A this point i believe i have plenty of justification to call you alot of nasty things, but ill try to refrain from it.
Used for emphasis. Which is needed in some cases.
Thats where you fall flat on your face. Like Vasili so correctly wrote, the chance of getting ANY combination of results are exactly the same for all results.
It doesnt matter how high the odds are, i might get that trillion to one odds combination NOW and then never AGAIN.
Or i might get a certain combination the last time i ever throw dice, or i might never get it.
Or i might throw the same "impossible" combination twice in a row.
Of course it is. But unlikely /=impossible. Thats a simple fact, live with it and stop coming up with stupid rants about how wrong i am, when im not.
Considering how you try to "correct me" without knowing what you´re babbling about, maybe you should just STFU?
No, people like you deserve it.
From what i can see there are two people in this thread who doesnt understand why the "impossible" happens thousands of times each and every day, and since you´re capable of showing off with "combinatorial probability", you just proved yourself a real donkeyfarm, since you came up with your BS after a halfdozen posts had already been made more or less clearly on how it actually works.
The chance of getting the above combinations are exactly the same.
Hell no it isnt! Not even close.
sigh
No im not exaggerating. More like the opposite. As i took an example i could specifically remember.
And again you fail to understand that yes it just not CAN be, it IS. Happens every day.
Because wether the combination is good or not, its a thing we tack on afterwards, it has no relation to the dieroll.
Oh and btw, in A&A, rolling low is best possible(except when developing). Which is why you remember rolling a lot of 1s, especially if said rolls involve attacking with infantry which only hits on 1s and nothing else in attack.
Except i could potentially see it a hundred times, while you and another 100000 people never see it happen.
Complete BS.
I already touched on the subject with one while i was at school a bunch of years ago.
He does not share your view.
They dont? LOL...
The best math teacher(and in physics and chemistry) i ever had, started his first lesson with every new class with "a problem" for the class to try and solve... With my class the problem was an absolutely perfect mathematical proof that the earth was flat. And then asked that considering what we know, what was wrong with it.
Ten minutes later or so he gave the answer that noone had come up with, the simple fact that the proof itself wasnt flawed in any way, it just wasnt true. And then spent the rest of that lesson going through how he had managed to construct it without "breaking" anything. Wished repeatedly i had the foresight to copy that, but no such luck...
Math is perfect, but numbers can always lie nevertheless.
Thats "redneck" reasoning.
Proof is either proof, or it is NOT. You can have indications or support for a thesis, theory etc, but if you have proof, then its proof.
True, but only one of those three usually attracts attention.
6 to the 18th power is, inarguably, huge, but not so huge compared to the number of times dice are rolled in the world every year.
DW's point is that things happen, they just do. Get used to it. Dice, cards - if it's possible, and you play a lot, it will happen, and you might even witness it, even if it's unlikely to happen and one would never "expect" it.
Personally, I find stangers' discussions of "amazing" die rolls quite dull - it's like hearing someone relate the best poker hands they were dealt, or the worst, or how they once threw a ball ~exactly~ where they wanted to... yeah, and your point is?
I had a friend who was in a car accident - more of an "incident". He had a tire blow out at very high speed - the car jerked, and he oversteered the other way. As it started to spin the other way, the (now leading) metal wheel edge caught hard and pitched the spinning car - so that it did a complete flip and complete spin, and landed rightside and going straight again on all 4 tires, blowing the other 3 tires out, and he was fine. And when the cops came, the only proof was that that one wheel was bent in, all 4 tires were flat, the skid marks stopped and then started again after 50 feet, and the cargo rack on top of the car had been scratched and bent on one corner. Not another mark on the car. That's at least 18 sixes worth of improbable.
Weird stuff happens. Not often, but life is long, and there are a lot of us out there. Sorry to rain on anyone's parade, but anyone should know that.
Direwolf, you are becoming unnecessarily rude and aggressive. Let's try to keep this civil, please.
