You and an opponent are each given a number uniformly at random between 0 and 1. The player with the higher number wins 1 point from the other. After seeing your own number (but not your opponent's), you can choose to offer 'double' odds or just continue. If you offer double, your opponent, having seen their own number, can either reject the offer (losing 1) or accept it. If they accept, the winner takes 2 points from the loser according to who has the higher number. What is the optimal strategy for playing this game?