This feels very similar to the “radio” or “restaurant” problem:

You’re driving down the street trying to decide which restaurant to stop at (or scanning through the radio trying to decide which song to stop on).

If you stop at the first, there’s a good chance something better is ahead. But if you wait too long then you risk getting stuck with something you don’t really like (the problem assumes you can’t go back).

If I remember correctly, mathematically you skip the first 1/3, but keep track of your “best”. Then stop at the next option that’s >= than your current best or maybe the next thing you like.

With respect to skis, I have the same issue every year with a ride on lawn mower. Do I just pay someone weekly or buy one outright and do it myself? In this case I loathe mowing, so I don’t mind paying. But with skis it’s a question of just how much I’ll ski after this stretch, regardless of whether or not this stretch is 1 or 20 days. Because there are additional costs (and benefits) to ownership beyond the initial purchase.

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eterm 4 days ago | parent | next [-]

It's known to wikipedia as the "Secretary Problem":

https://en.wikipedia.org/wiki/Secretary_problem

The optimum is actually based on 1/e rather than 1/3 but 1/3 is a good enough practical approximation.

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svat 4 days ago | parent [-]

In the secretary problem, you're trying to maximize the probability of selecting the absolutely best candidate. In other words you assume that you “win” if you select the best candidate and “lose” otherwise (even if you end up picking the second best who is almost as good!), and you're trying to maximize the probability of winning. (The optimal solution says you can win with probability 1/e ≈ 37%, meaning that ≈63% of the time you lose!)

This has always seemed the most unsatisfying assumption in the problem to me, with application to no real-life case that I can think of. The Wikipedia article has some stuff on relaxing this assumption, in its section titled “Cardinal payoff variant” (it seems that the optimal at least under one set of assumptions is √n rather than n/e, though those assumptions also seem unrealistic): https://en.wikipedia.org/w/index.php?title=Secretary_problem...

	▲	pge 4 days ago \| parent \| next [-]
		I would add that (having simulated this problem in code myself), the reason you have bad outcomes is that you run out of candidates and take a bad one because you have no choice. In real life, at some point you would grab a decent candidate even if s/he were not as good as a prior passed candidate. It is also true that even under the original assumptions, there is a wide range of thresholds around 1/e that yield a similar outcome.
	▲	recursivecaveat 4 days ago \| parent \| prev \| next [-]
		I think most people learning CS101 will at some point attempt to merge-sort a stack of physical papers alphabetically, and give up half way through. Everyone should have this experience: it teaches a lot about the importance of assumptions about the problem. Not to say that the math isn't important, but you have to think critically, because spherical cows are pretty rare.
	▲	borroka 3 days ago \| parent \| prev [-]
		It also assumes that the sequence is random and that there is no a priori information about the quality of the candidates. A similar problem occurs in dating today, when people tend to dismiss the current option in the hope or expectation of finding someone better later, intuitively treating it as a secretary problem. But too many people fail to take full advantage of the knowledge they have of themselves and the type of partner they can attract, of the dating market and of the world in general, and end up bitter and disappointed and victims of their own poor choices.

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svachalek 4 days ago | parent | prev | next [-]

Interesting. I once read somewhere that you should date at least... 6? people and leave before it gets too serious, before settling down with anyone. It seemed to imply there was math involved but it didn't explain. I think it must be the same statistics here, with some estimate of how many people you could meet and burn through without getting too old. I think people just don't really work this way but otherwise it makes some sense.

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fastasucan 2 days ago | parent | next [-]

I highly disagree with this, whats the point of dating others if you are perfectly happy with the one you are dating right now? Do you really lose out in life if there might be someone "better", even though you are happy?

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4 days ago | parent | prev | next [-]

[deleted]

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andai 4 days ago | parent | prev | next [-]

I've seen stats that correlated number of previous partners with divorce risk. But I always wondered if that was a correlation rather than causation (i.e. both of those factors sharing underlying causes).

An obvious example is that a person from a culture where sex before marriage is unacceptable is also from a culture where divorce is frowned upon.

	▲	paulryanrogers 4 days ago \| parent [-]
		Someone from Uzbekistan told me that a girl can only date one man, and must marry him or her reputation is ruined forever. So when her now-husband wanted to date her, he had to take care to avoid making it official before they were sure to marry. The US has a lot of subcultures, so I too doubt the usefulness of such studies. Then again, for some leaving the subculture they know carries a very high social cost. Hopefully new generations will break some of these barbarous traditions.

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tomr75 4 days ago | parent | prev [-]

it depends on how many people you expect to date in your lifetime though

these days with dating apps can prob date way more than 18..

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pmalynin 4 days ago | parent | prev | next [-]

I think it was 1/e but close enough (37%)

https://en.wikipedia.org/wiki/Secretary_problem#1.2Fe-law_of...

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jedberg 4 days ago | parent | prev | next [-]

Some would say this advice applies to finding a spouse as well. Date 37 people and keep track of the best. Then marry the next one that's better. :)

	▲	unixhero 3 days ago \| parent [-]
		Marry the next one that tangents the best experienced after 37 (or other optimal number).

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david422 4 days ago | parent | prev | next [-]

> I have the same issue every year with a ride on lawn mower. Do I just pay someone weekly or buy one outright and do it myself? In this case I loathe mowing,

I bought mine, ran great for 4 years, then ran into a bunch of trouble, which made me recognize the other hidden cost of ownership is simply just maintenance. A very expensive mower just sitting there, nearest potential repair shop far away, no idea how I'd even get it there let alone the cost. And if I decide I don't want it, I've got to pay to get rid of it now too.

Luckily I was able to watch a bunch of youtube videos and order myself some parts to get it up and running again, but definitely sunk quite a bit of time and energy into it.

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theoreticalmal 3 days ago | parent [-]

I just scrapped an ICE mower for a battery powered one. No more winterizing, changing oil, or worrying about filling with gas. I still don’t like mowing, but it sucks a little less now

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IncreasePosts 3 days ago | parent | next [-]

Sure, but you're just deferring moderate yearly maintenance cost for a rig that will need to be totally overhauled in 5 years due to battery degradation with current battery tech offered in mowers

At least, that's the conclusion I came to this year when researching ride-on battery mowers vs ICE. Electric push mowers seem like a no brainer though

	▲	namibj 3 days ago \| parent [-]
		LiFePO4 will be even cheaper in 5 years, so go for it and have a project for then?

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david422 3 days ago | parent | prev [-]

That's actually the situation I was in though. When your electric mower breaks you're probably on your own. I would not want to go back, but going forward definitely has it's own issues.

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mitch_f 4 days ago | parent | prev [-]

Derek Muller did a good overview of this concept on his Veritasium channel: https://www.youtube.com/watch?v=d6iQrh2TK98. Even more interesting for HN is a link in the description to one of the speaker's (Tom Magliery) websites: http://www.thirty-seven.org.