/* 

  Successive wins in Picat.

  From Mosteller "Fifty Challenging problems in Probability"
  """
  Problem 2: Successive Wins
        
  To encourage Elmer's promising tennis career, his 
  father offers him a prize if he wins (at least) two 
  tennis sets in a row in a three-set series to be played 
  with his father and the club champion alternately:  
  father-champion-father or champion-father-champion, 
  according to Elmer's choice.  The champion is a better 
  player than Elmer's father.  Which series should Elmer 
  choose?
  """

  It depends on Elmer's probability of winning against
  the father and the champion.

  Probability of Elmer winning against the father is 0.2 
  and against the champion 0.4:

  Cf my Gamble model gamble_successive_wins.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 : matches 1: father, champion, father
  Probabilities:
  [0,0,0]: 0.3890000000000000
  [0,1,0]: 0.2585000000000000
  [0,0,1]: 0.0946000000000000
  [1,0,0]: 0.0921000000000000
  [0,1,1]: 0.0636000000000000
  [1,1,0]: 0.0610000000000000
  [1,0,1]: 0.0252000000000000
  [1,1,1]: 0.0160000000000000
  mean = [[0,0,0] = 0.389,[0,1,0] = 0.2585,[0,0,1] = 0.0946,[1,0,0] = 0.0921,[0,1,1] = 0.0636,[1,1,0] = 0.061,[1,0,1] = 0.0252,[1,1,1] = 0.016]

  var : matches 2: champion, father, champion
  Probabilities:
  [0,0,0]: 0.2903000000000000
  [0,0,1]: 0.1976000000000000
  [1,0,0]: 0.1828000000000000
  [1,0,1]: 0.1275000000000000
  [0,1,0]: 0.0724000000000000
  [0,1,1]: 0.0478000000000000
  [1,1,0]: 0.0460000000000000
  [1,1,1]: 0.0356000000000000
  mean = [[0,0,0] = 0.2903,[0,0,1] = 0.1976,[1,0,0] = 0.1828,[1,0,1] = 0.1275,[0,1,0] = 0.0724,[0,1,1] = 0.0478,[1,1,0] = 0.046,[1,1,1] = 0.0356]

  var : success 1
  Probabilities:
  false: 0.8594000000000001
  true: 0.1406000000000000
  mean = [false = 0.8594,true = 0.1406]

  var : success 2
  Probabilities:
  false: 0.8706000000000000
  true: 0.1294000000000000
  mean = [false = 0.8706,true = 0.1294]

  Conclusion:
  Pick matches 1: father,champion,father


*/
go ?=>
  Champion = 4/10,
  Father   = 2/10,
  reset_store,
  run_model(10_000,$model(Champion,Father),[show_probs_trunc,mean % ,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  Store = get_store(),
  Success1 = Store.get("success 1").mean.new_map().get(true),
  Success2 = Store.get("success 2").mean.new_map().get(true),
  % println([success1=Success1,success2=Success2,total=Success1+Success2]),
  println("Conclusion:"),
  if Success1 > Success2 then
    println("Pick matches 1: father,champion,father")
  else
    println("Pick matches 2: champion,father,champion")  
  end,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  

test(M) = cond(append(_,[1,1],_,M),true,false).

model(Champion,Father) =>
  Seq1 = [Father,Champion,Father],
  Seq2 = [Champion,Father,Champion],

  Matches1 = [ bern(M) : M in Seq1],
  Matches2 = [ bern(M) : M in Seq2],  

  Success1 = test(Matches1),
  Success2 = test(Matches2),  

  add("matches 1: father, champion, father",Matches1),
  add("matches 2: champion, father, champion",Matches2),
  add("success 1",Success1),
  add("success 2",Success2).

/*
  Here's a more extensive test of some different probabilities of winning
  against the father and the champion. Note that the champion is 
  better than the father.


  [father = 0,champion = 0.001,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 0.2,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 0.4,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 0.5,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 0.6,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 0.8,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 0.99,success1 = 0,success2 = 0,best_strat = same]
  [father = 0,champion = 1,success1 = 0,success2 = 0,best_strat = same]
  [father = 0.001,champion = 0.2,success1 = 0,success2 = 0.002,best_strat = 2]
  [father = 0.001,champion = 0.4,success1 = 0.001,success2 = 0.001,best_strat = same]
  [father = 0.001,champion = 0.5,success1 = 0.001,success2 = 0,best_strat = 1]
  [father = 0.001,champion = 0.6,success1 = 0.001,success2 = 0.003,best_strat = 2]
  [father = 0.001,champion = 0.8,success1 = 0.001,success2 = 0,best_strat = 1]
  [father = 0.001,champion = 0.99,success1 = 0,success2 = 0.002,best_strat = 2]
  [father = 0.001,champion = 1,success1 = 0,success2 = 0.001,best_strat = 2]
  [father = 0.2,champion = 0.4,success1 = 0.154,success2 = 0.131,best_strat = 1]
  [father = 0.2,champion = 0.5,success1 = 0.164,success2 = 0.149,best_strat = 1]
  [father = 0.2,champion = 0.6,success1 = 0.219,success2 = 0.158,best_strat = 1]
  [father = 0.2,champion = 0.8,success1 = 0.308,success2 = 0.192,best_strat = 1]
  [father = 0.2,champion = 0.99,success1 = 0.384,success2 = 0.193,best_strat = 1]
  [father = 0.2,champion = 1,success1 = 0.37,success2 = 0.185,best_strat = 1]
  [father = 0.4,champion = 0.5,success1 = 0.331,success2 = 0.308,best_strat = 1]
  [father = 0.4,champion = 0.6,success1 = 0.373,success2 = 0.335,best_strat = 1]
  [father = 0.4,champion = 0.8,success1 = 0.519,success2 = 0.401,best_strat = 1]
  [father = 0.4,champion = 0.99,success1 = 0.629,success2 = 0.42,best_strat = 1]
  [father = 0.4,champion = 1,success1 = 0.636,success2 = 0.39,best_strat = 1]
  [father = 0.5,champion = 0.6,success1 = 0.454,success2 = 0.409,best_strat = 1]
  [father = 0.5,champion = 0.8,success1 = 0.626,success2 = 0.481,best_strat = 1]
  [father = 0.5,champion = 0.99,success1 = 0.749,success2 = 0.507,best_strat = 1]
  [father = 0.5,champion = 1,success1 = 0.755,success2 = 0.487,best_strat = 1]
  [father = 0.6,champion = 0.8,success1 = 0.671,success2 = 0.574,best_strat = 1]
  [father = 0.6,champion = 0.99,success1 = 0.849,success2 = 0.555,best_strat = 1]
  [father = 0.6,champion = 1,success1 = 0.796,success2 = 0.602,best_strat = 1]
  [father = 0.8,champion = 0.99,success1 = 0.947,success2 = 0.813,best_strat = 1]
  [father = 0.8,champion = 1,success1 = 0.971,success2 = 0.799,best_strat = 1]
  [father = 0.99,champion = 1,success1 = 1.0,success2 = 0.993,best_strat = 1]

