Re: The tennis serve problem
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In general for x{i} where x is speed of serve with i serves left:
Probability of successuful serve = (120 - x{i}) / 70
Probability of unsuccessful serve = (x{i} - 50)/ 70
Expectation{i} = x{i} * (120 - x{i}) / 70 + Expectation{i-1} * (x{i} - 50) / 70
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This ignores the fact that if we make it on the first serve, we can increase our speed for an even higher expectation. This leads to much more complicated multi-variable gradients.
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