/* 

  Ruin problem in Picat.

  Cf my Gamble model gamble_ruin_problem2.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.

/*
  How likely is a ruin? With some different limits.

  limit = 5
  var : len
  Probabilities:
  2: 0.4982000000000000
  6: 0.3775000000000000
  4: 0.1243000000000000
  mean = 3.7586

  var : p(ruin)
  Probabilities:
  true: 0.6814000000000000
  false: 0.3186000000000000
  mean = [true = 0.6814,false = 0.3186]


  limit = 10
  var : len
  Probabilities:
  2: 0.5056000000000000
  11: 0.2434000000000000
  4: 0.1252000000000000
  6: 0.0580000000000000
  8: 0.0392000000000000
  10: 0.0286000000000000
  mean = 5.137

  var : p(ruin)
  Probabilities:
  true: 0.7566000000000001
  false: 0.2434000000000000
  mean = [true = 0.7566,false = 0.2434]


  limit = 50
  var : len
  Probabilities (truncated):
  2: 0.4998000000000000
  4: 0.1272000000000000
  51: 0.1084000000000000
  6: 0.0667000000000000
  .........
  46: 0.0024000000000000
  32: 0.0024000000000000
  48: 0.0023000000000000
  50: 0.0020000000000000
  mean = 11.1642

  var : p(ruin)
  Probabilities:
  true: 0.8915999999999999
  false: 0.1084000000000000
  mean = [true = 0.8916,false = 0.1084]


  limit = 100
  var : len
  Probabilities (truncated):
  2: 0.4814000000000000
  4: 0.1224000000000000
  101: 0.0815000000000000
  6: 0.0632000000000000
  .........
  98: 0.0009000000000000
  80: 0.0009000000000000
  96: 0.0007000000000000
  94: 0.0006000000000000
  mean = 16.8273

  var : p(ruin)
  Probabilities:
  true: 0.9185000000000000
  false: 0.0815000000000000
  mean = [true = 0.9185,false = 0.0815]


  limit = 1000
  var : len
  Probabilities (truncated):
  2: 0.4811000000000000
  4: 0.1156000000000000
  6: 0.0724000000000000
  8: 0.0437000000000000
  .........
  196: 0.0001000000000000
  192: 0.0001000000000000
  184: 0.0001000000000000
  174: 0.0001000000000000
  mean = 48.3422

  var : p(ruin)
  Probabilities:
  true: 0.9766000000000000
  false: 0.0234000000000000
  mean = [true = 0.9766,false = 0.0234]


*/
go ?=>
  member(Limit,[5,10,50,100,1000]),
  println(limit=Limit),
  reset_store,
  run_model(10_000,$model(Limit),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  fail,
  nl.
go => true.

draw(A,Limit) = Res =>
  Len = A.len,
  if A.last == 0 ; Len > Limit then
    Res = A
  else
    Win = 1,
    Loose = 1,
    LastVal = A.last,
    C = uniform_draw([head,tail]),
    if C == head then
      Res = draw(A++[LastVal+Win],Limit)
    elseif LastVal-Loose <= 0 then
      Res = draw(A++[0],Limit)
    else
      Res = draw(A++[LastVal-Loose],Limit)
    end
  end.
model(Limit) =>
  Start = 1,
  A = draw([Start],Limit),
  Len = A.len, % Note: The sentential 0 is included 
  add("len",Len),
  add("p(ruin)",check(A.last==0)).