#include "stdstuff.h"
#include "odds.h"


double probabilityOfState (int AWins, int GWins) {

  double result;

  if ((AWins == 0) && (GWins == 0)) { // we always start at 0 0

    result = 1.0;

  } else  if ((AWins == 0) || (GWins == 4)) { // only Giants win

    result = probabilityOfState (AWins, GWins - 1) *
             (1 - probabilityOfAngelVictory (AWins, GWins - 1));

  } else if ((GWins == 0) || (AWins == 4)) { // only Angels win

    result = probabilityOfState (AWins - 1, GWins) *
             probabilityOfAngelVictory (AWins - 1, GWins);

  } else { // a mix of Angels and Giants wins

    result =
      ( probabilityOfState (AWins, GWins - 1) *
        (1 - probabilityOfAngelVictory (AWins, GWins - 1)) ) +
      ( probabilityOfState (AWins - 1, GWins) *
        probabilityOfAngelVictory (AWins - 1, GWins) );
  }

  return result;

}


void realMain () {

  int i;
  double P, AngelsP = 0, GiantsP = 0;

  cout << setiosflags (ios::fixed | ios::showpoint) << setprecision(6);

  for (i = 0; i <= 3; i++) { // calculate all probabilities (4,0), (0,4), (4,1), etc.
    P = probabilityOfState (4, i);
    cout << "The probability of the Angels winning in " << (4 + i)
         << " games is " << P << ".\n";
    AngelsP += P;
    P = probabilityOfState (i, 4);
    cout << "The probability of the Giants winning in " << (4 + i)
         << " games is " << P << ".\n";
    GiantsP += P;
  }

  cout << "\nThe probability of the Angels winning the series is "
       << AngelsP << ".\n";
  cout << "The probability of the Giants winning the series is "
       << GiantsP << ".\n";

  cout << "\nThe sum of all of the probabilities is "
       << (AngelsP + GiantsP) << ".\n";

}


int main () {

  try {

    realMain ();

  }
  catch (exception &e) { // catches all uncaught exceptions

    cout << "\nException <" << e.what() << "> occurred.\n";

  }

  pause ();
  return 0;

}