Suppose that you and a friend play a game with the following rules: there is a green player and a blue player, there are 2 green marbles and 2 blue marbles in a hat, the players alternate drawing a marble from the hat, and a coin is tossed to determine who goes first. To win, a player must draw their marble (the green player must draw a green marble to win), and if a player does not draw their marble, then they put the drawn marble back into the hat and add a marble of the opponents color to the hat. Suppose that the green player has won the coin toss. Determine the probability that the blue player wins on or before his/her second turn.