/* 

  Dice puzzle in Picat.

  From Berlin Bayesians:
  (https://app.slack.com/client/TFPMSKW3F/CFQHMRD6K)
  """
  What's likelier: Rolling at least one six in four throws of a single die,
  or rolling at least one double 6 in 24 throws of a pair of dice?
  """

  This is de Méré's classical dice puzzle (which induced the study of
  probability theory). See
  - https://mathworld.wolfram.com/deMeresProblem.html



  Cf my Gamble model gamble_dice_puzzle.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.
% import ordset.

main => go.

/*

  var : Rolling at least one six in four throws of a single die
  Probabilities:
  true: 0.5162000000000000
  false: 0.4838000000000000
  mean = 0.5162

  var : Rolling at least one double six in 24 throws of a pair of dice
  Probabilities:
  false: 0.5039000000000000
  true: 0.4961000000000000
  mean = 0.4961

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  % Case 1: Rolling at least one six in four throws of a single dice
  SingleDie = dice_n(6,4),
  P1 = check( count_occurrences(6,SingleDie) >= 1),

  % Case 2: Rolling at least one double six in 24 throws of a pair of dice
  TwoDice = [dice_n(6,2) : _ in 1..24],
  P2 = check( count_occurrences([6,6],TwoDice) >= 1),

  add("Rolling at least one six in four throws of a single die",P1),
  add("Rolling at least one double six in 24 throws of a pair of dice",P2).