/* 

  Nine spades and four clubs in Picat.

  From Statistics101
  """
  Compute the probability of getting in a 13 card hand: 
  Nine cards to be spades and four to be clubs. Order
  does not matter.
  From Resampling: The New Statistics, Julian Simon p. 125
  (Assumes that the numbers 1 through 13 represent spades.)
  """

  Cf my Gamble model gamble_nine_spades_four_clubs.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 : num spades
  Probabilities (truncated):
  3: 0.2506500000000000
  4: 0.2128500000000000
  2: 0.2046000000000000
  5: 0.1247000000000000
  .........
  7: 0.0184000000000000
  8: 0.0042000000000000
  9: 0.0010500000000000
  10: 0.0001000000000000
  mean = 3.2555

  var : num clubs
  Probabilities (truncated):
  3: 0.2501500000000000
  4: 0.2109500000000000
  2: 0.2061000000000000
  5: 0.1239500000000000
  .........
  7: 0.0202000000000000
  8: 0.0038000000000000
  9: 0.0010500000000000
  10: 0.0001000000000000
  mean = 3.2516

  var : p
  Probabilities:
  false: 0.9999500000000000
  true: 0.0000500000000000
  mean = 0.00005

*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  % spades: 1, clubs: 2 (and we don't care about 3 and 4 representing diamonds and heart)
  Cards = [random_integer1(4) : _ in 1..13],

  NumSpades = count_occurrences(1,Cards),
  NumClubs = count_occurrences(2,Cards),
  P = check( (NumSpades==9, NumClubs==4)),

  add("num spades",NumSpades),
  add("num clubs",NumClubs),
  add("p",P).