/* 

  Binomial dice in Picat.

  https://reference.wolfram.com/language/ref/BinomialDistribution.html
  """
  Two players roll dice. If the total of both numbers is less than 10, the second player 
  is paid 4 cents; otherwise the first player is paid 9 cents. Is the game fair?:

  ... 

  The game is not fair: mean scores are 1.5 and 3.33333.
  """


  Cf my Gamble model gamble_binomial_dice2.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.

/*

  var : player1
  Probabilities:
  4: 0.1704000000000000
  2: 0.1678000000000000
  1: 0.1676000000000000
  6: 0.1663000000000000
  3: 0.1646000000000000
  5: 0.1633000000000000
  mean = 3.4929

  var : player2
  Probabilities:
  6: 0.1730000000000000
  1: 0.1726000000000000
  5: 0.1675000000000000
  4: 0.1659000000000000
  2: 0.1644000000000000
  3: 0.1566000000000000
  mean = 3.5103

  var : total
  Probabilities (truncated):
  7: 0.1609000000000000
  6: 0.1395000000000000
  8: 0.1386000000000000
  9: 0.1115000000000000
  3: 0.0553000000000000
  11: 0.0535000000000000
  2: 0.0309000000000000
  12: 0.0301000000000000
  mean = 7.0032

  var : player1_sum
  Probabilities:
  0: 0.8294000000000000
  9: 0.1706000000000000
  mean = 1.5354

  var : player2_sum
  Probabilities:
  4: 0.8294000000000000
  0: 0.1706000000000000
  mean = 3.3176

  var : fair
  Probabilities:
  false: 1.0000000000000000
  mean = [false = 1.0]


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           presentation=[player1,player2,total,player1_sum,player2_sum,fair]]),
  nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Limit = 10,
  Player1 = random_integer1(6),
  Player2 = random_integer1(6),
  Total = Player1 + Player2,

  Player1Sum = 0,
  Player2Sum = 0,  
  if Total < Limit then
    Player2Sum := 4,
  else
    Player1Sum := 9,
  end,
  Fair = check(Player1Sum == Player2Sum),

  add_all([ [player1,Player1],
            [player2,Player2],
            [total,Total],
            [player1_sum,Player1Sum],
            [player2_sum,Player2Sum],
            [fair,Fair]]).