Your friend Psycho Sid has challenged you to a game. He has a bag containing redCount red marbles and blueCount blue marbles. There will be an odd number of marbles in the bag, and you go first. On your turn, you reach into the bag and remove a random marble from the bag; each marble may be selected with equal probability. After your turn is over, Sid will reach into the bag and remove a blue marble; if there is no blue marble for Sid to remove, then he wins. If the final marble removed from the bag is blue, you will win. Otherwise, Sid wins.
Given the number of red and blue marbles in the bag, determine the probability that you win the game.