Wrath of Dagon

The same way you always do. P(A and B) means: "If I were to repeat A and B an infinite number of times, what fraction of the time would both A and B occur?" You are confusing P(A and B) with P(A|B). The two are not the same thing. OK, so it is a matter of definitions as you say. I can have just as consistent a framework if I define any past event as having probability 1. And you can say that unlikely events are occuring every time you draw cards by your definition. None of it matters in practice though, because the only events we should consider as likely or unlikely are the ones it's possible to bet on, for the lack of a better definition. For example, saying some unlikely sequence of cards will happen does nothing to enable you to bet on that sequence. Saying a particular sequence (or a set of sequences) will happen enables you to compute odds and bet on that sequence and see if you've won or lost once the trial happens.

OK, so you say probability of P(A and B) is always P(A) * P(B). So given that A has already happened, how do you compute P(A and B)?

So every time you draw five cards a very unlikely event occurs. You have a very strange definition of "unlikely".

No, I'm saying for two independent events A and B, if you want to calculate P(A and B) before the trial, it's P(A) * P(B). If you know A already happened, then it's 1 * P(B) = P(B). If you have a formula for calculating the chance of a hand in Blackjack, and you need to calculate the odds knowing that certain cards have already been discarded, you would just substitute 0's for the cards already discarded, not derive a brand new formula just for that situation. As far as an event being a particular sequence, that is only true if the sequence can be defined before the trial, because if you can define it, the odds can be calculated. Otherwise it's just "some sequence" and it only becomes defined after the trial, and the chance of getting that sequence during that particular trial is 1, because it already happened. (and the chances of "some" sequence are also 1, which is how they're related)

So you're saying you guessed 1 number out of 37 correctly 9 times out of 10? That is indeed incredible and I have to admit I was wrong about low chance events not happening. Too bad there was no money involved, but of course it never happens then, heh. That's just wrong, sorry, the event that occurred had a probability of 1 of occurring, as I said. You're going back to the irrelevant debate of definitions. I'm going to define probability in this way: "if I were to repeat the experiment an infinite number of times, the probability of this result is the fraction of the time that this result would occur." This is a perfectly valid frequentist definition of probability, and as you can clearly see, when probability is thus defined it certainly does not "become 1" after an event has occurred. The experiment in this case is drawing several cards from a deck. The result is the exact sequence that I first got when I drew cards from the deck. It should be obvious that if I were to repeat that experiment an infinite number of times, that specific sequence would not come up 100% of the time, thus saying that the probability of that event is 1 because it already happened is complete nonsense with that definition of probability. I've gone over this several times in this thread, and this is the last time. No, I meant the probability of the event was 1 because the probability of drawing some sequence is 1, not because it already happened, although these things are related. As far as definition of the probability of a past event being 1, that's required by the probability theory I'm familiar with, don't know which one you're talking about, if that's not the case, how do you compute the probability of two independent events, one of which has already happened?

That's just wrong, sorry, the event that occurred had a probability of 1 of occurring, as I said.

Sounds quite non-sensical, don't see the appeal of watching a dream, but it's getting rave reviews.

OK, I understand that's your position, there's no point in repeating it ad infinitum.

Here's the actual Bio thread in question: http://social.bioware.com/forum/1/topic/14...209421&lf=8 (from Game Banshee)

Are those the only developers you buy from?

How do you know which ones those are?

http://www.gamasutra.com/view/news/29292/A...Happy_Place.php Some of the comments are quite interesting too.

See my edit in the post you're quoting, I took most of that back already. I still want Wals to verify we understood him correctly, because indeed what he seems to be recounting would be like someone buying a single ticket and winning the lottery, then buying another ticket and winning again. As far as the aces example, I stand by what I said about a certain set of sequences being far more likely than another set. Exactly, that's the crux of the matter. The event that happened is that you drew a sequence of cards, and the probability of that event is 1, because you have to draw some sequence. Had you predicted that exact sequence, then the event would be you drew a specific sequence, with the huge odds.

Meh, if he was the real Darth Vader, he'd have used a lightsaber and force choke, not a gun. Lame.

