/* 

  Dartboard in Picat.

  From Statistics101 (Resample Stats)
  http://www.statistics101.net/QuickReference.pdf
  Page 19
  """
  A dartboard is divided into twenty equal wedges, ignoring the bull's eye. 
  Only six of the twenty wedges are worth points, so the probability of scoring on 
  one throw is 6/20, or 0.3, assuming your throws always hit the board. 
  What is the chance of hitting at least one scoring region in three consecutive throws? 
  (From CliffsQuickReview Statistics, p.48).
  """

  Exact probabilities:

  s: 
  Picat> pdf_all($binomial_dist(3,6/20)).sort_down(2).printf_list
  1 0.441 
  0 0.343 
  2 0.189 
  3 0.027 

  p:
  Picat> X=1-binomial_dist_cdf(3,6/20,0)
  X = 0.657


  Cf my Gamble model gamble_dartboard.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.
% import ordset.

main => go.

/*
  Using resampling

  var : s
  Probabilities:
  1: 0.4380000000000000
  0: 0.3417000000000000
  2: 0.1932000000000000
  3: 0.0271000000000000
  mean = 0.9057

  var : p
  Probabilities:
  true: 0.6583000000000000
  false: 0.3417000000000000
  mean = [true = 0.6583,false = 0.3417]

*/
go ?=>
  ScoreProb = ones(3,score) ++ ones(7,no_score),
  reset_store,
  run_model(10_000,$model(ScoreProb),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model(ScoreProb) =>

  NumThrows = 3,
  ThreeThrows = resample(NumThrows,ScoreProb),
  S = count_occurrences(score,ThreeThrows),

  P = check(S >= 1),
  
  add("s",S),
  add("p",P).


/*
  Using binomial

  var : s
  Probabilities:
  1: 0.4377000000000000
  0: 0.3515000000000000
  2: 0.1853000000000000
  3: 0.0255000000000000
  mean = 0.8848

  var : p
  Probabilities:
  true: 0.6485000000000000
  false: 0.3515000000000000
  mean = [true = 0.6485,false = 0.3515]


*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  
  S = binomial_dist(3,6/20),
  P = check(S >= 1),
  
  add("s",S),
  add("p",P).