/* 

  Urn puzzle in Picat.

  From Berlin Bayesians
  https://app.slack.com/client/TFPMSKW3F/CFQHMRD6K/thread/CFQHMRD6K-1623812230.000500
  """
  Three urns, first blindly take one from the first and put in the second, 
  then blindly take one from the second and put in the third and then blindly pick 
  one from the third. How likely is it to pick a black one in the last step?

  (
    Urns
    1: white black black
    2: white white black
    3: white black
  )
  """

  Cf my Gamble model gamble_urn_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.

main => go.

/*

  var : b all is black
  Probabilities:
  false: 0.5288000000000000
  true: 0.4712000000000000
  mean = [false = 0.5288,true = 0.4712]

  var : ball
  Probabilities:
  white: 0.5288000000000000
  black: 0.4712000000000000
  mean = [white = 0.5288,black = 0.4712]

  var : urn2b
  Probabilities:
  [white,white,black,black]: 0.6713000000000000
  [white,white,black,white]: 0.3287000000000000
  mean = [[white,white,black,black] = 0.6713,[white,white,black,white] = 0.3287]

  var : urn3b
  Probabilities:
  [white,black,white]: 0.5864000000000000
  [white,black,black]: 0.4136000000000000
  mean = [[white,black,white] = 0.5864,[white,black,black] = 0.4136]

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  Urn1 = [white,black,black],
  Urn2 = [white,white,black],
  Urn3 = [white,black],  


  % From Urn 1 to Urn 2
  Urn2b = Urn2 ++ [uniform_draw(Urn1)],

  % From Urn 2 to Urn 3
  Urn3b = Urn3 ++ [uniform_draw(Urn2b)],

  % Pick a random ball from Urn3b
  Ball = uniform_draw(Urn3b),
  
  add("urn2b",Urn2b),
  add("urn3b",Urn3b),
  add("ball",Ball),
  add("b all is black",check(Ball == black)).