We play a game in which we are given a biased coin with probability 0.53 of landing heads and probability 0.47 of landing tails. We start the game with $1 and once a day, every day, we may bet any fraction of our current amount on the event that the coin lands heads. If the coin lands heads, we win an even money payoff; if the coin lands tails, we lose the amount bet. If we lose all of our money, the game is over. What fraction of our current amount should we bet every day to maximize our long-term profit?