duel_simulation.cpp

# include <cstdlib>
# include <iostream>
# include <ctime>

using namespace std;

int main ( );
int duel_result ( double a_accuracy, double b_accuracy );
double random_double ( );

//****************************************************************************80

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    DUEL_SIMULATION simulates a duel.
//
//  Discussion:
//
//    Player 1 fires at player 2, and hits with a probability of P(1).
//    If Player 2 misses, then Player 2 fires at Player 1, hitting with
//    a probability of P(2).
//
//    The duel continues with alternating shots until only one player 
//    survives.
//
//    The simulation is intended to estimate the probabilities that a
//    player will survive, and the number of turns required.
//
//    The exact probability that player 1 will survive is
//
//      P(1) / ( P(1) + P(2) - P(1) * P(2) )
//
//    Player 2's chance is
//
//     P(2) * ( 1 - P(1) ) / ( P(1) + P(2) - P(1) * P(2) )
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 November 2009
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Nahin,
//    Duelling Idiots and Other Probability Puzzlers,
//    Princeton University Press, 2000,
//    ISBN13: 978-0691009797,
//    LC: QA273.N29.
//
//    Martin Shubik,
//    "Does the Fittest Necessarily Survive?",
//    in Readings in Game Theory and Political Behavior,
//    edited by Martin Shubik,
//    Doubleday, 1954,
//    LC: H61.S53.
//
//  Parameters:
//
//    Input, double A_ACCURACY, B_ACCURACY, the probabilities that players A and
//    B will hit their opponent in a single shot.
//
//    Input, int DUEL_NUM, the number of duels to run.
//
//    Output, double A_PROB, B_PROB, the estimated probablities that players
//    A and B will survive.
//
//    Output, double TURN_AVERAGE, the average number of turns required to
//    complete the duel.
//
{
  double a_accuracy;
  double a_prob;
  int a_wins;
  double b_accuracy;
  double b_prob;
  int b_wins;
  int duel;
  int duel_num;
  int seed;
  int winner;

  cout << "\n";
  cout << "DUEL_SIMULATION:\n";
  cout << "  C++ version\n";

  cout << "Enter number of duels to run: ";
  cin >> duel_num;

  cout << "Enter player A's accuracy between 0.0 and 1.0: ";
  cin >> a_accuracy;

  cout << "Enter player B's accuracy between 0.0 and 1.0: ";
  cin >> b_accuracy;

  seed = time ( 0 );
  srand ( seed );

  a_wins = 0;
  b_wins = 0;

  for ( duel = 1; duel <= duel_num; duel++ )
  {
    winner = duel_result ( a_accuracy, b_accuracy );

    if ( winner == 1 )
    {
      a_wins = a_wins + 1;
    }
    else
    {
      b_wins = b_wins + 1;
    }
  }

  a_prob = ( double ) a_wins / ( double ) duel_num;
  b_prob = ( double ) b_wins / ( double ) duel_num;

  cout << "\n";
  cout << "  Player A wins with probability " << a_prob << "\n";
  cout << "  Player B wins with probability " << b_prob << "\n";

  cout << "\n";
  cout << "DUEL_SIMULATION:\n";
  cout << "  Normal end of execution.\n";

  return 0;
}
//****************************************************************************80

int duel_result ( double a_accuracy, double b_accuracy )

//****************************************************************************80
//
//  Purpose:
//
//    DUEL_RESULT returns the outcome of a single duel.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    17 September 2012
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Martin Shubik,
//    “Does the Fittest Necessarily Survive?”,
//    in Readings in Game Theory and Political Behavior,
//    edited by Martin Shubik,
//    Doubleday, 1954,
//    LC: H61.S53.
//
//  Parameters:
//
//    Input, double A_ACCURACY, B_ACCURACY, the probabilities that player A
//    and B will hit their opponent in a single shot.
//
//    Output, int DUEL_RESULT, the survivor of the duel.
//
{
  double r;
  int winner;

  while ( true )
  {
    r = random_double ( );

    if ( r <= a_accuracy )
    {
      winner = 1;
      break;
    }

    r = random_double ( );

    if ( r <= b_accuracy )
    {
      winner = 2;
      break;
    }
  }
  return winner;
}
//****************************************************************************80

double random_double ( )

//****************************************************************************80
//
//  Purpose:
//
//    RANDOM_DOUBLE returns a random number between 0 and 1.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 November 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double RANDOM_DOUBLE, the random value.
//
{
  double r;
  
  r = ( double ) rand ( ) / ( double ) RAND_MAX;

  return r;
}