/* 

  Three card problem in Picat.

  https://twitter.com/MathsEdIdeas/status/1769785845970796935
  """
  Three cards are dealt face down from a normal deck. Two are turned over and 
  are the same colour. What is the probability that the third card is the same 
  colour as the first two?

  HT Martin Gardner @WWMGT, but was his solution correct?

   [ 
     9 of spades    Queen of clubs     back of a card
   ]

  """

  Note: color is black or red (not clubs, hearts, spades, diamonds).

  Result (exact from my Gamble model):
  (#f : 13/25 (0.52))
  (#t : 12/25 (0.48))

  This is a port of my Gamble model gamble_three_cards.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.

main => go.

/*
  var : p
  Probabilities:
  0: 0.52386763333572606 (7298 / 13931)
  1: 0.47613236666427394 (6633 / 13931)
  mean = 0.476132

*/
go ?=>
  reset_store,
  run_model(30_000,$model,[show_probs_rat,mean]),
  nl.
go => true.

model() =>
  N = 52,
  Mod = 2,
  % Pick three cards
  [C1,C2,C3] = random_integer1_n(N,3),
  observe(C1 != C2, C1 != C3, C2 != C3, % different numbers
         (C1 mod Mod) == (C2 mod Mod)), % first two cards has the same color (black/red)

  if observed_ok then
    % Probability that the third card has same color as the other two cards
    P = cond( (C3 mod Mod) == (C1 mod Mod),1,0),
    add("p",P)

  end.