/* 

  To begin or not to begin in Picat.

   https://brainstellar.com/puzzles/probability/1002
  """
  A & B are alternately picking balls from a bag without replacement. 
  The bag has k black balls and 1 red ball. Winner is the one who picks the 
  red ball. Who is more likely to win, the on who starts first, or second?

  Answer: Begin!
  Solution: ... Hence, doesnt matter who starts first when k is odd. 
            The first player has higher chance of winning when k is even
  """

  For odd k: 1/2
  For even k: starter wins with p = (k div 2)+1 / (k+1)


  Cf my Gamble model gamble_to_begin_or_not_to_begin.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.

/*

  k = 1
  var : winner
  Probabilities:
  1: 0.5030000000000000
  0: 0.4970000000000000
  mean = 0.503


  k = 2
  var : winner
  Probabilities:
  0: 0.6643000000000000
  1: 0.3357000000000000
  mean = 0.3357


  k = 3
  var : winner
  Probabilities:
  0: 0.5031000000000000
  1: 0.4969000000000000
  mean = 0.4969


  k = 4
  var : winner
  Probabilities:
  0: 0.5944000000000000
  1: 0.4056000000000000
  mean = 0.4056


  k = 5
  var : winner
  Probabilities:
  1: 0.5000000000000000
  0: 0.5000000000000000
  mean = 0.5


  k = 6
  var : winner
  Probabilities:
  0: 0.5769000000000000
  1: 0.4231000000000000
  mean = 0.4231


  k = 7
  var : winner
  Probabilities:
  1: 0.5007000000000000
  0: 0.4993000000000000
  mean = 0.5007


  k = 8
  var : winner
  Probabilities:
  0: 0.5578000000000000
  1: 0.4422000000000000
  mean = 0.4422


  k = 9
  var : winner
  Probabilities:
  0: 0.5004999999999999
  1: 0.4995000000000000
  mean = 0.4995


  k = 10
  var : winner
  Probabilities:
  0: 0.5495000000000000
  1: 0.4505000000000000
  mean = 0.4505

*/
go ?=>
  member(K,1..10),
  println(k=K),
  reset_store,
  run_model(10_000,$model(K),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
f(A,I) = Res =>
  if A.first == red then
    Res = I
  else
    Res = f(A.tail,I+1)
  end.
  
model(K) =>

  Balls = ones(K,black) ++ [red],
  S = draw_without_replacement(Balls),
  
  A = f(S,0),
  Winner = A mod 2,
  
  % add("a",A),
  add("winner",Winner).