/* 

  Discarding n cards in Poker in Picat.

  From https://discourse.julialang.org/t/optimizing-a-puzzle-from-the-balatro-game-discarding-part-of-a-poker-hand-to-get-a-pair/121912
  """
  Optimizing a puzzle from the Balatro game: discarding part of a poker hand to get a pair

  Interesting problem from Balatro, from a hand of 8 without any pairs, if you discard 
  n and draw n from the remaining deck of 44 cards. What’s the optimum n to maximize 
  your chance of obtaining at least a pair?

  I am sure many of you are obsessed by Balatro. So I wrote some code to simulate this. 
  For 1m simulations it ran in about 0.077s per n.

  Anyone wanna challenge my algorithm?
  """

  The exact values are (see foobar_lv2's comment), see below:
  (1 21/44 0.4772727272727273)
  (2 657/946 0.6945031712473573)
  (3 10597/13244 0.8001359106010268)
  (4 115910/135751 0.8538426972913643)
  (5 136663/155144 0.8808784097354716)
  (6 6297931/7059052 0.8921780148382531)
  (7 34182305/38320568 0.8920093512183849)
  (8 156095218/177232627 0.880736355614703)

  So, the optimal value of the number of card to discard and get is 6, with 7 as very close.

  Cf my Gamble model gamble_discarding_n_cards_in_poker.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.

/*

  [discard = 1,p = 0.485345]
  [discard = 2,p = 0.713209]
  [discard = 3,p = 0.809673]
  [discard = 4,p = 0.858907]
  [discard = 5,p = 0.88615]
  [discard = 6,p = 0.89874]
  [discard = 7,p = 0.88949]
  [discard = 8,p = 0.857845]

  Ordered by probability:
  6 0.898739873987399 
  7 0.889490302210194 
  5 0.886149708650829 
  4 0.858906525573192 
  8 0.857845328565042 
  3 0.809673085535154 
  2 0.713209219858156 
  1 0.485344827586207 



*/
go ?=>
  Map = get_global_map(),
  member(Discard,1..8),
  reset_store,
  run_model(20_000,$model(Discard),[presentation=[]]),
  P = get_store().get("p").mean,
  println([discard=Discard,p=P]),
  Map.put(Discard,P),
  fail,
  nl.
go =>
  nl,
  Map = get_global_map(),
  println("Ordered by probability:"),
  Map.to_list.sort_down(2).printf_list,
  nl.
  
  
  
model(Discard) =>
  Deck = rep(4,1..13).flatten,

  NumCards = 8, % cards per hand

  % 0: Shuffle the deck
  ThisDeck = shuffle(Deck),

  % 1: Get the hand
  Hand = take(ThisDeck,NumCards),

  % Ensure there's no pairs in the hand, i.e. all values are unique
  observe(Hand.remove_dups.len == NumCards),

  % 2: Discard n card at random to get the second hand
  Hand2 = drop(Hand,Discard) ++ take(drop(ThisDeck,NumCards),Discard),

  % Check if there's at least one pair in the new hand
  TT = collect(Hand2).values,
  NumDuplicates = [ 1 : V in TT, V > 1].sum,

  P = check(NumDuplicates > 0),
  
  if observed_ok then
    add("p",P),
  end.