You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
A cup tournament system to determine the winner among 8 athletes involves pairing up players through a draw. Four matches determine four winners who participate in the second round; the third round is the final. The winner of the final match gets the first prize, and their opponent gets the second prize. Assume each player has a certain strength (similar to how each object has a certain weight) and that a stronger player always wins against a weaker one (similar to how a heavier object always outweighs a lighter one if placed on different sides of a scale). Under these assumptions, the described process is appropriate for determining the champion since the winner will indeed be stronger than all their opponents; however, the second place will not always be occupied by the second strongest player.

What is the probability that the runner-up in the final match truly deserves the second prize?
user
0.5714285714285714
rule
A cup tournament system to determine the winner among 8 athletes involves pairing up players through a draw. Four matches determine four winners who participate in the second round; the third round is the final. The winner of the final match gets the first prize, and their opponent gets the second prize. Assume each player has a certain strength (similar to how each object has a certain weight) and that a stronger player always wins against a weaker one (similar to how a heavier object always outweighs a lighter one if placed on different sides of a scale). Under these assumptions, the described process is appropriate for determining the champion since the winner will indeed be stronger than all their opponents; however, the second place will not always be occupied by the second strongest player.

What is the probability that the runner-up in the final match truly deserves the second prize?
train