racquetball.R

simulate_raquetball = function(number_of_games, prob_win_serve,
                               prob_win_noserve, points_to_win)
{    
  # variable to track the number of wins
  wins = 0
 
  # variable to track the number of simulated games
  total_games = 1
 
  # list where we will store the number of volleys per game
  volleylist = c()
 
  # running the game simulation loop
  while (total_games <= number_of_games)
  {
    # variable to count number of volleys in one game
    volleys = 0
   
    # variable to count my points in one game
    my_points = 0
   
    # variable to count opponent's points in one game
    opp_points = 0
   
    # variable to keep track of who is serving
    # (TRUE -> me, FALSE -> opponent)
    serving = TRUE
   
    # simulating a single game
    while (my_points < points_to_win & opp_points < points_to_win)
    {
      # simulating the outcome of a single serve
      x = runif(1)
     
      # updating the game results if it was my serve
      if (serving == TRUE)
      {
        # if I won  point, update  points in game
        if (x < prob_win_serve)
          my_points = my_points + 1
           
            # otherwise, pass next serve to the opponent
            else
              serving = FALSE
      }
     
      # updating game results if it was opponent's serve
      else
      {
        # if I won point, next serve is set to be mine
        if (x < prob_win_noserve)
          serving = TRUE
       
        # otherwise, update the opponent's earned points
        else
          opp_points = opp_points + 1
      }
     
      # in either case, update the number of served volleys
      volleys = volleys + 1
    }
   
    # save  number of serves that were made in the last game
    volleylist[total_games] = volleys
   
    # update the number of games played
    total_games = total_games + 1
   
    # if I won the last game, update the number of wins
    if (my_points == points_to_win)
      wins = wins + 1
  }
 
  # calculate the win probability
  win_probability = wins/number_of_games
   
    # calculate the expected number of volleys
    expected_num_volleys = mean(volleylist)
   
    print(paste('After', number_of_games,
                'simulated games win probability is',
                win_probability))
  print(paste('Average number of volleys per match was',
              expected_num_volleys))
}

simulate_raquetball(number_of_games = 10000,
                    prob_win_serve = 0.6,
                    prob_win_noserve = 0.5,
                    points_to_win = 21)