No, this isn't a Flappy Bird duplicate. Dylan starts with . He flips a fair coin times. For each head he receives, he adds to his current sum. For each tail he receives, he subtracts from his current sum. If Dylan ever reaches a point where he obtains a tail with only or left in his bank, he gives up the rest of his money, goes bankrupt, stops flipping, and the game immediately ends. Otherwise, the game ends at the end of the flips. Find Dylan's expected balance at the end of the game.