/* 

  Game show problem in Picat.

  From https://www.youtube.com/watch?v=WWAoh3XfWzA
  "A fun game show probability problem | Bonus cash stop riddle"
  """
  A fun probability problem for you! You've just won a game show and it's time to 
  play the bonus round for some extra cash! You play a random game where you open 
  up boxes and get the prize money inside until you open up a stop sign. How much 
  do you expect to make from playing this game?
  """

  There are 5 boxes with the following:
  - 1 * $10 
  - 2 * $1000
  - 1 * $10000
  - stop sign  

  You can draw until the stop sign and then you earn all the money 
  you picked. There is no penalty to draw until stop sign.

  Answer: Estimated value is $6005
  Calculated by:
     10*0.5 + 1000*0.5 + 1000*0.5 + 10000*0.5 = 6005
  where 0.5 is the probability that the value is to the left 
  of the stop sign, i.e. is selected.

  Cf my Gamble model gamble_game_show_problem.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_show_problem_theoretical(Boxes) = Boxes.sum / 2.

/*

  boxes = [10,1000,1000,10000,0]
  theoretical = 6005.0
  var : total
  Probabilities:
  0: 0.1981500000000000
  12010: 0.1967000000000000
  1000: 0.0999000000000000
  11010: 0.0996000000000000
  11000: 0.0710500000000000
  1010: 0.0673000000000000
  2010: 0.0516000000000000
  10000: 0.0513000000000000
  12000: 0.0509000000000000
  10: 0.0491000000000000
  2000: 0.0328500000000000
  10010: 0.0315500000000000
  mean = 6017.91


  boxes = [10,1000,1000,10000,12345,0]
  theoretical = 12177.5
  var : total
  Probabilities:
  0: 0.1702000000000000
  24355: 0.1622000000000000
  23355: 0.0655500000000000
  1000: 0.0639500000000000
  12345: 0.0349000000000000
  11000: 0.0346000000000000
  10000: 0.0339500000000000
  10: 0.0339500000000000
  13355: 0.0335000000000000
  11010: 0.0335000000000000
  13345: 0.0329000000000000
  23345: 0.0325500000000000
  12010: 0.0324000000000000
  1010: 0.0322000000000000
  24345: 0.0321500000000000
  14355: 0.0321000000000000
  2000: 0.0186000000000000
  14345: 0.0180000000000000
  12355: 0.0180000000000000
  22355: 0.0176500000000000
  2010: 0.0170500000000000
  10010: 0.0167500000000000
  12000: 0.0167000000000000
  22345: 0.0166500000000000
  mean = 12063.6

*/
go ?=>
  member(Boxes,[[10,1000,1000,10000,0],[10,1000,1000,10000,12345,0]]),
  println(boxes=Boxes),
  println(theoretical=game_show_problem_theoretical(Boxes)),
  reset_store,
  run_model(20_000,$model(Boxes),[show_probs,mean]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.
  

% Pick a box and continue until the stop box (value = 0) is picked
% Note: Since we have duplicate values we use boxes indices
% instead of the values which makes it slightly more elaborate
pick_a_box(Boxes,BoxesIxLeft,ValSoFar) = Ret =>
  Len = BoxesIxLeft.len,
  if Len <= 1 then
    Ret = ValSoFar
  else
    BoxIx = random_integer1(Len), % Pick an index
    
    % Lookup the value of this selected index    
    Val = Boxes[BoxesIxLeft[BoxIx]],
    
    % Stop if stop box is selected or just the stop box is left
    % (If the length is 1 then it must be the stop box)
    if Val == 0 then
      Ret = ValSoFar
    else
      NewBoxesIx = delete(BoxesIxLeft,BoxesIxLeft[BoxIx]),
      Ret = pick_a_box(Boxes,NewBoxesIx,ValSoFar+Val)
    end
  end.

model(Boxes) =>
  Total = pick_a_box(Boxes,1..Boxes.len,0),
 
  add("total",Total).