> The probability of selecting the best applicant in the classical secretary problem converges toward 0.368
There are also some pretty big tradeoffs with this strategy. There seems to be a roughly 1/3 chance that you already rejected the best candidate. That's all good if not coming up with a result is acceptable and practically free of cost.
If the stakes are higher though, more conservative strategies might be in order. For example, you might want to sample a much smaller group than n/e first and make a decision based on their median, or even look at their standard deviation to get a reasonable sense about the value distribution - as in the real world values are seldomly distributed uniformly.
If there is a cost to coming up empty, you may also want to employ a hybrid solution, such as going with "1/e-law of best choice" until you hit the 70% mark and then accept the first candidate that is higher than a linear interpolation of the highest value and zero, lerped across the remaining percentage of samples.
If the stakes are higher though, more conservative strategies might be in order. For example, you might want to sample a much smaller group than n/e first and make a decision based on their median, or even look at their standard deviation to get a reasonable sense about the value distribution - as in the real world values are seldomly distributed uniformly.
If there is a cost to coming up empty, you may also want to employ a hybrid solution, such as going with "1/e-law of best choice" until you hit the 70% mark and then accept the first candidate that is higher than a linear interpolation of the highest value and zero, lerped across the remaining percentage of samples.
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