The tennis serve problem

[TomCollins]

The optimum for 2 serves is to serve 75mph first, 97 if you make, and 60 if you miss.

This will give an EV of 71.226.

You should always choose 60mph if you miss the first serve. If you make the first serve, you should choose (x/2)+60 for your second serve, where x is the speed you had on the first serve.