*/
go2 ?=>
  Ps = [0,1/1000,2/10,4/10,5/10,6/10,8/10,99/100,1],
  member(Father,Ps),
  member(Champion,Ps),
  if Champion > Father then
    reset_store,
    run_model(1000,$model(Champion,Father),[presentation=[]]),
    Store = get_store(),
    Success1 = Store.get("success 1").mean.new_map().get(true,0),
    Success2 = Store.get("success 2").mean.new_map().get(true,0),
    % println([success1=Success1,success2=Success2,total=Success1+Success2]),
    if Success1 > Success2 then
      BestStrat = 1
    elseif Success1 == Success2 then
      BestStrat = same    
    else
      BestStrat = 2
    end,
    println([father=Father,champion=Champion,success1=Success1,success2=Success2,best_strat=BestStrat]),
  end,
  fail,
  nl.
go2 => true.
  

/*
  Random probabilities: Champion is always better than the father (which means 
  less probability for Elmer to win against the Champion).

  var : success 1
  Probabilities:
  false: 0.6420798065296252
  true: 0.3579201934703748
  mean = [false = 0.64208,true = 0.35792]

  var : success 2
  Probabilities:
  false: 0.6975010076582023
  true: 0.3024989923417977
  mean = [false = 0.697501,true = 0.302499]

  var : best
  Probabilities:
  0: 0.6769447803305119
  1: 0.1892382103990327
  2: 0.1338170092704555
  mean = 0.456872

  var : matches 1: father, champion, father
  Probabilities:
  [0,1,0]: 0.3022974607013301
  [0,0,0]: 0.2033454252317614
  [1,1,1]: 0.1291817815397017
  [0,1,1]: 0.1154776299879081
  [1,1,0]: 0.1132607819427650
  [0,0,1]: 0.0540104796453043
  [1,0,0]: 0.0475614671503426
  [1,0,1]: 0.0348649738008867
  mean = [[0,1,0] = 0.302297,[0,0,0] = 0.203345,[1,1,1] = 0.129182,[0,1,1] = 0.115478,[1,1,0] = 0.113261,[0,0,1] = 0.0540105,[1,0,0] = 0.0475615,[1,0,1] = 0.034865]

  var : matches 2: champion, father, champion
  Probabilities:
  [1,0,1]: 0.2885933091495365
  [1,1,1]: 0.2019347037484885
  [0,0,0]: 0.1432889963724305
  [1,0,0]: 0.1273679967754938
  [0,0,1]: 0.1072148327287384
  [0,1,1]: 0.0505844417573559
  [1,1,0]: 0.0499798468359532
  [0,1,0]: 0.0310358726320032
  mean = [[1,0,1] = 0.288593,[1,1,1] = 0.201935,[0,0,0] = 0.143289,[1,0,0] = 0.127368,[0,0,1] = 0.107215,[0,1,1] = 0.0505844,[1,1,0] = 0.0499798,[0,1,0] = 0.0310359]


*/
go3 ?=>
  reset_store,
  run_model(10_000,$model3,[show_probs_trunc,mean]),
  nl.
go3 => true.


model3() =>
  Father = random_integer1(100) / 100,
  Champion = random_integer1(100) / 100,

  % Champion is better (lower probabilities for Elmer to win) than the father
  observe(Champion > Father),

  Seq1 = [Father,Champion,Father],
  Seq2 = [Champion,Father,Champion],

  Matches1 = [ bern(M) : M in Seq1],
  Matches2 = [ bern(M) : M in Seq2],  

  Success1 = test(Matches1),
  Success2 = test(Matches2),  

  Best = cases( [[ (Success1, not Success2), 1],
                 [ (not Success1, Success2), 2],
                 [true,0]]),

  if observed_ok then
    add("success 1",Success1),
    add("success 2",Success2),
    add("best",Best),
    add("matches 1: father, champion, father",Matches1),
    add("matches 2: champion, father, champion",Matches2),    
  end.