Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The Ski Rental Problem

lesves.github.io

Post reply on HN
Print view View original

41–50 of 98 posts

Re: The Ski Rental Problem

#41

Post by jedberg »

massung wrote: post #15

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…

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. :)

Re: The Ski Rental Problem

#42

Post by Noumenon72 »

lisbbb wrote: post #13

Oh man, I had no idea that the decision of whether to rent or buy skis required calculus to solve. I just figured that if you ski more than say, 3 times a season, it's probably better to own your own gear for reasons unrelated to the entry cost, but more to do with comfort, tuning, quality, and so on. Anyone who has rented skis knows that the rental fleets are trashed.

I have rented skis perhaps 70 times in my life and I have nothing bad to say about them. Maybe a broken buckle once or twice.

Re: The Ski Rental Problem

#43

Post by robocat »

RealStickman_ wrote: post #34
xandrius wrote: post #31

Earlier quoted context omitted.

Buy second-hand and worst case resell. Best of both worlds.

In many stores you can ask for "test skis". These would have been used for a few weeks as rentals and you usually get a significant discount from the normal retail price

You also get 'test bindings' that both toe and heel can be shifted forward/back to adjust to fit most boots. Disadvantage: weight. Advantage: adjustable.

On normal bindings the toe is often screwed in at one location to fit your boots and cannot be shifted later.

Re: The Ski Rental Problem

#44

Post by svat »

eterm wrote: post #19
massung wrote: post #15

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…

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.

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...

Re: The Ski Rental Problem

#45

Post by Daviey »

SteveNuts wrote: post #27
Cerium wrote: post #23

Earlier quoted context omitted.

At least yours are in the garage. I have a friend who spent years storing a couple of hundred dollars of outdoor gear in a rental storage locker costing $50 per month.

I have relatives that have spent $60/mo for a storage unit for 12 years for some furniture they "might want to use some day if they buy a new house". Even pointing out that the furniture will likely look extremely dated by now and they've spent almost $10k so far doesn't seem to click at all.

But now it's a sunk cost, might as well keep it going, right?

Re: The Ski Rental Problem

#46

Post by matchagaucho »

gyomu wrote: post #38
matchagaucho wrote: post #21

Every time my wife brings up the skis collecting dust in our garage, I’m reminded of the S.K.I. model — Storage Kills Investment.

> the S.K.I. model — Storage Kills Investment What is this? Google doesn't return anything for me...

/s

Re: The Ski Rental Problem

#47

Post by SteveNuts »

Daviey wrote: post #45
SteveNuts wrote: post #27

Earlier quoted context omitted.

I have relatives that have spent $60/mo for a storage unit for 12 years for some furniture they "might want to use some day if they buy a new house". Even pointing out that the furniture will likely look extremely dated by now and they've spent almost $10k so far doesn't seem to click at all.

But now it's a sunk cost, might as well keep it going, right?

Exactly! Why cut your losses now when it’ll surely pay off in 10 more years

Re: The Ski Rental Problem

#48

Post by mitch_f »

massung wrote: post #15

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…

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.
Post reply on HN