/* 

  Number of double heads in Picat.

  https://brainstellar.com/puzzles/probability/118
  """
  A coin is tossed 10 times and the output written as a string. 
  What is the expected number of HH? Note that in HHH, number of HH = 2. 
  (eg: expected number of HH in 2 tosses is 0.25, 3 tosses is 0.5)

  Solution: E[n] = (n-1)/4 ... E[10]=2.5.
  """

  Cf my Gamble model gamble_number_of_double_heads.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.

/*

  n = 10
  var : double heads
  Probabilities:
  2: 0.2333000000000000
  1: 0.2279500000000000
  3: 0.1854000000000000
  0: 0.1402500000000000
  4: 0.1136000000000000
  5: 0.0626500000000000
  6: 0.0233500000000000
  7: 0.0101000000000000
  8: 0.0023500000000000
  9: 0.0010500000000000
  mean = 2.25745


  n = 20
  var : double heads
  Probabilities:
  4: 0.1629500000000000
  5: 0.1574000000000000
  3: 0.1466000000000000
  6: 0.1284000000000000
  2: 0.1068000000000000
  7: 0.0923500000000000
  8: 0.0589500000000000
  1: 0.0584500000000000
  9: 0.0369000000000000
  10: 0.0204000000000000
  0: 0.0153000000000000
  11: 0.0096500000000000
  12: 0.0039000000000000
  13: 0.0015500000000000
  14: 0.0003000000000000
  17: 0.0000500000000000
  16: 0.0000500000000000
  mean = 4.75415

*/
go ?=>
  member(N,[10,20]),
  println(n=N),
  reset_store,
  run_model(20_000,$model(N),[show_probs,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  

model(N) =>
  Tosses = bern_n(1/2,N),

  DoubleHeads = [cond(Chunk == [1,1],1,0) : Chunk in sublists(Tosses,2)].sum,
  
  add("double heads",DoubleHeads).