/* 

  Bridge in Picat.

  From Statistics101 (Resampling Stats)
  """
  What is the probability of getting a total
  of 15 points in a bridge hand when
  ace = 4, king =3, queen = 2, and jack = 1.
  From Simon, "The New Statistics", p 126

  -> probability: 0.04404
  """

  Cf my Gamble model gamble_bridge.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 : s
  Probabilities (truncated):
  8: 0.0866000000000000
  9: 0.0849000000000000
  10: 0.0837000000000000
  7: 0.0774000000000000
  .........
  29: 0.0003000000000000
  33: 0.0001000000000000
  30: 0.0001000000000000
  26: 0.0001000000000000
  mean = 10.0435

  var : p
  Probabilities:
  false: 0.9562000000000000
  true: 0.0438000000000000
  mean = [false = 0.9562,true = 0.0438]

*/
go ?=>
  reset_store,
  Deck = ones(4,4) ++ ones(4,3) ++ ones(4,2) ++ ones(4,1) ++ ones(36,0),
  run_model(10_000,$model(Deck),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model(Deck) =>
  Hand = resample(13,Deck),

  S = Hand.sum,
  P = check(S == 15),  
  add("s",S),
  add("p",P).