Obviously that is the case, but that misses the point entirely. The odds of getting a sequence which might strike one as in some way remarkable (all numbers the same, increasing or decreasing sequences, repeated sub-patterns, your telephone number, etc.) are far more than the odds of any particular sequence. Getting some kind of pattern is not necessarily all that noteworthy. However the 18 6s is not merely a remarkable pattern; in the context of the game it is also the qualitatively best (luckiest) outcome. This is the difference between throwing ten darts at a dart board and having them all hit different places in some recognisable pattern, or having them all hit the bullseye. Choose any sports metaphor you like. A hole-in-one is just as likely as having your golf ball land at any other specific spot on the green. Yet a hole-in-one is generally celebrated as a very rare, lucky feat, because in the context of that game, in the hole is the qualitatively best place for the ball the end up.
So how often do you think it happens then? Let's see some numbers here.
But this IS something we know in advance. We know in advance that (in most games) a six is best and a one is worst. Any kind of pattern is irrelevant; what matters is the number of best outcomes.
No you couldn't. If you want to see something with a chance of 100 trillion to one 100 times, then you need to witness it approximately 10,000 trillion times. This is basic statistical theory (look up binomial distribution).
LOL. My statement is patently true. Why has no-one ever managed to catch a falling meteorite in their hand? Why has no-one ever drowned in kumquat-flavoured yoghurt? Why has no-one ever won the lottery jackpot for ten consecutive weeks? Why has no-one ever rolled thirty consecutive sixes on a (random) dice, or flipped 100 consecutive heads on a (random) coin? Because the odds of these things happening are absurdly low.
Feel free to discuss these specific claims at, say, talkstats.com. That way, we can all see what the experts think and whether they believe you (hint: they won't).
Looking it up, I see that that particular quote is attributed to a professor of sociology and traces back to the thinking of the philosopher David Hume, who was sceptical of claimed miracles. Hardly "redneck reasoning".
In the context of this quote, "proof" means "evidence" - it's not talking about a mathematical proof. It means that the more unlikely the claim, the more compelling the evidence needs to be. So, for me to believe that (e.g.) Kim Jong Il really shot 18 holes-in-one in a single round, as is claimed, the evidence needs to be REALLY good.
I agree that he should calm down. But dude, you flat out called him a liar and a cheater and tried to brush it aside with the words "no offence". You owe the man an apology. And the more you fight to prove your esoteric point abbout probability, the worse you are making it.
And I still don't believe you at all. The more I think about it, 18 "6's" is not that absolutely bizzare. It is strange and mst uncommon, but not so bizzare that you needed to impune the man's character. I once rolled 9 "6's" while playing risk. I saw a craps shooter make his point over twenty times in a row (which is way more statistically abnormal). In old D&D, I saw a guy roll a 20 three six times in a row (and it was my die he used, he was not a cheater).
As "improbable" as it might be, it is not "imposible". I feel you ow DW an apology.
But I really don't care if you give him one or not. Just stating the facts
And my point is that some things don't. In cards, have you ever seen four players each dealt a 13-card hand consisting of a complete suit? I would be surprised if you had, because the odds are much smaller than a trillion-trillion to one. I mean, that's like really small. Reeeeaaaaaaaaallllly small. If you witnessed such a thing, you would be a fool not to think that the deck wasn't rigged.
AP - um... I think 1) you have mispoken, because 2) I think you know better than this.
That's like saying that you need to witness a single d6 approximately 6 times to see one result of "6", which is not the case.
I forget my stadistics, but there's a formula that shows the standard deviation of a result - it's used to create the "bell curve" for tests, etc. If you were to see an unexpected roll the first time, it's ~very~ unexpected, but it would be equally unexpected to see it at the end of that number - and not impossible to not see it before 100x that number of rolls.
Yes, they will, depending on how you phrase the question - and the two of you are each making different statements, both of which are more or less true.
The seed of this tangent was that it's very unlikely, but not impossible - and here, exactly what "unlikely" means in practical terms for the average gamer or SG in the average Saga may not be the same as for a statistician who is accustomed to the vagaries of the field.
(And if you two keep saying "is not" "is so!" someone is going to have to slap th' both o' ye!)
I have already apologised if I had caused offence. However I still don't believe the tale. I am not obliged to believe everything that is claimed by people on the internet, and my disbelief should not be interpreted as insult, especially when not expressed in insulting language (as mine was not). If you make an extraordinary claim, you should not be offended if people don't believe you.
