howrar

tldr: Always flip the switch

Edited with some of TauZero's suggested changes.

• Let N be the size of the population that the villain abducts from
• Let X be the event that you are abducted
• Let R be the outcome of the villain's roll
• Let C be the event that you have control of the real switch

• If 1-5 is rolled, then the probability that you are abducted is P(X|R∈{1,2,3,4,5}) = 1/N
• If 6 is rolled, then P(X|R=6) = (N-1 choose 9)/(N choose 10) = ((N-1)!/(9! * (N-10)!)) / (N!/(10! * (N-10)!)) = 10/N
• The probability of getting abducted at all is P(X) = P(X|R∈{1,2,3,4,5})P(R∈{1,2,3,4,5}) + P(X|R=6)P(R=6) = (1/N)*(5/6) + (10/N)*(1/6)
• The probability that a six was rolled given that you were abducted: P(R=6|X) = P(X|R=6)P(R=6)/P(X) = (10/N)*(1/6)/((1/N)*(5/6) + (10/N)*(1/6)) = 2/3

So as it turns out, the total population is irrelevant. If you get abducted, the probability that the villain rolled a 6 is 2/3, and the probability of rolling anything else is its complement, so 1/3.

Let's say you want to maximize your chances of survival. We'll only consider the scenario where you have control of the tracks.

• P(C|R∈{1,2,3,4,5}) = 1/10
• P(C|R=6) = 1
• P(C) = P(C|R∈{1,2,3,4,5})P(R∈{1,2,3,4,5}) + P(C|R=6)P(R=6) = (1/10)(5/6) + (1)(1/6) = 1/4
• P(R=6|C) = P(C|R=6)P(R=6)/P(C) = (1)(1/6)/(1/4) = 2/3
• P(R∈{1,2,3,4,5}|C) = P(C|R∈{1,2,3,4,5})P(R∈{1,2,3,4,5})/P(C) = (1/10)(5/6)/(1/4) = 1/3
• If you flip the switch, you have a 1/3 chance of dying.
• If you don't flip it, you have a 2/3 chance of dying.

If you want to maximize your own probability of survival, you flip the switch.

As for expected number of deaths, assuming you have control of the tracks:

• If you flip the switch, the expected number of deaths is (1/3)*1+(2/3)*0 = 0.33.
• If you don't flip it, the expected number of deaths is (1/3)*0+(2/3)*10=6.67.

So to minimize the expected number of casualties, you still want to flip the switch.

No matter what your goal is, given the information you have, flipping the switch is always the better choice.

Sure, cracks still exist, but I've stopped downloading them in favour of buying off Steam because the user experience was a lot better. I'm sure I can't be the only one to do this.

That's assuming there's a hard-coded limit. There very likely isn't, but things can break when you push the limits of software like this. You won't be able to easily see what those are by looking at the code.

I have torrents that have never completed due to lack of seeds and peers.

That's what failing means here. You know how you sometimes see a torrent site list a non-zero number of seeders but when you try to download it, you don't connect to any of them and it shows 0 seeders in your client? That's what happens when neither you nor the seeders have port forwarding set up.

What happens if you just let the leaves be? I would think that letting organic matter decompose on your lawn would be good because it provides nutrients for the plants underneath.

This just keeps getting more and more exciting every week. Literally every single QoL issue I've ever had is being addressed all at once.

Ah, okay. When I said "throughout the day", I actually mean throughout the day. As in making a large pot of rice in the morning and eating from that same pot for breakfast lunch and dinner. One of the main appeals of rice cookers is the ability to do that. It may not be recommended by food safety guidelines, but it's standard practice in any household that consumes a lot of rice and it's never been a problem.

What pressure cooker do you use? I just tried today with an Instantpot and the bottom completely solidified after a few hours with the rest of the rice turned into mush. This is with the keep warm setting.

Please tell me where I can be paid for publishing papers.

Depends on how you do the capture. If you need to engineer the system and feed it energy in a form that we can instead use to power other stuff, then yeah, it doesn't make sense. But if you for example, plant a tree, then that tree would use energy from the sun that you wouldn't otherwise be able to use as easily.

I don't know enough of these words to think it's made up.

Uh.. what? This is a fructose molecule