Classic coin-flipping problem

If John flips 2017 coins and Jonathon flips 2016 coins, what is the chance that John gets strictly more heads that Jonathon?

1 2 \frac{1}{2} 2016 2017 \frac{2016}{2017} 2015 2017 \frac{2015}{2017} 2015 2016 \frac{2015}{2016} 1014 2017 \frac{1014}{2017}

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