/* 

  Number of dice throws until a target is reached  in Picat.

  What is the number of dice throws needed to reach a cumulative
  sum:
   *  larger or equal to a target number.
   *  exactly on target

  We test with some different sum.

  This is a port of my Gamble model gamble_number_of_dice_trows_to_target.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.

main => go.

/* 

target = 6
mode = exactly_on_target
var : n
Probabilities:
1: 0.4661016949152542
2: 0.3720612356478950
3: 0.1407873154729360
4: 0.0196828868234008
5: 0.0013668671405139
mean = 1.71815


mode = on_or_above_target
var : n
Probabilities:
2: 0.5609000000000000
3: 0.2272000000000000
1: 0.1698000000000000
4: 0.0392000000000000
5: 0.0027000000000000
6: 0.0002000000000000
mean = 2.1447

var : s
Probabilities:
6: 0.3620000000000000
7: 0.1955000000000000
8: 0.1668000000000000
9: 0.1291000000000000
10: 0.0940000000000000
11: 0.0526000000000000
mean = 7.5554


target = 10
mode = exactly_on_target
var : n
Probabilities:
3: 0.4318341531974701
2: 0.2856640899508082
4: 0.2189037245256500
5: 0.0544624033731553
6: 0.0077301475755446
7: 0.0014054813773717
mean = 3.07098


mode = on_or_above_target
var : n
Probabilities:
3: 0.4566000000000000
4: 0.2817000000000000
2: 0.1659000000000000
5: 0.0806000000000000
6: 0.0129000000000000
7: 0.0021000000000000
8: 0.0002000000000000
mean = 3.3251

var : s
Probabilities:
10: 0.2900000000000000
11: 0.2453000000000000
12: 0.1936000000000000
13: 0.1304000000000000
14: 0.0918000000000000
15: 0.0489000000000000
mean = 11.6354


target = 21
mode = exactly_on_target
var : n
Probabilities:
6: 0.3203716448726772
5: 0.2450103234686855
7: 0.2298692360633173
8: 0.1135581555402615
4: 0.0540261527873365
9: 0.0268410185822436
10: 0.0092911218169305
11: 0.0006882312456986
12: 0.0003441156228493
mean = 6.22712


mode = on_or_above_target
var : n
Probabilities:
6: 0.3199000000000000
7: 0.2586000000000000
5: 0.2029000000000000
8: 0.1315000000000000
9: 0.0470000000000000
4: 0.0269000000000000
10: 0.0109000000000000
11: 0.0018000000000000
12: 0.0005000000000000
mean = 6.4615

var : s
Probabilities:
21: 0.2847000000000000
22: 0.2405000000000000
23: 0.1883000000000000
24: 0.1424000000000000
25: 0.0966000000000000
26: 0.0475000000000000
mean = 22.6682


target = 61
mode = exactly_on_target
var : n
Probabilities (truncated):
18: 0.1921367521367521
17: 0.1890598290598291
19: 0.1490598290598291
16: 0.1473504273504274
.........
24: 0.0034188034188034
25: 0.0020512820512821
12: 0.0010256410256410
27: 0.0006837606837607
mean = 17.7108


mode = on_or_above_target
var : n
Probabilities (truncated):
17: 0.1913000000000000
18: 0.1909000000000000
16: 0.1476000000000000
19: 0.1463000000000000
.........
25: 0.0016000000000000
12: 0.0006000000000000
26: 0.0003000000000000
27: 0.0001000000000000
mean = 17.876

var : s
Probabilities:
61: 0.2878000000000000
62: 0.2359000000000000
63: 0.1879000000000000
64: 0.1481000000000000
65: 0.0919000000000000
66: 0.0484000000000000
mean = 62.6656


target = 100
mode = exactly_on_target
var : n
Probabilities (truncated):
28: 0.1580985915492958
29: 0.1535211267605634
27: 0.1235915492957746
30: 0.1225352112676056
.........
37: 0.0028169014084507
22: 0.0021126760563380
21: 0.0007042253521127
38: 0.0003521126760563
mean = 28.8264


mode = on_or_above_target
var : n
Probabilities (truncated):
29: 0.1485000000000000
28: 0.1439000000000000
30: 0.1357000000000000
27: 0.1201000000000000
.........
38: 0.0012000000000000
21: 0.0005000000000000
40: 0.0002000000000000
39: 0.0002000000000000
mean = 29.0575

var : s
Probabilities:
100: 0.2865000000000000
101: 0.2370000000000000
102: 0.1927000000000000
103: 0.1416000000000000
104: 0.0949000000000000
105: 0.0473000000000000
mean = 101.663

*/
go ?=>
  member(Target,[6,10,21,61,100]),
  println(target=Target),
  member(Mode,[exactly_on_target,on_or_above_target]),
  println(mode=Mode),
  reset_store(),
  run_model(10_000,$model(Target,Mode),[show_probs_trunc,mean]),
  nl,
  fail,
  nl.
go => true.

model(Target,Mode) =>
  Range = 1..6,
  S = 0,
  N = 0,
  Run = true,
  while(Run == true)
    if S >= Target then
      Run := false
    else
      S := S + uniform_draw(Range),
      N := N + 1
    end
  end,
  
  if Mode = exactly_on_target then
    observe(S == Target)
  else
    observe(S >= Target)
  end,
  
  if observed_ok then
    add("n",N),
    if Mode == on_or_above_target then
      add("s",S)
    end
  end.