Oblarg

Pitiful. On a somewhat related note, I saw Fates Warning back in June and they played a nearly 2-hour setlist indoors in ~110 degree heat. No complaining from them, though the bassist did have a towel to mop the sweat off his instrument after every song.

American Kenpo, I believe.

What a terrible book that is. First time I read it I thought so. Then I realised that it's excellent... because it's so bad precisely because the protagonist has no emotions. No, it's bad because the writing style is inconsistent at best and completely incoherent at worst. It's even worse when Camus just abandons all remnants of his esoteric writing style and starts preaching at the end.

Blizzard RTS: tabclicktabclicktabclicktabclicktabclick For my RTS needs, I think I'll stick to SoaSE. Micro sucks. I'll buy SCII if (and only if) the modding community is active enough to make it worthwhile in bnet. If it just ends up being DotA 2.0, I'll pass.

What a terrible book that is.

**** yeah, Armored Saint

I found DA:O to be the exact opposite of fun, tbh. I recently tried playing through it again, and lost interest even earlier this time.

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.

Yes. It's a concept you have to be able to grasp if you're going to understand statistics. You have many mutually exclusive outcomes with tiny probabilities that add up to 1. Every time you get a specific outcome, it was a very unlikely outcome, yet you will still *always* have an outcome. Now, admittedly, in a situation like this the probability of each specific outcome isn't particularly useful - most of the useful information you can gain from this system revolves around operating with a specific class of outcomes.

Nope. The probability of P(A and B) is always P(A) * P(B). If A has already occurred then the question is now P(B|A). P(A) remains unchanged. And the sequence existed before the trial. It makes no difference if I had it written down on a piece of paper or not. It is still a unique sequence. You don't seem to quite grasp the idea that the probability of "some sequence being drawn" is 1 because the probabilities of all unique sequences add up to that, and they are not independent. If you draw a sequence, the probability that you would draw that particular sequence is tiny, albeit somewhat meaningless as, as we have established, it's not a particularly significant sequence as it was not defined beforehand. The fact remains that a very unlikely event did occur.

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? Except you did not draw "some sequence" you drew a specific sequence. Whether or not you predicted that sequence before is irrelevant. As for the probability of a past event being one, that's not required at all - that's only required for a very narrow and rather bad definition of probability. It doesn't matter if one event has already happened, the probability of any given outcome is unchanged. Unless, of course, you're asking the probability of getting a specific result given that one occurs in a specific way, in which case you are defining the probability of the first event as 1. This is a completely different situation. Assuming A and B are independent events: In the first case, you're asking P(A and B) In the second case, you're asking P(A|B). The two are not the same thing. Now, going back to the deck of cards: Let's call our sequence of cards A. The probability of drawing A, regardless of whether or not A has already been drawn, is P(A). The sequence A is a unique sequence that existed before we drew any cards from the deck - whether or not we specifically predicted A is irrelevant. You, however, are making the mistake of treating the probability of drawing A as P(A|A), because we already know that A was drawn. This is faulty logic . When the cards were drawn, it was not a given that A would be drawn. You cannot revise the probability of A based on your observation of the result of A after you conducted the experiment. That's not how probability works. Once again, read my definition of probability and you'll see that the probability of an event in the past is certainly not 1.

John Arch mentions the vulture on at least two tracks. Though, making sense of his lyrics can be tough at times - he's a great lyricist, and most of his songs are pretty clear if you read through the lyrics carefully, but for the life of me I simply can't understand what The Sorceress is supposed to be about.

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.

The moon and the vulture thing? That just makes that album cover beyond art. The album cover for is just as awesome. If you look closely, you can even spot some repeated objects from the previous album cover.

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. In this case, there is no difference between theory and practice. A chance is a chance, no matter how low. It's nonzero, therefore it is possible. 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. Unfortunately, Dagon, that's not how statistics work. It is still a unique sequence of cards, whether or not he predicted beforehand what sequence he would draw. Thus, something with an "impossibly low" probability did occur. He did not only draw "a sequence of cards," he drew "that sequence of cards." The probability of him drawing that sequence of cards might be somewhat meaningless as you can't use it to make any meaningful predictions of conclusions, but it is still the probability of that event occurring, and that event did occur.

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. Dagon, claiming something is too unlikely to happen in one trial is faulty logic - if you believe that, you must believe that it is also impossible in any number of trials because you can break any number of trials into a sequence of single trials, thus leading to a contradiction. In short, anything with a nonzero probability can indeed happen in one trial. It may be very unlikely, but it is possible.

It can. Anything with a nonzero probability is effectively possible, however unlikely. That's not a question of belief, that's a question of mathematics. You have to remember that the distribution is random - an unlikely event is just as likely to happen on the first attempt than it is on any other. And, beyond that, there are plenty of events that fall into the "drawing a sequence of cards from a deck" model in which something incredibly unlikely happens on the first trial, always, because the only possible outcome is going to be incredibly unlikely if you take the probability of that specific outcome occurring. Yes, that probability is effectively meaningless, but the fact remains that something with that extremely low probability did indeed occur. The important point is that, in this case, the chance of it happening legitimately is negligible compared to the chance of it being fraudulent, which I have been saying from page 1.

