That doesn't implement the algorithm nor does it meet the problem because you were able to evaluate all options and not one at a time (whereas you would need to make a irreversible decision on the spot).
Following the above heuristic, isn't there a chance you never look at another apartment that would be "better than the others you've looked at" once you enter the decision window, and therefore keep looking until you reach N and have to take the last option?
(the implications for dating should be obvious here, with it being fairly common for young lovers to break up so they can "see what's out there", and not uncommon for people to reach an age where they feel the need to settle for "what they can get" at that point)
Yes, obviously. As Wikipedia says:
> The probability of selecting the best applicant in the classical secretary problem converges toward 1/e ~ 0.368.
The classic solution to the classic secretary problem works in less than 37% of cases.
But in reality, you tend to know a bit about the distribution beforehand, and you are also interested in getting eg the second best secretary (if the best is no longer available), instead of just going for best-or-bust.
Either you use broad filter criteria and you look at a few houses before you say "this is a better option than what we've seen, let's make an offer". In which case you can ignore the filter for purposes of fitting the house search to the secretary problem.
Or like the parent post, you think you can express what you're looking for exactly through facts that appear in the ads, in which case you look at a few houses, then you buy the first house to appear that exceeds best of what you've seen.
What you do not have in most markets is the option to go back and buy a house you looked at two weeks ago. Houses that sit on the market aren't houses that are appealing to buyers who intend to live in them.
Unsure what part doesn't meet the criteria, I consciously used that approach to make the decision.
n is finite as time provides the limit to n. We were looking to move within 6 months (this was a hard requirement based on personal circumstances) and I'd already established the number of likely options according to the rate they appeared on the market.
In all of the part of greater London you considered, 7 or fewer possibilities seems quite low, but I don’t know how tight your criteria were in practice relative to that market. If your criteria were that tight, I congratulate you on securing 1 of the 7 suitable properties.
The question then becomes: how much do the simplifications made affect the outcome of applying what we know about the secretaries problem to the real world situation? Someone could probably write a neat article about it.
OP has not understood the significant differences between this clearly defined mathematical problem and his own experiences, not sure why people are indulging him.
Most real life problems will never perfectly match to this kind of math problem simply because real life usually offers more flexibility than a strictly defined mathematical scenario.
Reminds me of the joke with the mathematician and the engineer who can take as many steps as they want to get to the pot of gold in front of them with the condition that every step is maximum half of the distance remaining. The mathematician is absolutely livid because he knows he'll never reach it, while the engineer is happy because he'll be there for all practical purposes.
Instead, it sounds like you arbitrarily decided to use 2 examples to pick a selection threshold for the "price to square foot" at which you'd accept a property.
2. You established a threshold of acceptability and took a candidate that met that threshold rather than saying, after X properties, I’ll take the next property that’s better than the best so far.
Your approach is much closer to the standard method of buying a house - you have constraints, needs, and wants, and buy a house that fits those.