/* 

  Craps in Picat.

  https://en.wikipedia.org/wiki/Craps
  """
  Craps is a dice game in which players bet on the outcomes of a pair of dice. 
  Players can wager money against each other (playing "street craps") or against 
  a bank ("casino craps").

  ... 
  
  If the come-out roll is 7 or 11, the bet wins.
  If the come-out roll is 2, 3 or 12, the bet loses (known as "crapping out").
  If the roll is any other value, it establishes a point.
  - If, with a point established, that point is rolled again 
    before a 7, the bet wins.
  - If, with a point established, a 7 is rolled before the point is 
    rolled again ("seven out"), the bet loses.
  """

  Cf 
  - ppl_craps.pi
  - my Gamble model gamble_craps2.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.

/*
  As expected, the bank/casino has a small edge over the customer: it wins with a 
  probability of 0.504 (outcome) according to this model.
  With a small probability (0.0012), there are very long runs, e.g. more than 20 
  throws.
 
  var : a
  Probabilities (truncated):
  [7]: 0.1710000000000000
  [3]: 0.0560000000000000
  [11]: 0.0546000000000000
  [2]: 0.0289000000000000
  [12]: 0.0279000000000000
  [8,7]: 0.0250000000000000
  [6,7]: 0.0225000000000000
  [6,6]: 0.0201000000000000
  [9,7]: 0.0193000000000000
  [8,8]: 0.0193000000000000
  .........
  [4,2,6,3,7]: 0.0001000000000000
  [4,2,5,9,7]: 0.0001000000000000
  [4,2,5,8,6,11,4]: 0.0001000000000000
  [4,2,5,7]: 0.0001000000000000
  [4,2,5,2,6,3,9,6,4]: 0.0001000000000000
  [4,2,5,2,5,5,9,7]: 0.0001000000000000
  [4,2,3,12,4]: 0.0001000000000000
  [4,2,2,11,4]: 0.0001000000000000
  [4,2,2,8,11,7]: 0.0001000000000000
  [4,2,2,6,8,7]: 0.0001000000000000
  mean = []

  var : len
  Probabilities (truncated):
  1: 0.3384000000000000
  2: 0.1890000000000000
  3: 0.1316000000000000
  4: 0.0953000000000000
  5: 0.0689000000000000
  6: 0.0516000000000000
  7: 0.0369000000000000
  8: 0.0245000000000000
  9: 0.0185000000000000
  10: 0.0119000000000000
  .........
  19: 0.0010000000000000
  18: 0.0008000000000000
  21: 0.0003000000000000
  27: 0.0002000000000000
  23: 0.0002000000000000
  38: 0.0001000000000000
  28: 0.0001000000000000
  26: 0.0001000000000000
  25: 0.0001000000000000
  20: 0.0001000000000000
  mean = 3.3371

  var : outcome
  Probabilities:
  lose: 0.5042000000000000
  win: 0.4958000000000000
  mean = []

  var : long run
  Probabilities:
  false: 0.9988000000000000
  true: 0.0012000000000000
  mean = 0.0012

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,truncate_size=10]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  

game(A,Point) = Res =>
  [D1,D2] = dice_n(2),
  S = D1 + D2,
  NewA = A ++ [S],
  if Point == 0 then
    Res = cond((S == 7 ; S == 11),[NewA,win],
               cond((S == 2 ; S == 3 ; S == 12),[NewA,lose],
                     game(NewA,S)))
  else
    Res = cond(S == 7,[NewA,lose],
               cond(S == Point,[NewA,win],
                    game(NewA,Point)))
  end.

model() =>
  [A,Outcome] = game([],0),

  Len = A.len,
  PLongRun = check(Len >= 20), % Long runs

  add("a",A),
  add("len",Len),
  add("outcome",Outcome),
  add("long run",PLongRun).