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. I think the point is that your original assumption that something can be so unlikely that it couldn't possibly happen is absurd because extremely unlikely events happen all the time, especially in the case of lottery winners in which pretty much any outcome can be made arbitrarily unlikely up to the somewhat meaningless point of "the probability of this exact outcome."

Guys, Dagon is correct when he says the probability of "a person winning four times" is different than the chance of "this person winning four times." This should be obvious to anyone who has taken statistics. The main issue is that, while this is true, it's also irrelevant. I have explained why earlier in the thread.

Well, I saw Iron Maiden last night. Dream Theater opened for them, and really, I can't stand James LaBrie's voice - especially live. He sounds like he's whining. Iron Maiden was fantastic, though.

There's no sinking to anyone's level anymore - as far as I can tell, the argument is over. It looks like you're just sticking around and taking potshots at WoD, which (and mind you, I usually don't agree with WoD on anything) just makes you look bad.

I really don't think it was supposed to be interpreted as being that close of an analogue to real-world events - yeah, the "middle eastern terrorists but with a twist" plot has been beaten to death, but I really doubt the game was intended to indicate that the US is behind Al Qaeda. I'd give AP an 8.7/10 - for reference, I'd give ME1 a 9/10 and ME2 a 7.5/10.

You're right that 4 pre-selected individuals each winning once has the same odds as 1 pre-selected individual winning 4 times, but that's not what we're talking about here. We're talking about a non-pre-selected individual somewhere in the world winning 4 times. That is not the same as 4 non-preselected individuals somewhere in the world each winning once. Do you see the difference? Edit: Btw Oblarg, I do have to congratulate you on applying the Binomial probability correctly, even though you figured out the wrong probability. You, Balthamael and Amantep are the only guys arguing with me who've shown any understanding of probability at all. The others are a lot better at insults than math, and should be ashamed of themselves. That's meaningless, though - you just have to multiply by the number of people playing the lottery. It's still an arbitrary group of people - the only significance once person winning four lotteries has is the information that it was most likely a scam. The thought that unlikely events cannot happen is absurd, because unlikely events happen all the time. You can create any arbitrary class of outcomes with an absurdly low probability to which the actual result belongs and claim that "this could not happen, because the probability is too low" (the logical extreme of this is what I did above - the chance of that specific outcome alone). The class of outcomes in which one person wins four times is just that - an arbitrary class of outcomes.

Why are you guys still arguing that definition? It's irrelevant. The fact is that you can point to any four lottery winners and claim "the probability that these four people would win is so small that it could only have possibly happened due to supernatural forces," which is exactly equivalent to saying "the probability that this person would win four lotteries is so small that it could only have possibly happened due to supernatural forces." The math is identical, as I have shown above - all the math cares about is that it is a unique group of four successes. As no one would claim that the fact that four specific individuals won four lotteries is proof of god, this argument is pointless.

Wrong, this is a binomial distribution. The actual probability if she buys 10,000 lottery tickets (which is an awful lot, it's probably more around 500) would be: (10,000 choose 4)(1/10million)^4(1-(1/10million))^(10,000-4) = 416416712497500 * (1/10000000)^4 * (9999999/10000000)^9996 = 4.16001x10^-14. This is completely ****ing irrelevant, though. If you actually understand the math, you'll see that this is simply the probability of four lotteries being won from a pool of 10,000 tickets, each ticket having a chance of winning of one in ten million. It does not care if the lottery tickets were all bought by the same person. This pool of 10,000 tickets is being arbitrarily decided because we like to think that there is something special about the same person winning each lottery. In actuality, you could construct an identical arbitrary pool of 10,000 tickets for any unique group of four lottery winners and claim that an equally unlikely event has transpired - I'll demonstrate this with a simpler situation below. Perhaps an easier way to demonstrate why this argument is pointless would be to assume that each player buys exactly four lottery tickets. In this case, the probability of one player winning four lotteries is simply (10^-7)^4 = 10^-28 (which, if you notice, is lower than the actual probability we calculated above). Surely this occurrence is impossible, if the chance is so low? Well, no, not really - by symmetry, this is the exact same chance as any outcome in which there are exactly four unique winners, regardless of whether or not the winner is the same person, because each unique combination of four winners results in four successes out of a pool of four tickets - the exact same situation as one person winning four times. Math does not care who holds the tickets - this is simply the human tendency to think that there is something significant about one person winning four times. It's an emotional response, not a logical one. The argument that "that event already transpired, thus the probability is one" is also irrelevant, as one can simply define probability as "the fraction of successes if the experiment were repeated an infinite number of times" instead of "the fraction of the time that the experiment succeeds," as obviously with the latter definition asking the probability of something which has already succeeded or failed is meaningless. This is a pointless debate of definitions which has absolutely no bearing on the issue at hand. Can this discussion please die now?