/* 

  Tug of war in Picat.

  This is a port of the Church ForestDB model (via 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 : alice strength
  Probabilities:
  10: 0.75000000000000000 (3 / 4)
  5: 0.25000000000000000 (1 / 4)
  mean = 8.75

  var : bob strength
  Probabilities:
  10: 0.78378378378378377 (29 / 37)
  5: 0.21621621621621623 (8 / 37)
  mean = 8.91892

  var : c
  Probabilities:
  1: 0.25843333333333335 (7753 / 30000)
  2: 0.16586666666666666 (311 / 1875)
  3: 0.13156666666666667 (3947 / 30000)
  4: 0.11436666666666667 (3431 / 30000)
  5: 0.10596666666666667 (3179 / 30000)
  6: 0.10496666666666667 (3149 / 30000)
  7: 0.09170000000000000 (917 / 10000)
  0: 0.01726666666666667 (259 / 15000)
  8: 0.00986666666666667 (37 / 3750)
  mean = 3.3228

  var : sue strength
  Probabilities:
  5: 0.83108108108108103 (123 / 148)
  10: 0.16891891891891891 (25 / 148)
  mean = 5.84459

  var : team1 strength
  Probabilities:
  20: 0.53378378378378377 (79 / 148)
  15: 0.46621621621621623 (69 / 148)
  mean = 17.6689

  var : team1,team2
  Probabilities:
  [15,10]: 0.46283783783783783 (137 / 296)
  [20,15]: 0.32770270270270269 (97 / 296)
  [20,10]: 0.20608108108108109 (61 / 296)
  [15,15]: 0.00337837837837838 (1 / 296)
  mean = not_numeric

  var : team2 strength
  Probabilities:
  10: 0.66891891891891897 (99 / 148)
  15: 0.33108108108108109 (49 / 148)
  mean = 11.6554

  var : tom strength
  Probabilities:
  5: 0.83783783783783783 (31 / 37)
  10: 0.16216216216216217 (6 / 37)
  mean = 5.81081


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


sample_strength(P) = condt(flip(), 10, 5).
lazy(Person) = flip(1/3).
winner(TotalPullingTeam1,TotalPullingTeam2) = cond(TotalPullingTeam1 <= TotalPullingTeam2,team2,team1).
   
model(Obs) =>
  Len = Obs.len,
  NumPeople = 4,
  Alice = 1,
  Bob   = 2,
  Sue   = 3,
  Tom   = 4,

  Team1 = [Alice,Bob],
  Team2 = [Sue,Tom],
  
  % We keep strength constant (memoized),
  % but laziness can fluctuate during each session
  Strengths = [sample_strength(P) : P in 1..NumPeople],
  Team1Strength = [Strengths[P] : P in Team1].sum,
  Team2Strength = [Strengths[P] : P in Team2].sum,  
  
  C = 0, % Number of correct observations
  Winner = [],
  foreach(I in 1..Len)
     TP1 = sum([ condt(lazy(P), SP/2,SP) : P in Team1, SP = Strengths[P]]),
     TP2 = sum([ condt(lazy(P), SP/2,SP) : P in Team2, SP = Strengths[P]]),
     W = winner(TP1,TP2),
     Winner := Winner ++ [W],
     if W == Obs[I] then
       C := C +1 
     end
  end,
  observe(C == Len),  
  add("c",C),
  if observed_ok then
     add_all([["alice strength",Strengths[Alice]],
              ["bob strength",Strengths[Bob]],
              ["sue strength",Strengths[Sue]],
              ["tom strength",Strengths[Tom]],
              ["team1 strength",Team1Strength],
              ["team2 strength",Team2Strength],
              ["team1,team2",[Team1Strength,Team2Strength]]
              ])
  end.