A person has to find the best among N potential candidates (pick the envelope with the highest amount of money, find the best candidate for a job, the best partner to marry, etc.). The quality of individual candidates can be discovered by examining candidates one-by-one. However, a candidate, once rejected, cannot be chosen later on. The person who decides knows N, but has no idea about the properties of the actual distribution (like the range) of qualities. How many candidates should the person examine? What is the optimal rule with regard to stopping and accepting a particular candidate?

This optimal stopping problem was first presented in Martin Gardner´s Mathematical Recreations column in the February 1960 issue of Scientific American. Gardner showed that the probability of finding the best among N potential candidates is maximized by following a simple rule: Review the first 37 percent of candidates (without accepting any), then take the next best (the first who is better than the best of the first 37 percent).

Why 37 percent? The reason is mathematical. With N going to infinity, the optimal number of candidates to be examined before accepting goes to 1/e =0.36787..., i.e., towards approximately 37 percent (see Peter Todd, Searching for the best next best mate). If an individual is risk-averse or if there are search costs, the optimal pre-decision sample is smaller than 37 percent of available candidates. If an individual could reasonably evaluate between fifty and one hundred potential partners, "take a dozen" looks like a reasonable rule.

Later on, Gardner posed the optimal stopping problem under the name Googol. This term, introduced by the mathematician Edward Kasner (1878-1955) in 1938, refers to a high number: a 1 followed by 100 zeros. Legend has it that "googol" was the answer Kasner got when he asked his nine-year-old nephew, Milton Sirotta, what he should call a very large number. "Googol" became synonymous with the "search among a vast number of possibilities" and was the inspiration behind the name of the internet search engine Google.

Read more on search models in Chapter 5 of Information Economics.