The tennis serve problem

[alThor]

We need to know the benefit (payoff) of having a successful serve of X mph for any X, and also the payoff of having no successful serve.

After that, it's a simple backwards induction computation. Figure out how fast your last serve should be to maximize expected payoff, given the status of the previous attempts. Then analyze 2nd last serve, etc.

Also, do we get 3 attempts even if the first attempt is a successful serve? That's not how tennis works, of course, so be clear how the game actually works.

Regardless, with no further information about payoffs, it seems one cannot deduce anything.

alThor