/* 

  Tug of war in Picat.

  From Hakaru example documentation/tugofwar_rejection.hk

  $ hakaru tugofwar_rejection.hk | head -100000 | collect
  1.0	true: 69223
  1.0	false: 30777

  In this model we observe that Alice wins of Bob.

  This is a port of my Gamble model gamble_tug_of_war3.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.

/*

  var : match1
  mean = [alice = 1.0]
  Probabilities:
  Probabilities:
  alice: 1.00000000000000000 (1 / 1)

  var : match2
  mean = [carol = 0.675987,bob = 0.324013]
  Probabilities:
  Probabilities:
  carol: 0.67598651596272064 (3409 / 5043)
  bob: 0.32401348403727942 (1634 / 5043)

  var : match3
  mean = [alice = 0.654967,carol = 0.345033]
  Probabilities:
  Probabilities:
  alice: 0.65496728138013083 (1101 / 1681)
  carol: 0.34503271861986912 (580 / 1681)

  var : strength alice
  mean = 0.926202
  Probabilities (truncated):
  3.926296048892903: 0.00019829466587349 (1 / 5043)
  3.814918957298187: 0.00019829466587349 (1 / 5043)
  3.756409292296722: 0.00019829466587349 (1 / 5043)
  3.586995465768223: 0.00019829466587349 (1 / 5043)
  3.58477511925162: 0.00019829466587349 (1 / 5043)
  .........
  0.001056742929101: 0.00019829466587349 (1 / 5043)
  0.000648192265858: 0.00019829466587349 (1 / 5043)
  0.000573474206892: 0.00019829466587349 (1 / 5043)
  0.000280188191874: 0.00019829466587349 (1 / 5043)
  0.000052394800002: 0.00019829466587349 (1 / 5043)

  var : strength bob
  mean = 0.657199
  Probabilities (truncated):
  3.040586572182948: 0.00019829466587349 (1 / 5043)
  2.88355263074314: 0.00019829466587349 (1 / 5043)
  2.861466190334316: 0.00019829466587349 (1 / 5043)
  2.787325168975777: 0.00019829466587349 (1 / 5043)
  2.783159592013704: 0.00019829466587349 (1 / 5043)
  .........
  0.001583370791069: 0.00019829466587349 (1 / 5043)
  0.00113930090667: 0.00019829466587349 (1 / 5043)
  0.000961877452675: 0.00019829466587349 (1 / 5043)
  0.00087867150733: 0.00019829466587349 (1 / 5043)
  0.000102015539829: 0.00019829466587349 (1 / 5043)

  var : strength carol
  mean = 0.789783
  Probabilities (truncated):
  4.0741016897302: 0.00019829466587349 (1 / 5043)
  3.482268483523745: 0.00019829466587349 (1 / 5043)
  3.302073659342756: 0.00019829466587349 (1 / 5043)
  3.245158884284827: 0.00019829466587349 (1 / 5043)
  3.085044528888897: 0.00019829466587349 (1 / 5043)
  .........
  0.000824997528792: 0.00019829466587349 (1 / 5043)
  0.000766496095747: 0.00019829466587349 (1 / 5043)
  0.000181480639208: 0.00019829466587349 (1 / 5043)
  0.000164103879448: 0.00019829466587349 (1 / 5043)
  0.000013565272156: 0.00019829466587349 (1 / 5043)

  var : pulls alice
  mean = 1.58928
  Probabilities (truncated):
  5.597369437736634: 0.00019829466587349 (1 / 5043)
  5.421232790485462: 0.00019829466587349 (1 / 5043)
  5.131874004385718: 0.00019829466587349 (1 / 5043)
  5.048577786378422: 0.00019829466587349 (1 / 5043)
  5.037140718487107: 0.00019829466587349 (1 / 5043)
  .........
  0.051208555055472: 0.00019829466587349 (1 / 5043)
  0.048228795409385: 0.00019829466587349 (1 / 5043)
  0.045408469191927: 0.00019829466587349 (1 / 5043)
  0.03708151175543: 0.00019829466587349 (1 / 5043)
  0.027291174263397: 0.00019829466587349 (1 / 5043)

  var : pulls bob
  mean = 0.664278
  Probabilities (truncated):
  3.770481212237693: 0.00019829466587349 (1 / 5043)
  3.510507522769754: 0.00019829466587349 (1 / 5043)
  3.330499732396831: 0.00019829466587349 (1 / 5043)
  3.296319706673931: 0.00019829466587349 (1 / 5043)
  3.246099613001593: 0.00019829466587349 (1 / 5043)
  .........
  0.000826343223272: 0.00019829466587349 (1 / 5043)
  0.000774201855797: 0.00019829466587349 (1 / 5043)
  0.000764936121971: 0.00019829466587349 (1 / 5043)
  0.000679155188567: 0.00019829466587349 (1 / 5043)
  0.000410844123178: 0.00019829466587349 (1 / 5043)

  var : pulls carol
  mean = 1.14123
  Probabilities (truncated):
  6.100363602428722: 0.00019829466587349 (1 / 5043)
  5.201296550063526: 0.00019829466587349 (1 / 5043)
  4.714558199873927: 0.00019829466587349 (1 / 5043)
  4.504175184788844: 0.00019829466587349 (1 / 5043)
  4.386651172102522: 0.00019829466587349 (1 / 5043)
  .........
  0.002658116390014: 0.00019829466587349 (1 / 5043)
  0.002213740089024: 0.00019829466587349 (1 / 5043)
  0.001354507434717: 0.00019829466587349 (1 / 5043)
  0.001011699446403: 0.00019829466587349 (1 / 5043)
  0.000899694872041: 0.00019829466587349 (1 / 5043)

*/
go ?=>
  reset_store,
  Obs = [team1,team2,team1,team1,team1,team1,team1,team1], % Note team2 won match 2
  run_model(10_000,$model(Obs),[mean,show_probs_rat_trunc,truncate_size=5]),
  fail,
  nl.
go => true.


winner(A,B,Pulls) = cond(Pulls[A] > Pulls[B],A,B).
   
model(Obs) =>
  Alice = 1,
  Bob   = 2,
  Carol = 3,
  People = [Alice,Bob,Carol],
  PeopleMap = new_map([Alice=alice,Bob=bob,Carol=carol]),
  
  % We caches the Strengths and Pulls
  Strengths = [abs(normal_dist(0,1)) : P in People],
  Pulls     = [abs(normal_dist(Strengths[P],1)) : P in People],

  % The matches
  Match1 = winner(Alice,Bob,Pulls),
  Match2 = winner(Bob,Carol,Pulls),
  Match3 = winner(Alice,Carol,Pulls),

  observe(Match1 == Alice),

  if observed_ok then
    add_all([ ["match1",PeopleMap.get(Match1)],
              ["match2",PeopleMap.get(Match2)],
              ["match3",PeopleMap.get(Match3)],
              ["strength alice",Strengths[Alice]],
              ["strength bob",Strengths[Bob]],
              ["strength carol",Strengths[Carol]],
              ["pulls alice",Pulls[Alice]],
              ["pulls bob",Pulls[Bob]],
              ["pulls carol",Pulls[Carol]]])
  end.