/* 

  Colored runs of cards in Picat.

  https://brainstellar.com/puzzles/probability/201
  """
  There are 26 black(B) and 26 red(R) cards in a standard deck. A run 
  is number of blocks of consecutive cards of the same color. For example, 
  a sequence RRRRBBBRBRB of only 11 cards has 6 runs; namely, 
  RRRR, BBB, R, B, R, B. Find the expected number of runs in a 
  shuffled deck of cards.

  Answer: 27
  """

  Cf my Gamble model gamble_colored_runs_of_cards.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 : num_runs
  Probabilities:
  27: 0.1103000000000000
  26: 0.1061000000000000
  28: 0.1036000000000000
  25: 0.0989000000000000
  29: 0.0913000000000000
  30: 0.0845000000000000
  24: 0.0788000000000000
  23: 0.0622000000000000
  31: 0.0543000000000000
  32: 0.0445000000000000
  22: 0.0435000000000000
  21: 0.0270000000000000
  33: 0.0247000000000000
  20: 0.0205000000000000
  34: 0.0163000000000000
  19: 0.0086000000000000
  35: 0.0079000000000000
  18: 0.0059000000000000
  36: 0.0035000000000000
  37: 0.0024000000000000
  17: 0.0021000000000000
  16: 0.0013000000000000
  38: 0.0008000000000000
  15: 0.0004000000000000
  39: 0.0003000000000000
  14: 0.0002000000000000
  13: 0.0001000000000000
  mean = 26.8947
  Percentiles:
  (0.001 16)
  (0.01 18.990000000000009)
  (0.025 20)
  (0.05 21)
  (0.1 22)
  (0.25 24)
  (0.5 27)
  (0.75 29)
  (0.84 30)
  (0.9 32)
  (0.95 33)
  (0.975 34)
  (0.99 35)
  (0.999 38)
  (0.9999 39)
  (0.99999 39)



*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs,mean,show_percentiles]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.


  
model() =>
  N = 26,
  Cards = shuffle(ones(N,r) ++ ones(N,b)),
  NumRuns = num_runs(Cards),
  add("num_runs",NumRuns).