Re: The tennis serve problem
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What do you mean by benefit/payoff? Lets just assume you get a dollar for every mph of your fastest of the three serves. You get 3 serves, regardless of whether previous serves are successful. Disregard any real tennis rules. If you miss, it counts as 0mph (zero $). If your fastest serve is 100mph, you receive 100$.
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That's an example of what I meant by payoffs. Another example payoff could have been: you are trying to win a tennis point, so failing all your serves gives 0, while making faster serves could give you non-linear higher chances of winning. For example, payoff of sqrt(X) if X is speed of serve.
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Could you please elaborate on how you would work backwards?
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Perhaps the others have elaborated by now; sorry I was busy earlier. But backwards induction means calculate the last serve you'd make, assuming you know how you did on the previous ones.
alThor
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