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The Ski Rental Problem

lesves.github.io

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Re: The Ski Rental Problem

#51

Post by pge »

svat wrote: post #44
eterm wrote: post #19

Earlier quoted context omitted.

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% o…

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.

Re: The Ski Rental Problem

#52

Post by einarfd »

bee_rider wrote: post #20
comrade1234 wrote: post #2

Do like many people in Switzerland and just rent skis for the full season. That way you get a new pair every year. You should own your own custom-fitted boots though.

When people in the US think of rental skis, we think of weekend rentals that are usually not very specialized and pretty beat up. What you describe here sounds more like leasing a car vs renting one—technically a lease is a rental, but practically it is a bit closer to owning the thing.

Are you sure that there aren't multiple tiers of rental skies in resorts in the USA? I have friends in the rental business in Norway, and they rent out skies from the kind of beginner friendly skies that would fit your description. To top of the line Stockli and Van Deer kit. I think they keep all of their gear in at least decent shape, with the top gear kept in the best shape, as it makes the most difference for those customers. Btw. haven't rented much in the Alps. But my impression is that you can rent gear for all ability levels there aswell, and that that gear is kept in good shape.

Re: The Ski Rental Problem

#53

Post by speed_spread »

JohnKemeny wrote: post #36
xandrius wrote: post #30

Earlier quoted context omitted.

Always decide to walk, especially for just 10 minutes. Good for health, mental wellbeing and it's just easy. If the question was 1h+ then maybe the answer would be different.

It's a computational problem, I thought (mistakenly) that the HN crowd would understand.

Your explanation was too good, people go straight for the answer to your example. There might be a bit of cheekiness too!

Re: The Ski Rental Problem

#54

Post by _kyran »

Tycho wrote: post #49

Skiing is incredibly fun but I wonder if it should be put in the same category as cycling (on roads): too dangerous to be sane.

There’s a large spectrum between skiing on an uncrowded slope alone, a crowded beginner trail, hucking cliffs and backcountry in avy prone terrain.

I don’t think the risk profile can be all lumped together.

Much in the same way that cycling on the road has a different risk profile to on a bike path vs downhill or freeride mountain biking.

Re: The Ski Rental Problem

#55

Post by svachalek »

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…

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.

Re: The Ski Rental Problem

#56

Post by recursivecaveat »

svat wrote: post #44
eterm wrote: post #19

Earlier quoted context omitted.

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% o…

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.

Re: The Ski Rental Problem

#57

Post by [deleted] »

svachalek wrote: post #55
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…

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…

[deleted]

Re: The Ski Rental Problem

#58

Post by ip26 »

xandrius wrote: post #31
thrawa8387336 wrote: post #17

Rent until you know what you want to buy. Done

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

The second-hand market is a bit of a mess unless you're comparing among the most popular skis. The depreciation is also brutally steep.

You can avoid the depreciation issue with old skis, but that comes with other problems.

Re: The Ski Rental Problem

#60

Post by bee_rider »

einarfd wrote: post #52
bee_rider wrote: post #20

Earlier quoted context omitted.

When people in the US think of rental skis, we think of weekend rentals that are usually not very specialized and pretty beat up. What you describe here sounds more like leasing a car vs renting one—technically a lease is a rental, but practically it is a bit closer to owning the thing.

Are you sure that there aren't multiple tiers of rental skies in resorts in the USA? I have friends in the rental business in Norway, and they rent out skies from the kind of beginner friendly skies that would fit your description. To top of the line Stockli and Van Deer kit. I think they keep all of their gear in at least decent shape, with the top gear kept in the best shape, as it makes the most difference for tho…

I’m not sure there aren’t, in fact I bet there are! I’m just talking about the typical case that I think most people think of.
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