/* 

  Lotto not two consecutive numbers in Picat.

  From some unknown source, but I quoted it here: http://www.hakank.org/sims/simulering.html
  """
  One day I was asked 
  
  What is the probability that no two numbers are consecutive in
  a lottery draw?
  
  Information:

  National Lottery in UK is to draw 6 different numbers from 1 to 49.
  so, for example,

    (a)   1  4  7   12  19  44    - no consecutive numbers
    (b)   3  6  17  18  44  46    - 17 and 18 are consecutive 
    (c)   1  2  3   17  29  49    - 1, 2 and 3 are consecutive

  We are asking the probability that class (a) occurs. Hope this is clear.

  Observation shows that it is NOT a small number (actually near half-and-half).
  ......

  A Monte Carlo simulation experiment produced 50,558 sets of six numbers 
  between 1 and 49 with none consecutive out of 100,000 trials giving an 
  estimated probability of .50558.
  """



  Cf my Gamble model gamble_lotto_not_two_consecutive_numbers.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 : prob
  Probabilities:
  true: 0.5066666666666667
  false: 0.4933333333333333
  mean = [true = 0.506667,false = 0.493333]

  var : s
  Probabilities:
  0: 0.5066666666666667
  1: 0.3849666666666667
  2: 0.0988666666666667
  3: 0.0092666666666667
  4: 0.0002333333333333
  mean = 0.611433

*/
go ?=>
  reset_store,
  run_model(30_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
 
model() =>
  N = 49, % Numbers 1..49
  M = 6,  % 6 numbers are drawn

  A = 1..N,

  % The selected Lotto numbers
  Lotto = draw_without_replacement(M,A).sort,
  
  % Check if there's any consecutive numbers
  S = sum([1 : I in 1..M-1, Lotto[I+1]-Lotto[I] == 1]),

  Prob = check(S == 0),
  add("s",S),
  add("prob",Prob).