TLDR: Math problem about optimal strategy for hiring job applicants has similar (but not same) assumptions to searching for a company. Does anyone have a set # of deals they want to seriously evaluate before pulling the trigger on an LOI?

The secretary problem ( is a scenario in optimal stopping theory that derives an optimal policy for selecting a job applicant. The formulation assumes there is one position to fill, a known number of applicants (n) interviewed in random order, and that each applicant must be accepted/rejected immediately after the interview. The mathematically optimal approach is to reject the first n / e applicants (where e is approx[redacted]and to then accept the first applicant that is better than all prior applicants. This is supposed to balance the risk of committing too early against waiting too long and missing your best chance.

Replace "applicant" with "company", and this sounds a little bit like a search fund. Assume you can seriously diligence/evaluate one business per week or 104 during a two-year search. If the secretary problem assumptions hold, you should theoretically evaluate ~38 companies before making an investment.

The secretary problem assumptions aren't exactly applicable (the company must also "accept" you, companies cannot be unambiguously ranked, LP experience can help you avoid the risk of committing too early, search can be extended, etc.).

However, does anyone have a set # of deals they plan to seriously diligence before committing to an LOI?