/* 

  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 model uses another approach (recursion) than ppl_game_of_ur_problem.pi

  This is a port of my Gamble model gamble_game_of_ur_problem2.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 : len
  Probabilities:
  6: 0.2304781818634406
  7: 0.2015034973738581
  5: 0.1894307121698653
  8: 0.1341448236377667
  9: 0.0834889104622508
  4: 0.0800288751151271
  10: 0.0452293829188759
  11: 0.0209344584671297
  12: 0.0087372115600030
  13: 0.0034849276877505
  14: 0.0015184327782341
  15: 0.0006472008562965
  16: 0.0002240310656411
  17: 0.0001493540437607
  mean = 6.75503


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

roll(A) = Ret =>
  S = A.sum,
  if (S == 13) then
    Ret = A
  else
    if S > 13 then
      Ret = []
    else
      Ret = roll( A++ [random_integer(5)])
    end
  end.
model() =>
  A = roll([]),
  observe(A.sum == 13),
  if observed_ok then    
    add("len",A.len)
  end.