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.
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.
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...
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.
these days with dating apps can prob date way more than 18..
https://en.wikipedia.org/wiki/Secretary_problem#1.2Fe-law_of...
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.
What is this? Google doesn't return anything for me...
Renting skiis is okay. lets you try out a lot of different kinds. They all ride different
The best decision is literally a bunch of equations that you want to solve / optimize. It is sometimes school level math, but that's rare.
I was also delighted when I realized that instead of going through the hassle and cost of moving everything across the country, I could just sell it and buy roughly the same thing in the new place... again for net zero dollars! Teleportation!
You can avoid the depreciation issue with old skis, but that comes with other problems.
For hobbies, they say "buy once, cry once", but there are so many ways to be unhappy! I won't limit myself! I say buy all, cry all, and learn all the different ways to cry. I don't ski, but for the analogy, I'd try short ones, long ones, cross country ones, racing ones, red ones, blue ones, etc and then only buy really nice ones once I understand exactly what the nice ones do that the others don't. There's a good chance that I'll learn I like skis more than I like skiing, and that's okay.
It takes 10 minutes to walk home from the bus central. The bus is late but should be here any minute now. The bus takes one minute. Do you wait or walk?
You want to optimize for when you get home, not for your health or environment.
If the question was 1h+ then maybe the answer would be different.
There is a strategy that allows you to never be worse than 2x if you knew exactly when the bus arrived: Wait for 10 minutes, and if the bus didn't arrive, walk home.
In all cases when the bus arrives between now and in 10 minutes, you do the optimal thing, and whenever the bus arrives after 10 minutes have passed, you will be home after 20 minutes, which is not worse than 2x worse than optimal.
Could someone who groks this math tell me why not buy the skis once you’ve paid half their price on rentals?
Paying at 1/2 will be optimal if it ends before you buy, very bad (3x optimal) if it ends right after you buy, and slightly better than the solution in the post if it lasts at least twice that long (1.5x optimal vs e/(e-1)).
The metric in the post is just the worst of those ratios. Assuming the unproven statement in the post (that the solution which is a constant factor worse than optimal is best), any solution of the form you suggest is going to have similar tradeoffs. If we had a distribution, we could choose.
I would preach this with snowboard boots (+ helmet), made travel easier as well when you live nowhere near snow. Trying to take up skiing now and have no idea why I didn't think to do this with ski boots. Would probably help, a lot.
As for rentals it's easy to avoid beat-up janky gear. Have to go places just outside the ski town areas. Usually have to find a shop outside the resort for snowboards if you bring your own boots anyway, but easier to find better gear options. I remember getting a new (or basically new) K2 board from a general sports store in Reno, same for getting rentals in Queenstown or Denver or Vancouver before hopping on a bus.
Shops outside the resorts tend to have reasonably priced demo rentals, newer high end gear they are hoping you buy afterwards. Far better equipment that is nicely tuned than anything the resorts offer.
Not paying the oversize/ski baggage fee and lugging that gear around the whole trip while having quality rentals available levels the rent vs buy equation -- if buying a season lift pass makes sense so does buying your own gear, otherwise it's more hassle than it needs to be, imo.
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.
Maybe for us in the US, this is more equivalent to buying every year and then reselling? Haha.
Stop paying the SaaS tax.
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.