Things usually don't, or rarely do, or "haven't yet and certainly aren't expected to soon", or "would surprise us if it happened in our lifetimes" - but "haven't yet" is not "don't".
No one has ever "caught" a meteorite - but people have been hit by them, and lived. That is something that would not be expected and "simply doesn't happen", but did.
For your card example, neither of us can say whether it's ever happened or not in history - and frankly, I don't care, because that proves nothing either way.
But if I saw it, and somehow I "knew" it wasn't rigged (say I dealt it), I'd shrug and say "wow, don't see that every day". (Okay, a little more, but along those lines.)
It's possible, because it's not impossible. Weird stuff does happen, even if any single weird thing you name might not have yet.
1/101,559,956,668,416* > 0.
That's all the mathematical proof and information anyone needs to understand the entire situation (along with a loose grasp of how many times a d6 is rolled in the world.)
(* 6 to the 18th power.)
[i]
Edit - actually, if my math is correct (a big "if", admittedly), your example is a magnitude MORE likely than rolling 18 6's in a row.
8,916,100,452,352
which is 4 (suits) to the 12th power (12, because the first card doesn't matter, only the ones that follow that one), times 3 suits to the 12th, times 2 to the 12th.
So, ~IF~ that math is correct, the the odds of dealing all the cards in a deck into 4 hands, one of each suit, is about 11x greater than rolling 18 sixes - and no one here was overly surprised at that.)[/i]
Allow me to clarify. Suppose the probability of something succeeding is 1 / 100 trillion, and you make 10,000 trillion (independent) attempts. The expected number of successes is 100, and the standard deviation is almost exactly 10. This means it is 95% likely that the number of successes is between 80 and 120, and it's something like 99.99% likely that it's between 60 and 140. (Binomial distribution approximated by normal distribution)
If you make, say "only" 1,000 trillion attempts, then the expectation is 10 and the standard deviation is slightly more than 3. The odds of getting 100 successes are astronomically small.
This is a way of quantifying the concept that, while you may get lucky on any given attempt, the number of attempts required to achieve a given number of successes becomes increasingly more predictable as the required number of successes increases.
His initial claim seems pretty simple unambiguous and clear: He once rolled 18 consecutive 6s on a fair d6.
Sorry for *****ing up this thread! All I was trying to convey is that some things are so astronomically unlikely that if they are claimed, one should be sceptical. Imagine hearing that the same person won the lottery three weeks in a row. And then for a fourth week... At what point do the authorities start to suspect fraud? And would they be right to do so, or should the lucky winner be given the benefit of the doubt, indefinitely? Checking how unlikely something is is actually a pretty good indicator of fraud.
But the aspect you're not taking into consideration (and we have no stats for, thankfully!) is how often 18 d6's are rolled in a row. In the gaming world, I would say that's quite a few.
Maybe that one douse was not "fair", maybe it had a small % chance more to roll a 6 than normal - quite possible, easily as possible (and moreso?) than the claim itself. And both certainly a cause for "incredulousness" - but I've seen some pretty incredulous things in my day, and heard about more.
If this is one of them... meh.
(And that's only if you discount any form of "telepathy", which, ~IF~ it existed even at fractional percentages would alter the odds considerably, ahem.)
Edit - no, you're right - for one, actually I (predictably) screwed up my own math, above. They don't show their math, but upon reflection my formula is badly flawed, and far too simple. I can believe their number, which is about 12 magnitudes larger than what I should have had.
Since you didn't even bother to read my previous post, or you weren't able to grasp its meaning let me explain it to you:
As I said, basically the chance of you getting 18 specific results one after the other, be it 18'6, or 1,2,4,1 ,5,1,4,1, 5,6,4,5, 2,4,1,1, 5,4 is =(1/6)^18
With the example of the 18 random digit string I thought it was pretty clear that I meant any specific string of numbers, and I still thing that certain specific strings of 18 consecutive random numbers have never happened.
Lol, Maybe the fact that it was written just below this quote from you was a clue, but maybe it was too subtle
It was done it response to your direct attack to a guy (not me) that was just trying to point out the error in your ways, and you needlessly offended him.
