/* 

  Unbiased coin in Picat.

  https://brainstellar.com/puzzles/probability/19
  """
  We have a weighted coin that shows a Head with probability p and tails with 1-p
  (0.5 < p < 1). How to define two equally likely events using this coin?

  Each event is a function of the outcomes of one or more coin tosses. For example, 
  we can toss 2 times and define Event1 as [HH, TT] and Event2 as [TH, HT].

  Hint: Since p is unknown, the probability of HH and TT are unreliable.
  Answer: Toss 2 times, event1 is HT, event2 is TH, and repeat the process otherwise.
  """

  Cf 
  - ppl_fair_coin_from_a_biased_coin.pi
  - my Gamble model gamble_unbiased_coin.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 : a
  Probabilities:
  t: 0.5185000000000000
  h: 0.4815000000000000
  mean = [t = 0.5185,h = 0.4815]

  var : p
  Probabilities (truncated):
  0.999960983686323: 0.0001000000000000
  0.999929550392266: 0.0001000000000000
  0.999893648393781: 0.0001000000000000
  0.999886199716169: 0.0001000000000000
  .........
  0.500246085503899: 0.0001000000000000
  0.500095186221973: 0.0001000000000000
  0.500079638665432: 0.0001000000000000
  0.500053389352538: 0.0001000000000000
  mean = 0.749964

  var : two coins
  Probabilities:
  hh: 0.5835000000000000
  th: 0.1670000000000000
  ht: 0.1649000000000000
  tt: 0.0846000000000000
  mean = [hh = 0.5835,th = 0.167,ht = 0.1649,tt = 0.0846]


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

coin(P) = condt(flip(P),h,t).
f(P) = Res =>
  C1 = coin(P),
  C2 = coin(P),
  if C1 != C2 then
    Res = C1
  else
    Res = f(P)
  end.
  
model() =>
  % P should be > 0.5
  P0 = beta_dist(1,1),
  % P0 = 0.8,
  P = cond(P0 < 0.5,1-P0,P0),

  TwoCoins = [coin(P) : _ in 1..2],

  % The strategy in the Answer above
  A = f(P),
  
  add("p",P),
  add("two coins",TwoCoins),
  add("a",A).