Someone asked Teacher Ma why the kill threshold in the US is exactly around 1/e?

Actually, this is a very classic problem, a common brain teaser in quant job interviews.

And it only requires basic higher mathematics knowledge to solve.

The basic version of this problem includes but is not limited to: assuming you date once a year for ten years without repeating, which time should you get married?

Picking wheat from the field, assuming each wheat stalk can only be harvested once, how do you find the largest wheat stalk?

These types of problems share a common point: given a sample size range, with only one observation opportunity per sample (i.e., either choose or skip), how to operate to maximize the probability of finding the optimal sample?

To find the optimal solution here, three points need to be considered. First, we want to assess the general level of this sample set to estimate the level of the best sample as accurately as possible. To achieve this, we need to observe several samples in advance before making a choice;

Second, for each sample, there is only one observation opportunity. Naturally, we hope that the optimal solution does not appear in the pre-observed sample set;

Finally, after completing the preliminary observation of samples, as long as the newly observed sample is better than the local best in the pre-observed set, it is considered the best among all samples, and the observation ends. Naturally, we hope the second-best solution appears in the pre-observed sample set, and assume the second-best appears before the best.

Once these three points are clear, we can start solving this problem.

The problem is not difficult to prove; I leave it to fellow brain teaser enthusiasts to verify. Here, I’ll give the answer directly:
1/e

That is, after pre-observing at the position of 1/e, as long as the new observed sample is better than the local best in the pre-observed set, you can maximize the probability of obtaining the optimal sample.

A note: this theory requires certain conditions to be applicable, most importantly: the second-best solution must come before the best solution; the sample size must be large enough.

Additionally, each sample may not have only one observation opportunity.

#Kill Threshold