/* 

  Lucky dip task in Picat.

  From
  Pascal Bercker:
  "Lucky Dip Task — Is This A Fair Game? Three Ways of Modeling with A Bayesian Network"
  https://medium.com/@pbercker/lucky-dip-task-is-this-a-fair-game-three-ways-of-modeling-with-a-bayesian-network-8b393583aa34
  """
  I got this simple puzzle from a dissertation [https://openscholar.uga.edu/record/17924/files/molnar_robert_a_201508_phd.pdf] 
  on teaching conditional probability in a high school context.

  Lucky Dip Task
  Dominic has devised a simple game. Inside a bag he places 3 black and 3 white balls. 
  He then shakes the bag.
  He asks Amy to take two balls from the bag without looking.

  If the two balls are the same color, then Amy wins.
  If they are different colors, then Dominic wins.

  Is the game fair, meaning Dominic and Amy have equal probability if winning?
  If not, then who is most likely to win?
  """

  The game is not fair: 
  Dominic has 3/5 probability of winning, while Amy only has 2/5 probability.

  However, if Amy draws with replacement, then the game is fair.

  Cf my Gamble model gamble_lucky_dip_task.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 : amy wins
  Probabilities:
  false: 0.5969500000000000
  true: 0.4030500000000000
  mean = 0.40305

  var : dominic wins
  Probabilities:
  true: 0.5969500000000000
  false: 0.4030500000000000
  mean = 0.59695


*/
go ?=>
  reset_store,
  run_model(20_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() =>
  Bag = [b,b,b,w,w,w],
  
  AmyDraw = draw_without_replacement(2,Bag),
  AmyWins = check(AmyDraw[1] == AmyDraw[2]),

  DominicWins = check(not AmyWins),

  add("amy wins",AmyWins),
  add("dominic wins",DominicWins).


/*

  What if Amy draw _with_ replacement? Then it's a fair game:

  var : amy wins
  Probabilities:
  false: 0.5034333333333333
  true: 0.4965666666666667
  mean = 0.496567

  var : dominic wins
  Probabilities:
  true: 0.5034333333333333
  false: 0.4965666666666667
  mean = 0.503433

*/
go2 ?=>
  reset_store,
  run_model(30_000,$model2,[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.
go2 => true.
  
  
model2() =>
  Bag = [b,b,b,w,w,w],
  
  AmyDraw = uniform_draw_n(Bag,2),
  AmyWins = check(AmyDraw[1] == AmyDraw[2]),

  DominicWins = check(not AmyWins),

  add("amy wins",AmyWins),
  add("dominic wins",DominicWins).