OK, but you're assuming that it's I who's misunderstanding and not Calax, which you really can't judge unless you understand the issues involved. The real reason the posts have gone nowhere is there's a fundamental disagreement on what very small probabilities mean in practice, and this issue doesn't seem like it will get resolved here.

That's funny, you yourself admitted you don't know much about math, yet feel entitled to critisize both my understanding of math and of English. See, that isn't actually a criticism. It is a simple statement, one which you decided not to refute. My math skills may be weak, but I am a confident English teacher, and your writing has flaws. It could be a number of reasons, but being an English language learner is nothing to be ashamed of. I also recall something about you being from another country and becoming a US citizen after birth, but I could easily be mistaking you for another poster. No, you're not mistaken, but why don't you point out the flaws in my writing instead of critisizing my math, which you admit you don't understand?

No, if you can define a set of sequences, you can calculate the probability of the set instead of an individual sequence. Thus a set of all possible sequences is much larger than of the set of sequences with the same rank repeating, thus you're much less likely to see something from that set than from the universal set. That's funny, you yourself admitted you don't know much about math, yet feel entitled to critisize both my understanding of math and of English. I'm not claiming the probability is actually 0, I'm saying it's practically 0 for a single trial. For a million trials it is indeed significant. What's theoretically possible isn't necessarily practically possible, but we just keep going around in circles on this.

I never claimed it does, you keep arguing against something you think I'm saying instead of what I'm actually saying. As far as Wals's sequence, those would only be the odds he first predicted that specific sequence, getting some sequence means nothing since you'll always get some sequence. The only way this wouldn't be true if you pulled some pattern that's much rarer, like your example of a 100 Aces from 100 decks of cards. Any sequence of only one value would be much more rare than a sequence of mixed values, thus the odds that you'd pull all the same value instead of mixed would be appropriately lower. Edit: Actually I take that back. If I understand you correctly and you actually got the same number 7 times in a row, those are indeed incredible odds. I would have to assume that either the roulette was fixed, or everyone was too drunk to know the difference.

Yes, he did use p in the formula instead of a number, I didn't pay attention to that. He should be able to assume a probability of the lottery (it's usually twice the jackpot she won) and replace 100 with the total amount of money she spent playing the lottery, but we can only guess what that is. nvm, that's what he did anyway, I didn't quite realize he was just changing p in my original reply. Edit: You still don't seem to understand that what's relevant is someone in the pool of possible winners winning, not an individual person winning. And individual odds are not 1 in a million, for example if each spends $100,000 playing, the odds go from 1 in a million to 1 in 10.

Which math is that? The one you just invented?

Well, I'd like to see an example of something incredibly unlikely happening on the first trial. And we're going back to the same argument. Yes, it's just as likely to happen on the 1st as on the millionth, but it's hugely more unlikely to happen on one specific one (1, 2, 1000000) than it is on any of the million attempts. Edit: Probability is about prediction. I can confidently predict if will not happen in one trial. I can confidently predict it will happen in 100 million trials, but I can not predict on which one.

Yes, but what I was saying if an event has a 1 in a million chance for all practical purposes it will not occur in a single trial. However, it will almost certainly occur in millions of trials. I understand some people believe it can still occur in a single trial, but I don't, and this thread illustrates that it's useless to argue about.

If you're saying the chance of "you" winning is worse than the chance of "not you" winning amid players of the lottery than that's true. Yes, that's what I've been saying for more than 20 pages. I keep making the distinction between a specific individual and someone at all in the entire group, but it just doesn't seem to be getting through. Oblarg is right, except I don't understand why that's irrelevant. But may be it's best not to get into that again. @Wals: My point for this thread was to come up with a solution for how someone could've won the lottery 4 times. I think I showed a while back that the chances of someone winning are not as great as I previously thought, but could plausibly be quite reasonable. If there's some other point I'm missing, please explain what it is.

No, that's what you're saying I'm saying. I don't know why you insist on arguing about something you clearly know nothing about.

That's not what I'm saying at all, I don't even know what that means, you're talking gibberish again.