/* 

  Rolling dice problem in Picat.

  From https://dtai.cs.kuleuven.be/problog/tutorial/basic/03_dice.html
  """
  We now consider yet another way to model dice, using fair ones only. This representation 
  allows for convenient use of the results in arithmetic expressions, e.g., to add up the 
  results from several dice. We query for the probabilities of the possible sums we can get 
  from two dice given that the first number is even and the second odd.
  """ 

  This is the exact probabilities (from my Racket/Gamble model gamble_rolling_dice3.rkt)
  (7 : 1/3 (0.3333333333333333))
  (5 : 2/9 (0.2222222222222222))
  (9 : 2/9 (0.2222222222222222))
  (3 : 1/9 (0.1111111111111111))
  (11 : 1/9 (0.1111111111111111))
  (mean: 7.0)

  This is a port of my Racket/Gamble model gamble_rolling_dice3.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.

main => go.


/*

  Var S:
  Probabilities:
  7: 0.33380421806605648 (16777 / 50260)
  5: 0.22347791484281734 (2808 / 12565)
  9: 0.22089136490250696 (793 / 3590)
  3: 0.11215678471945881 (5637 / 50260)
  11: 0.10966971746916036 (1378 / 12565)
  mean = 6.98488

*/
go ?=>
  reset_store,
  run_model(200_000,$model,[show_probs_rat,mean]),
  fail,
  nl.
go => true.

roll(D) = dice(6).

model() =>
  D1 = roll("d1"),
  D2 = roll("d2"),
  
  if even(D1), odd(D2) then
    S = D1 + D2,
    add("S",S)
  end.