/* 

  Two dice wager in Picat.

  From https://puzzlewocky.com/brain-teasers/the-two-dice-wager/
  """
  A gambler presents you with an even-money wager. You will roll two dice, and if the highest 
  number showing is one, two, three or four, then you win. If the highest number on either die 
  is five or six, then she wins. Should you take the bet?
  """

  No, this is not a fair game. The 1..4 player will win 4/9 (~ 0.444) of the games and 
  lose 5/9 (~ 0.555)  of the game.

  However, it game be made more fair if we add weights to the wins: 5/9 and 4/9 respectively.
  Now, the expected outcome of the two players are the same.

  Cf my Gamble model gamble_two_dice_wager.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.

/*

  Game 1: The original game.

  No, this is not a fair game. The 1..4 player will win 4/9 (~ 0.444) of the games and 
  lose 5/9 (~ 0.555)  of the game.

  var : m
  Probabilities:
  6: 0.3015000000000000
  5: 0.2531000000000000
  4: 0.1990000000000000
  3: 0.1359000000000000
  2: 0.0841000000000000
  1: 0.0264000000000000
  mean = 4.4728

  var : p 1..4
  Probabilities:
  false: 0.5546000000000000
  true: 0.4454000000000000
  mean = [false = 0.5546,true = 0.4454]

  var : p 5..6
  Probabilities:
  true: 0.5546000000000000
  false: 0.4454000000000000
  mean = [true = 0.5546,false = 0.4454]


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  D1 = random_integer1(6),
  D2 = random_integer1(6),  
  M = max(D1,D2),

  P1_4 = check(M <= 4),
  P5_6 = check(M >= 5),
 
  add("m",M),
  add("p 1..4",P1_4),
  add("p 5..6",P5_6).

/*
  Modified game.
  Multipling the revenues by 5/9 and 4/9 respectively yields a fair game:
  P1_4 and P5_6 are now (about) the same (0.246944 and 0.246889 in this run).

  var : m
  Probabilities:
  6: 0.3046000000000000
  5: 0.2509000000000000
  4: 0.1943000000000000
  3: 0.1328000000000000
  2: 0.0877000000000000
  1: 0.0297000000000000
  mean = 4.4628

  var : p 1..4
  Probabilities:
  0.0: 0.5555000000000000
  0.555556: 0.4445000000000000
  mean = 0.246944

  var : p 5..6
  Probabilities:
  0.444444: 0.5555000000000000
  0.0: 0.4445000000000000
  mean = 0.246889

*/
go2 ?=>
  Mult1 = 5/9,
  Mult2 = 4/9,
  reset_store,
  run_model(10_000,$model2(Mult1,Mult2),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2(Mult1,Mult2) =>
  D1 = random_integer1(6),
  D2 = random_integer1(6),  
  M = max(D1,D2),

  P1_4 = Mult1 * cond(M <= 4, 1, 0),
  P5_6 = Mult2 * cond(M >= 5, 1, 0),
 
  add("m",M),
  add("p 1..4",P1_4),
  add("p 5..6",P5_6).