """

  Cf my Gamble model gamble_innocent_monkey.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.

main => go.

/*

  var : len
  Probabilities:
  1: 0.8342000000000001
  2: 0.1377000000000000
  3: 0.0238000000000000
  4: 0.0039000000000000
  5: 0.0004000000000000
  mean = 1.1986

  var : total
  Probabilities (truncated):
  2: 0.1689000000000000
  4: 0.1687000000000000
  5: 0.1680000000000000
  3: 0.1647000000000000
  .........
  16: 0.0006000000000000
  24: 0.0002000000000000
  25: 0.0001000000000000
  23: 0.0001000000000000
  mean = 4.0054

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  

f(A,N) = Res =>
  R = random_integer1(N),
  if R <= 5 then
    Res = A ++ [R]
  else
    Res = f(A ++ [5],N)
  end.

model() =>
  N = 6,
  A = f([],N),
  Len = A.len,
  Total = A.sum,
  add("len",Len),
  add("total",Total).