/* 
  Three players coin toss in Picat.

  From https://x.com/Riazi_Cafe_en/status/1978749212150878208
  """
  Three players take turns tossing a coin. If a player gets heads, they 
  are eliminated; if tails, they remain in the game.

  On average, how many coin tosses occur before all players are eliminated?
  """

  Picat> X=pascal_dist_mean(3,1/2)           
  X = 6.0

  Histogram (random generated)
  Picat> pascal_dist_n(3,1/2,10000).show_histogram
  Histogram:
      3:  1216 #######################################                      (0.122 / 0.122)
      4:  1836 ##########################################################   (0.184 / 0.305)
      5:  1884 ############################################################ (0.188 / 0.494)
      6:  1590 ###################################################          (0.159 / 0.653)
      7:  1179 ######################################                       (0.118 / 0.771)
      8:   821 ##########################                                   (0.082 / 0.853)
      9:   526 #################                                            (0.053 / 0.905)
     10:   378 ############                                                 (0.038 / 0.943)
     11:   232 #######                                                      (0.023 / 0.966)
     12:   129 ####                                                         (0.013 / 0.979)
     13:    92 ###                                                          (0.009 / 0.988)
     14:    48 ##                                                           (0.005 / 0.993)
     15:    37 #                                                            (0.004 / 0.997)
     16:    19 #                                                            (0.002 / 0.999)
     17:     7                                                              (0.001 / 0.999)
     18:     4                                                              (0.000 / 1.000)
     19:     2                                                              (0.000 / 1.000)




  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 : tosses
  Probabilities:
  4: 0.1896000000000000
  5: 0.1867000000000000
  6: 0.1541000000000000
  3: 0.1230000000000000
  7: 0.1208000000000000
  8: 0.0845000000000000
  9: 0.0539000000000000
  10: 0.0318000000000000
  11: 0.0238000000000000
  12: 0.0129000000000000
  13: 0.0067000000000000
  14: 0.0055000000000000
  15: 0.0023000000000000
  16: 0.0018000000000000
  17: 0.0016000000000000
  19: 0.0003000000000000
  18: 0.0003000000000000
  20: 0.0002000000000000
  23: 0.0001000000000000
  21: 0.0001000000000000
  mean = 6.0009

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs,mean]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 3,
  Tosses = 0,
  while (N > 0)
    Tosses := Tosses + 1,
    if flip(1/2) == true then
      N := N -1
    end
  end,
  add("tosses",Tosses).