Posts from Reimian Empire Auto-translated

Wait. Let's use a revolver as an example. I have one bullet. I spin the cylinder, then shoot myself in the head. I don't die. I spin the cylinder again, shoot myself in the head again, and still don't die. What's stopping me from spinning the cylinder and shooting myself for the rest of my life without ever actually dying? What's wrong with my example?

That's correct. The probability will approach one, but it will never actually reach it. As Uran wrote, after 100 readings, the probability of dying is 99.6%. After the 686th reading, it will be 99.9999999999999, and so on (my phone can't calculate further than that).

Even if you read it for the sake of role-playing, why would you reread it later?

You could play a kind of "Arena Roulette" with someone this way.

Wait. Let's use a revolver as an example. I have one bullet. I spin the cylinder, then shoot myself in the head. I don't die. I spin the cylinder again, shoot myself in the head again, and still don't die. What prevents me from spinning the cylinder and shooting myself for the rest of my life without ever actually dying? What's wrong with my example?

Yes, everything is as you said. A twenty-round revolver with one bullet.
In principle, nothing prevents you from surviving until you die a natural death.
Let's calculate: suppose you have 10 years left to live, and you can shoot (taking into account breaks for sleep, food, finding bullets, etc.) once a day.
That is, even assuming that there are no more than 365 days in a year, you have 3650 attempts to die. Each time, you need the cylinder to be empty, and there are 19 empty chambers out of 20.
0.95^3650 = 5 * 10^-82. That is, the chances of surviving are not just small. They are very small. It's like the chance of finding a specific water molecule in 63 liters of water.

So, does the probability increase due to the increased number of attempts?

Yeah, that's true. If you roll a thousand dice (or roll one die 1000 times, which is essentially the same thing), then one of them is bound to be a six.

But in Revan's case, it might be that after drawing a white ball once, you somehow "recognize" it when you draw again, so increasing the number of attempts won't help.
Or maybe the revolver is slightly broken, and every time you spin the cylinder, you end up with the same empty chamber.
In that case, increasing the number of attempts is pointless.

due to the increased number of attempts?

The key word is: successful attempts. In general, the probability itself always remains unchanged, set in advance. Everything else is just deviations from the norm, which are balanced by its arbitrary fluctuation in either direction. In other words, it only changes for you personally at this specific point in time relative to all previous attempts. A probability of 5% means that, ideally, out of one hundred people, five will go to the next world, that is, every twentieth person, and this truth will not change much. Well, yes, once four people will die, another time six, it doesn't really matter. However, if only two people have died before you, and you are the ninety-ninth, your chances are not very good, although they exist. The more the total number of attempts (regardless of the result), the stronger the probability will tend towards its initially set value. In four coin flips, you may get one side three times, but this will not mean that the real probability of it appearing is 75% to 25%, whereas with a million flips, the deviation from the norm will be very small, something like 50.1% to 49.9%. We are talking about the increase in probability in your situation only due to your incredible luck, because of which it naturally begins to grow in order to finally get rid of you and return to the required 5%. And only the notorious factor of supposedly possible "infinite" luck prevents it from guaranteeing your death.

Actually, when the outcome of previous attempts is known in advance, the chance for a new attempt is basic, 5%.
If two out of 99 people who read it died, then the chance of the hundredth person dying is 5%. It doesn't increase because these events are independent.
What dependent events are – Google "Monty Hall problem".

when the outcome of previous attempts is known in advance, the chance for a new attempt is basic, 5%.

No, you are wrong if you mean the object itself; what if it has already produced the same result a million times? If you mean the overall chance for an independent observer, then yes, but this only confirms what I said.

If two out of 99 readers died, then the chance of the hundredth dying is 5%. It does not increase, as these events are independent.

I don't remember exactly, but in any case, are you saying that if ninety-nine people flip the same (and this is important) coin and it lands on tails, will the probability for the last person still be 50%?

suddenly, he had thrown the same result a million times before this

The funny thing is that it doesn't actually have any effect.
It's a kind of cognitive bias. When throwing numbers 1-2 twice, we have a low chance of throwing a 1 twice, right?
1, 1
1, 2
2, 1
2, 2
Four possible outcomes. The probability of (1,1) = 1/4
But... if you've already thrown a 1... the possible outcomes are (1, 1) and (1, 2), the other two are impossible. So the probability of throwing a 1 again is 1/2, just like with an independent throw.

What are you even writing? I'm well-versed in the many theories and puzzles about the three doors, and I can even guess why they've become popular now, so it would be a sin not to use them in any situation. However, this is not the case here.
Nebok has read the book a million times and didn't die; the probability of dying next is almost one, as it was already confirmed on the previous page. Your case here is completely irrelevant, and you shouldn't try to fit it into a completely different situation.

Nebok read the book a million times and didn't die; the probability of dying next is almost one, as if it was confirmed on the previous page.

No! The probability that if you read a book a million times and die – is almost 1.
But – if you read the book 999999 times and didn't die, then the probability of dying on the millionth read – is still 5%!
See conditional probability.

You'll read the book a million times and then you'll kick the bucket.

You'll read the book 999999 times and still won't kick the bucket.

Oh Lord, now is the time to nitpick the inaccuracies in the wording, when I'm simply trying to explain something. Anyway, Nebas, if you're reading this, know that the more you read, the more likely you are to kick the bucket, and don't listen to these guys, they'll just confuse you and you'll lose your character because of them.

It’s obvious that if I flipped a coin and it landed heads up 19 times, the chance of it landing heads up on the 20th flip would still be 50%. So, read as much as you want, Nebok, the chance will still be only 5%.

Uran came and organized a mathematical congress here.