/* 

  A Marble Chance Puzzle in Picat.

  From Cole Frederick: "A Marble Chance Puzzle - A simple test of logic"
  https://colefp.medium.com/a-marble-chance-puzzle-c93e3224deb4
  """
  You have two boxes. One box has a blue marble, and the other box has one blue 
  marble and one black marble. You cannot see into either box. You simultaneously 
  reach into each box, grab one marble from each, then switch them quickly without 
  looking. You then randomly pick a box, and then randomly pick a marble 
  from that box. What is the probability you pick a blue marble?
  """


  Cf my Gamble model gamble_a_marble_chance_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 : pick from A
  Probabilities:
  blue: 1.0000000000000000
  mean = []

  var : pick from B
  Probabilities:
  blue: 0.5031000000000000
  black: 0.4969000000000000
  mean = []

  var : box A 2
  Probabilities:
  [blue]: 0.5031000000000000
  [black]: 0.4969000000000000
  mean = []

  var : box B 2
  Probabilities:
  [black,blue]: 0.5031000000000000
  [blue,blue]: 0.4969000000000000
  mean = []

  var : pick box
  Probabilities:
  [black]: 0.2529000000000000
  [blue]: 0.2522000000000000
  [black,blue]: 0.2509000000000000
  [blue,blue]: 0.2440000000000000
  mean = []

  var : pick = blue
  Probabilities:
  true: 0.6172000000000000
  false: 0.3828000000000000
  mean = 0.6172

  var : scenario A
  Probabilities:
  true: 0.5031000000000000
  false: 0.4969000000000000
  mean = 0.5031

  var : scenario B
  Probabilities:
  false: 0.5031000000000000
  true: 0.4969000000000000
  mean = 0.4969



*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean % ,
                           % show_simple_stats % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.84,0.9,0.94,0.99,0.99999],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  % First step
  BoxA_1 = [blue],
  BoxB_1 = [blue,black],

  % Pick one marble from each box
  PickFromA = uniform_draw(BoxA_1),
  PickFromB = uniform_draw(BoxB_1),

  % And move it to the other box
  BoxA_2 = delete(BoxA_1,PickFromA) ++ [PickFromB],
  BoxB_2 = delete(BoxB_1,PickFromB) ++ [PickFromA],

  % Pick a box at random
  PickBox = uniform_draw([BoxA_2,BoxB_2]),
  % And draw a marble at random
  Pick = uniform_draw(PickBox),

  % Probability of each scenario
  % 1. A: blue  B: black blue
  % 2. A: black B: blue blue
  ScenarioA = check( (BoxA_2 == [blue],  BoxB_2 == [black,blue])),
  ScenarioB = check( (BoxA_2 == [black], BoxB_2 == [blue,blue])),  

  % What is the probability that the drawn marble is blue
  PickBlue = check(Pick == blue),
  
  add("pick from A",PickFromA),
  add("pick from B",PickFromB),
  add("box A 2",BoxA_2),
  add("box B 2",BoxB_2),
  add("pick box",PickBox),
  add("pick = blue",PickBlue),  
  add("scenario A",ScenarioA),
  add("scenario B",ScenarioB).