Legolas flips a fair coin 2008 times, and Gimli flips another fair coin 2009 times. What is the probability that Gimli flips more heads than Legolas?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Legolas flips a fair coin 2008 times, and Gimli flips another fair coin 2009 times. What is the probability that Gimli flips more heads than Legolas?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{2}
Legolas flips a fair coin 2008 times, and Gimli flips another fair coin 2009 times. What is the probability that Gimli flips more heads than Legolas?
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