There is a 10% chance at any iteration of choosing a value in the top 10% (duh) when you are just selecting linearly numbers on a number line. So, the probability of choosing a number in the top 10% over 30 iterations is simply:
I don't see the magic of the number 30 here-- the cost/benefit of iterations to improved results appears to be linear to me. You get results that are twice as good by doing twice as many iterations.
It's easy to conceive of a non-linear results set where you are likely to come nowhere near the maximum value by picking some smallish number of random iterations.
Try, for instance, finding the maximum value of 1/10**N where N is an integer between 0 and 1,000,000. What is the percent error between your randomly selected max over thirty iterations and the actual max value? My money says it is 100%. Of course, evaluating the linear variance of an exponential function may be a bit of a stretch...
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