You are right, if I roll 18 dices just now, a specific string will have happened today, because the probability of me rolling a nonspecific string of 18 numbers, if I roll 18 dices is 1, but, and this is the key, that doesn't mean that I'll roll a certain string of numbers, or that I ever will, in all this thread we have been talking about a specific string of number, and you've been saying silly things, like I just rolled 18 random numbers in a roll. Well the chance of rolling 18 straight 6's is [1/6]^18 but the chance of rolling anything else, basically what we've all been doing is; 1- [1/6]^18
I also think this is not the place to discuss this, if you need a math 101 curse I'll gladly give it to you by, and if you feel like you need to further discuss this please use the PM system.
PS: The little thingy with PM written on it, not that hard to find, even for you
The probability in this case is not a small set of possible outcomes, but an open ended die-roll.
In other words....
2,3,4,5,6,7,8,9 != 1 != 0
Your chances of rolling a second 1, is a fraction of your chances of rolling the first 1. In order to get the second 1, you first have to roll the first 1.
Your chances of rolling a third 1, is a fraction of your chances of rolling the second 1. In order to get the third 1, you first have to roll the second 1.
And so on...
So your chances of rolling 2,2,2,2,2,2,2,2,9... (or any other sequence not starting with a 1 or 0) does not matter because after the first 2, you stop rolling.
As long as it is not zero, it cant be small enough for "practically, no" to be a correct answer. Simple as that, end of story.
I offended the guy who started the matter by calling people in the thread cheaters and/or liars?
You have a problem with both math and other things then.
Well duh, why would i? You did your best to be offensive and insulting and you still dont have a clue.
Now thank you very much Chuchulainshound for writing it up a far lot better than i did.
It is...
Which is why this is pointless. Facts and reality says the "improbable" happens all the time, people who reject reality isnt worth the effort.
How likely is it to survive getting a 3 feet iron rod through your head and brain and survive? Well it happened, and they guy lived for another 13 years. frontiernet.net/~docbob/hole.htm
The odds of surviving such a thing were maybe one in a thousand? One in a million? It is extremely difficult to quantify.
I'm not sure what your point is. Yes, extremely unlikely or extremely lucky events do sometimes occur. No-one is disputing that. What you, and some others in this thread, seem to have difficulty grasping is just HOW unlikely some things are - you do not seem to have any concept of the relative magnitudes of low probabilities. To you, any sufficiently low probability falls into the same category. Any probability smaller, you mentally round up to a millionth or so, which "could happen".
There are some things which, even relative to very unlikely things, are entire orders of magnitude MORE unlikely. The chances of you being hit by a meteorite in your lifetime are probably something like one in a hundred million, or one in a billion, or so. Extraordinarily rare, nevertheless documented cases do exist. However the odds of catching a meteorite must be orders of magnitude smaller, say one in a trillion or so. Which is why it's never happened. Another example: Getting a hole in one is very rare, although it's considerably more likely than getting hit by a meteorite. The odds of getting consecutive holes-in-one, however, decrease exponentially. There are (very rare) cases of two consecutive holes-in-one. I'm not sure about three, but it might have conceivably happened, somewhere. Four or five, however, is just too unlikely, which is why the claim of (e.g.) Kim Jong Il is absurd.
It is difficult to quantify the odds of many real-world events. Many amazing things are not as unlikely as they may seem. The probabilities of certain events, however, such as in cards, dice, lotteries, etc., can be measured exactly, and thus the credibility of claimed feats can be gauged. The odds of the perfect deal, or of thirty consecutive sixes are absurdly low, and thus these things do not occur in practice. If anyone claims them, there is almost certainly an alternative explanation other than luck. Your claims in this thread are not quite so utterly absurd as that, but in my opinion they fall into the category of "extremely difficult to believe".
There are aproximately 3 billion women and around the same amount of men in the world. One of them is my mother and one of them is my father, what is the chance that those two met and made me? The chance is so small that I probably doesn't exists Strange things do happen though, I was born and some people actually are delt a straight flush in poker or roll a lot of ones in a row...
Note: If someone says that he is skeptical of a thing, it doesn't mean he automatically assumes the other person is lying or cheating. It just means he hasn't seen enough proof either for or against.
Strange things do happen though, I was born and some people actually are delt a straight flush in poker or roll a lot of ones in a row...