The Easter bunny has a bag containing 23 blue Easter eggs and 23 red Easter eggs. He proposes the following game to one of his helpers, stating that the one that wins receives the big chocolate replica of the Easter bunny himself. The game proceeds as follows. Each time, two eggs are taken from the bag (without looking which eggs). If one of them is blue and the other is red, the blue one will be put aside and we put the red one back in the bag. If both eggs have the same color, both eggs are put aside and we put a blue one in the bag (there are enough of them). The game proceeds until the last eggs are taken out of the bag. The color that needs to be put back into the bag, red or blue, wins the game. The Easter bunny says he wants to play for red. Model this game as a Markov Chain. What is the probability that the helper will win the game?