/* 

  Poker in Picat.

  https://en.wikipedia.org/wiki/Poker_probability
  """
  Hand                Probability(%) Probability  1/Probability
  --------------------------------------------------------------------------
  Royal straight flush  0.000154%    0.00000154   ~649350.64935064935064935065
  Straight flush        0.00139%     0.0000139    ~71942.44604316546762589928    (excluding royal flush)
  Four of a kind        0.02401%     0.0002401    ~4164.93127863390254060808 
  Full House            0.1441%      0.001441     ~693.96252602359472588480
  Flush                 0.1965%      0.001965     ~508.90585241730279898219      (excluding royal flush and straight flush)
  Straight              0.3925%      0.003925     ~254.77707006369426751592      (excluding royal flush and straight flush)
  Three of a kind       2.1128%      0.021128     ~47.33055660734570238546
  Two pair              4.7539%      0.047539     ~21.03536044090115484129
  Pair                 42.2569%      0.422569     ~2.36647742735505917377
  No pair              50.1177%      0.501177     ~1.9953030566047524128
  """

  Cf my Gamble model gamble_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.

/*

var : count values
Probabilities:
[1,1,1,1,1]: 0.5039666666666667
[1,1,1,2]: 0.4266666666666667
[1,2,2]: 0.0476666666666667
[1,1,3]: 0.0204000000000000
[2,3]: 0.0011000000000000
[1,4]: 0.0002000000000000
mean = [[1,1,1,1,1] = 0.503967,[1,1,1,2] = 0.426667,[1,2,2] = 0.0476667,[1,1,3] = 0.0204,[2,3] = 0.0011,[1,4] = 0.0002]

var : no hand
Probabilities:
false: 0.5019666666666667
true: 0.4980333333333333
mean = 0.498033

var : pair
Probabilities:
false: 0.5733333333333334
true: 0.4266666666666667
mean = 0.426667

var : two pairs
Probabilities:
false: 0.9523333333333334
true: 0.0476666666666667
mean = 0.0476667

var : three of a kind
Probabilities:
false: 0.9796000000000000
true: 0.0204000000000000
mean = 0.0204

var : straight
Probabilities:
false: 0.9964666666666666
true: 0.0035333333333333
mean = 0.00353333

var : flush
Probabilities:
false: 0.9976000000000000
true: 0.0024000000000000
mean = 0.0024

var : full house
Probabilities:
false: 0.9989000000000000
true: 0.0011000000000000
mean = 0.0011

var : four of a kind
Probabilities:
false: 0.9998000000000000
true: 0.0002000000000000
mean = 0.0002

var : straight flush
Probabilities:
false: 1.0000000000000000
mean = 0.0

var : royal straight flush
Probabilities:
false: 1.0000000000000000
mean = 0.0


no hand              : 0.4980333 -> 2.0078977
pair                 : 0.4266667 -> 2.3437500
two pairs            : 0.0476667 -> 20.9790210
three of a kind      : 0.0204000 -> 49.0196078
straight             : 0.0035333 -> 283.0188679
flush                : 0.0024000 -> 416.6666667
full house           : 0.0011000 -> 909.0909091
four of a kind       : 0.0002000 -> 5000.0000000
straight flush       : 0.0000000 -> 0.0000000
royal straight flush : 0.0000000 -> 0.0000000


*/
go ?=>
  reset_store,
  run_model(30_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  Hands = ["no hand","pair","two pairs","three of a kind","straight","flush",
           "full house","four of a kind","straight flush","royal straight flush"],
  Store = get_store(),
  foreach(Hand in Hands)
    P = Store.get(Hand,[0]).mean,
    printf("%-21w: %0.7f -> %0.7f\n",Hand,P,cond(P > 0,1/P,0))
  end,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.


value(I) = I mod 13.
suite(I) = I mod 4.

model() =>
  N = 52,
  M = 5,

  Cards = draw_without_replacement(M,1..N),
  Values = Cards.map(value),
  Suites = Cards.map(suite),  

  NumUniqueValues = Values.remove_dups.len,
  NumUniqueSuites = Suites.remove_dups.len,  

  MinVal = Values.min,
  MaxVal = Values.max,  

  CountValues = collect(Values).values.sort,

  Pair = check( CountValues = [1,1,1,2]) ,
  ThreeOfAKind = check( CountValues = [1,1,3]),
  TwoPairs = check( CountValues = [1,2,2]),

  Straight = check((NumUniqueValues == 5,
                    MaxVal-MinVal == 4,
                    NumUniqueSuites > 1)),

  Flush = check((NumUniqueSuites == 1, not Straight)),

  FullHouse = check(CountValues = [2,3]),
  FourOfAKind = check(CountValues = [1,4]), 

  StraightFlush = check( (NumUniqueSuites == 1,
                          MaxVal-MinVal == 4,
                          MaxVal < 12)),
  RoyalStraightFlush = check( (NumUniqueSuites == 1,
                               MaxVal-MinVal == 4,
                               MaxVal == 12)),

  NoHand = check( (CountValues == [1,1,1,1,1],
                   not Flush,
                   not Straight)),

  add_all([["count values",CountValues],
           ["no hand",NoHand],
           ["pair",Pair],
           ["two pairs",TwoPairs],
           ["three of a kind",ThreeOfAKind],
           ["straight",Straight],
           ["flush",Flush],
           ["full house",FullHouse],
           ["four of a kind",FourOfAKind],
           ["straight flush",StraightFlush],
           ["royal straight flush",RoyalStraightFlush]
          ]).