/* 

  Highest dice roller in Picat.

  From https://www.reddit.com/r/Probability/comments/1dxtfe5/probability_of_being_the_highest_roller/
  """
  Probability of being the highest roller

  What are the probability percentages for each person rolling the highest number 
  when all three each of them rolls their specific die once. In case of a tie, 
  the person with the largest number of sided die gets the tiebreaker.

  Person 1 rolls a 12 sided die Person 2 rolls an 8 sided die Person 3 rolls a 4 sided die.
  """


  Cf my Gamble model gamble_highest_dice_roller.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.

/*
  For the original question (no observation), the player with D12 wins:
  var : winner
  Probabilities:
  d12: 0.6777000000000000
  d8: 0.2834000000000000
  d4: 0.0389000000000000
  mean = [d12 = 0.6777,d8 = 0.2834,d4 = 0.0389]


  Here we check the cases were we observe that none, d4, d8, and d12 
  respectively is the winner.

  observation = none
  var : d4
  Probabilities:
  4: 0.2582000000000000
  3: 0.2564000000000000
  1: 0.2436000000000000
  2: 0.2418000000000000
  mean = 2.5292

  var : d8
  Probabilities:
  3: 0.1307000000000000
  5: 0.1275000000000000
  8: 0.1271000000000000
  6: 0.1250000000000000
  2: 0.1248000000000000
  1: 0.1243000000000000
  7: 0.1234000000000000
  4: 0.1172000000000000
  mean = 4.5029

  var : d12
  Probabilities:
  12: 0.0881000000000000
  10: 0.0877000000000000
  6: 0.0860000000000000
  2: 0.0856000000000000
  1: 0.0840000000000000
  8: 0.0827000000000000
  3: 0.0822000000000000
  9: 0.0819000000000000
  5: 0.0819000000000000
  4: 0.0803000000000000
  11: 0.0799000000000000
  7: 0.0797000000000000
  mean = 6.5182

  var : winner
  Probabilities:
  d12: 0.6777000000000000
  d8: 0.2834000000000000
  d4: 0.0389000000000000
  mean = [d12 = 0.6777,d8 = 0.2834,d4 = 0.0389]


  observation = d4
  var : d4
  Probabilities:
  4: 0.6756032171581769
  3: 0.2627345844504022
  2: 0.0616621983914209
  mean = 3.61394

  var : d8
  Probabilities:
  1: 0.4182305630026810
  2: 0.3860589812332439
  3: 0.1957104557640751
  mean = 1.77748

  var : d12
  Probabilities:
  1: 0.4396782841823056
  2: 0.3243967828418231
  3: 0.2359249329758713
  mean = 1.79625

  var : winner
  Probabilities:
  d4: 1.0000000000000000
  mean = [d4 = 1.0]


  observation = d8
  var : d4
  Probabilities:
  1: 0.2692862292718097
  2: 0.2563085796683490
  3: 0.2429704397981254
  4: 0.2314347512617159
  mean = 2.43655

  var : d8
  Probabilities:
  8: 0.2490987743330930
  7: 0.2271088680605624
  6: 0.1842105263157895
  5: 0.1532083633741889
  4: 0.1088680605623648
  3: 0.0598413842826244
  2: 0.0176640230713771
  mean = 6.10418

  var : d12
  Probabilities:
  1: 0.2339581831290555
  2: 0.2173756308579668
  3: 0.1683489545782264
  4: 0.1546503244412401
  5: 0.1204037490987743
  6: 0.0699351117519827
  7: 0.0353280461427541
  mean = 3.06128

  var : winner
  Probabilities:
  d8: 1.0000000000000000
  mean = [d8 = 1.0]


  observation = d12
  var : d4
  Probabilities:
  1: 0.2572058823529412
  2: 0.2557352941176471
  3: 0.2477941176470588
  4: 0.2392647058823529
  mean = 2.46912

  var : d8
  Probabilities:
  2: 0.1588235294117647
  1: 0.1541176470588235
  4: 0.1422058823529412
  3: 0.1407352941176471
  5: 0.1220588235294118
  6: 0.1144117647058824
  7: 0.0916176470588235
  8: 0.0760294117647059
  mean = 4.00912

  var : d12
  Probabilities:
  8: 0.1261764705882353
  11: 0.1227941176470588
  10: 0.1219117647058824
  9: 0.1198529411764706
  12: 0.1182352941176471
  7: 0.1076470588235294
  6: 0.0898529411764706
  5: 0.0786764705882353
  4: 0.0614705882352941
  3: 0.0323529411764706
  2: 0.0163235294117647
  1: 0.0047058823529412
  mean = 8.14309

  var : winner
  Probabilities:
  d12: 1.0000000000000000
  mean = [d12 = 1.0]

*/
go ?=>
  member(Obs,[none,d4,d8,d12]),
  println(observation=Obs),
  reset_store,
  run_model(10_000,$model(Obs),[show_probs,mean]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.
  
  
model(Obs) =>
  D4 = random_integer1(4),
  D8 = random_integer1(8),
  D12 = random_integer1(12),  

  Winner = cases([[(D4 > D8, D4 > D12),d4],
                  [(D8 >= D4, D8 > D12),d8], % with tie break D8 over D4
                  [(D12 >= D4, D12 >= D8),d12], % with tie break D12 over D4 and D8
                  [true,"someone else"]]),
                  
  if Obs == none then
      add("winner",Winner),
      add("d4",D4),
      add("d8",D8),
      add("d12",D12),      
  else 
    observe(Winner == Obs),
    if observed_ok then
      add("winner",Winner),
      add("d4",D4),
      add("d8",D8),
      add("d12",D12),      
    end
  end.