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Vaniver comments on The wandering rationalist - Less Wrong
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My favorite way to cross the US, especially if you're not in a hurry, is by Amtrak train, though I don't have too much experience with buses (Amtrak or otherwise; I've taken one Amtrak bus and no Greyhound buses). Train tickets tend to be cost-competitive with bus tickets, except that the routes are way more limited. (Their train route map is here, and so you can see that going from Minneapolis to Oklahoma City requires going east then south then west then north, rather than just south, but you may end up having to do similar things on buses.)
If you're old enough, renting a car might be a good option, especially if you want to do a lot of touristy stuff.
I've done Amtrak before and I quite liked it. What I'm wavering on is whether to buy the $450 30-day bus pass which allows me unlimited travel for that period or be a bit riskier and hope I'll find enough rides to get me across for cheaper. I need to sit down and do the research and the maths really.
I can rent a car for sure (I'm 31) but I haven't driven in ten years and considering it'll be December I'm not confident in my driving ability in bad weather conditions...
Interestingly, there are two ways to do this and I'm not sure which is better. The first is estimating a probability that you'll be able to find a ride across any particular arc, and then calculating the cost (and stopping and buying the pass if it's more than $450/(1-p)). The second is calculating the cost C, and then asking "is p>(C-$450)/C?" (Both assuming risk neutrality.)
If Ridejoy publishes any numbers about success rates, then the first is probably the better choice, but if you're guessing, it might be psychologically easier to do the second (though it also puts you at risk for anchoring).
Wise choice!