/* 

  Guess the toss in Picat.

  From https://brainstellar.com/puzzles/probability/108
  """
  A and B are in a team called AB, playing against C. If AB team 
  wins they win Rs 3, nothing otherwise.

  The Game: A and B are placed in 2 separate rooms far away. A will 
  toss a coin and B will also toss a coin; A will have to guess the 
  outcome of B's toss and B will guess A's. If both guesses are right, 
  team AB wins Rs 3, nothing otherwise. Should they play the game, 
  by paying Rs 1 at the start?

  Answer: 1/2
  Solution: Let's list down all the possibilities.
      A B
      H H
      H T
      T H
      T T
  Observe that 2 out of 4 times, their coins have the same face, i.e. either 
  both heads or both tails.

  They can speak their own coin's face as their guess. They win the game with a probability of 
  1/2.

  The pay-off will be positive (1/2)*3 - 1 = 0.5
  and hence they should play this game.
  """


  Cf my Gamble model gamble_guess_the_toss.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.

/*

  My initial take was the no-strategy which is a loss of 1/4.
  With the strategy mentioned, it's a game of 1/2.

  var : outcome no strategy
  Probabilities:
  0: 0.7441000000000000
  3: 0.2559000000000000
  mean = 0.7677

  var : profit no strategy
  Probabilities:
  -1: 0.7441000000000000
  2: 0.2559000000000000
  mean = -0.2323

  var : outcome strategy
  Probabilities:
  3: 0.5159000000000000
  0: 0.4841000000000000
  mean = 1.5477

  var : profit strategy
  Probabilities:
  2: 0.5159000000000000
  -1: 0.4841000000000000
  mean = 0.5477


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 2,
  [AToss,BToss] = [ cond(flip() == true, h, t) : _ in 1..N],
  [AGuess,BGuess] = [ cond(flip() == true, h, t) : _ in 1..N],


  AGuess2 = AToss,
  BGuess2 = BToss,

  % No Strategy
  OutcomeNoStrategy = cond( (AToss == BGuess, BToss == AGuess), 3, 0),
  ProfitNoStrategy = OutcomeNoStrategy - 1,

  % Strategy: guess the same as your own toss
  OutcomeStrategy = cond( (AToss == BGuess2, BToss == AGuess2), 3, 0),
  ProfitStrategy = OutcomeStrategy - 1,

  add("outcome no strategy",OutcomeNoStrategy),
  add("profit no strategy",ProfitNoStrategy),    
  add("outcome strategy",OutcomeStrategy),
  add("profit strategy",ProfitStrategy).