/* 

  Random walk roulette (Mosteller) in Picat.

  From Mosteller "Fifty Challenging Problem in Probability"
  """
  7. Curing the Compulsive Gambler
  Mr. Brown always bets a dollar on the number 13 at roulette against the
  advice of Kind Friend To help cure Mr Brown of playing roulette, Kind Friend
  always bets Brown $20 at even money that Brown will be behind at the end of
  36 plays. How is the cure working?
  (Most American roulette wheels have 38 equally likely numbers. If the
  player's number comes up, he is paid 35 times his stake and gets his original
  stake back; otherwise he loses his stake)
  
  ... 

  And so all told Mr. Brown gains +4.68 - 1.89 = +2.79 dollars per 36
  trials; he is finally making money at roulette. Possibly Kind Friend will be
  cured first. Of course, when Brown loses all 36, he is out $56, which may
  jolt him a bit.
  """ 

  According to this model:   
  Estimated gain of Mr. Brown is $3.875400000000003, and of Kind Friend: $-4.792000000000001



  Cf my Gamble model gamble_random_walk_roulette.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.

/*
  According to this model:   
  Estimated gain of Mr. Brown is $3.8195, and of Kind Friend: $-4.688


  var : final
  Probabilities:
  -36: 0.3828000000000000
  1: 0.3694500000000000
  38: 0.1797500000000000
  75: 0.0540000000000000
  112: 0.0118000000000000
  149: 0.0018500000000000
  186: 0.0003500000000000
  mean = -0.8685

  var : outcome
  Probabilities:
  false: 0.6172000000000000
  true: 0.3828000000000000
  mean = 0.3828

  var : brown
  Probabilities:
  -56: 0.3828000000000000
  21: 0.3694500000000000
  58: 0.1797500000000000
  95: 0.0540000000000000
  132: 0.0118000000000000
  169: 0.0018500000000000
  206: 0.0003500000000000
  mean = 3.8195

  var : kind friend
  Probabilities:
  -20: 0.6172000000000000
  20: 0.3828000000000000
  mean = -4.688



*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean % ,
                           % show_simple_stats % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.84,0.9,0.94,0.99,0.99999],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 36, % 36 plays

  Final = [cond(random_integer1(38)==13,36,-1) :  _ in 1..N].sum,
  Outcome = check(Final < 0),

  Brown = Final + cond(Final > 0,20,-20),
  KindFriend = cond(Final < 0, 20,-20),
  
  add("final",Final),
  add("outcome",Outcome),
  add("brown",Brown),
  add("kind friend",KindFriend).