20. A spinner with three equal sections is being used in a game. One section is labelled "0 points," and two sections are labelled "2 points." A player can decide not to spin the spinner and score 1 point. Each player gets one turn, and the player with the higher score wins; in case of a tie, the winner is decided by one flip of a fair coin. Alex takes his turn first. Eddie, knowing Alex's score, takes his turn next. If both players use strategies that maximize their winning probabilities, what is the probability that Alex wins?

Fig: 1

Fig: 2