/* 

  Chuck-a-luck (Mosteller) in Picat.

  From Mosteller "Fifty Challenging problems in Probability"
  """
  Chuck-a-Luck is a gambling game often played at carnivals and gambling
  houses. A player may bet on anyone of the numbers I, 2, 3, 4, 5, 6. Three
  dice are rolled. If the player's number appears on one, two, or three of the
  dice, he receives respectively one, two, or three times his original stake plus
  his own money back; otherwise he loses his stake. What is the player's
  expected loss per unit stake? (Actually the player may distribute stakes on
  several numbers, but each such stake can be regarded as a separate bet.)

  ...

  Thus you lose about 8% [17/216 ~ ~0.079] per play.
  """

  Cf my Gamble model gamble_chuck_a_luck.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.
% import ordset.

main => go.

/*

  var : num hits
  Probabilities:
  0: 0.5829000000000000
  1: 0.3393000000000000
  2: 0.0735000000000000
  3: 0.0043000000000000
  mean = 0.4992

  var : outcome
  Probabilities:
  -1: 0.5829000000000000
  1: 0.3393000000000000
  2: 0.0735000000000000
  3: 0.0043000000000000
  mean = -0.0837


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 3, % Num dice to roll

  UserNum = dice(),

  Roll = dice_n(N),

  NumHits = [cond(V == UserNum,1,0) : V in Roll].sum,
  
  % Outcome. We assume that the user bets 1 unit
  Outcome = cond(NumHits > 0,NumHits,-1),
  
  add("num hits",NumHits),
  add("outcome",Outcome).