In a robotic long jump contest, each robot advances from position 0 to the takeoff point at 1 by repeatedly drawing a real number uniformly from [0, 1] and adding it to their position. After each advance, the robot must choose to either jump or continue. If the robot crosses 1 without jumping, it scores 0. If it jumps before crossing 1, it draws a final number from [0, 1] and adds it to its position as its score. In a head-to-head, each robot is programmed to maximize its probability of winning and knows the other's strategy. Without knowing the other’s result, what is the probability that a robot's first attempt scores 0?