/* 

  Game of Ur problem in Picat.

  https://www.allendowney.com/blog/2018/10/21/the-game-of-ur-problem/
  """
  Here’s a probability puzzle to ruin your week.

  In the Royal Game of Ur, players advance tokens along a track with 14 spaces. 
  To determine how many spaces to advance, a player rolls 4 dice with 4 sides. Two corners 
  on each die are marked; the other two are not. The total number of marked corners — 
  which is 0, 1, 2, 3, or 4 — is the number of spaces to advance.

  For example, if the total on your first roll is 2, you could advance a token to space 2. 
  If you roll a 3 on the next roll, you could advance the same token to space 5.

  Suppose you have a token on space 13. How many rolls did it take to get there?
   """

  See:
  https://www.allendowney.com/blog/lions-and-tigers-and-bears/

  Allen Downey's solution:
  http://nbviewer.jupyter.org/github/AllenDowney/ThinkBayes2/blob/master/solutions/game_of_ur_soln.ipynb?flush=true


  This is a port of my Gamble model gamble_game_of_ur_problem.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 : num_rolls
  Probabilities:
  7: 0.2115047351806384
  6: 0.1988775868116450
  5: 0.1662574535250789
  8: 0.1560855840056121
  9: 0.0964573833742546
  4: 0.0729568572430726
  10: 0.0487548228691687
  11: 0.0298141003156787
  12: 0.0122763942476324
  13: 0.0056120659417748
  14: 0.0007015082427219
  16: 0.0003507541213609
  15: 0.0003507541213609
  mean = 6.97019

*/
go ?=>
  reset_store,
  time2(run_model(100_000,$model,[show_probs,mean])),
  nl.
go => true.

model() =>
  NumRolls = random_integer(17) + 3, % 0..16 + 3

  SumRolls = random_integer_n(5,NumRolls).sum, % 0..4

  observe(SumRolls == 13),

  if observed_ok then
    add("num_rolls",NumRolls)
  end.