Statistics 101

On what planet?If you win, the odds are the number of combinations of numbers that result in your winning - 1 - to the number of possible combinations of numbers in total.You're just being glib, I guess, but you're also being completely inaccurate. Even if you were the only one who played the lottery that time, unless you bought every single number combination, the odds of you winning were not 1 - even if you did win.This is a thread about understanding statistics. Let's not undercut that aim with glib misrepresentations of mathematics, ok?

The odds don't change after you win.You still figure the odds by looking at the outcome sample space - the total number of different combinations of lotto numbers - compared to the subset of those outcomes that results in your victory.In the case of the Powerball, that's 1 in 146 million. Before, after, it doesn't matter. The actual outcome doesn't change the probabilities of any of the outcomes. That something happened or didn't happen doesn't change the probability of it happening.

Irrelevant.We know how lotto numbers are generated, so we can develop a sample space of outcomes. We know exactly how many different combinations (not permutations, the lottery doesn't work like that) of numbers are possible.And it doesn't matter what number any particular individual picks; they all have the same probability of being the winning numbers (because the game isn't fixed.) They won because they picked the winning numbers. Given the average size of the population who buys tickets (and assuming they all play different numbers) we can tell you, on average, how long it will be before somebody wins.That they picked the winning numbers is not significant. Imagine that you have two machines running - one generates one random lotto number every night, and the other machine generates a hundred thousand random lotto numbers every day. It shouldn't surprise anyone that, every few days or so, there's a match between the number generated by the first machine and one of the numbers generated by the second.

What different thing? I still don't understand. The odds that you've just won the Powerball are the odds that you hold the winning ticket; the odds that that's the case are still one out of all the possible combinations of numbers; that's one in 146 million (or so.)I mean, think about it, Mod. What happened to all the people who didn't win? They didn't fall off the Earth. They still hold losing tickets. They're still in the sample space.We don't clear the sample space just because an outcome occurred. The fact that an outcome happened doesn't change the probabilities of the outcomes.You're showing the kind of thinking that leads people to misunderstand things like the Monty Hall Problem. The odds don't change just because an outcome happened.

I don't understand how that's a question of probability, then. It's like saying "the probability that Modulus's screen name is "Modulus", given that it is "Modulus", is 1." It's kind of a nonsense question.I think posing nonsense questions that aren't applicable to probabilistic thinking obfuscates the issue. Mod only has the winning ticket if it's the winning ticket; and the odds of that being the case (assuming he's not a cheater) is only one in 146 million.

Then I have no explanation for why you're so adamantly, resolutely wrong. You are, though. (Please don't take my word for it, of course, but read on as I try to explain how.) It's the number of winning tickets - 1 - over the number of all possible tickets (that is, the number of possible combinations of numbers. It's not possible to buy a lottery ticket that isn't in the space of outcomes generated by the lotto drawing.)So, it's one in 146 million, like I said. The fact that it's been confirmed by the lotto people as having the winning numbers on it doesn't change the probability that that ticket won the lottery. That's still 1 in 146 million.The outcome doesn't change the odds. The simple fact that you won the lottery doesn't change the fact that it was very unlikely that you would have won. The probability of the outcome doesn't become 1/1 just because that was the outcome that occurred. I'm not sure I understand the question. How do they know if they've won? They look at the ticket, the read the numbers on it, and then they compare those numbers to the numbers generated in the lotto drawing. If they're the same, they won.Everybody knows how to check if you've won the lottery. They're exactly the same question, only, in the first question, you've used a different construction to indicate the subjunctive mood. What are the odds that you won the lottery? One in 146 million, just like for everybody else. Before, after, during - it doesn't matter; the odds of the outcomes don't change just because one of them happened.

1 in 146 million, the same as it was before you knew what the winning numbers are.It is the winning ticket, obviously. And the odds that it is are 1 in 146 million. This doesn't make any sense, I guess. What does being delusional have to do with it? I do know how to read statements in English, Mod. They're the same question, but the subjunctive mood was indicated in two different ways. You're still not making sense. The odds that you are looking at heads is 50%, even though the coin landed heads-up.The outcome doesn't change the probability. Only one outcome can happen, which I think we agree on. But that's already conceptually part of the initial calculation of the odds. So recognizing that only one outcome can happen doesn't change the odds, and it doesn't change the odds when the outcome - only one outcome out of many - happens.The fact that an outcome happened doesn't change the odds of it happening, or having happened. Odds are the same in the past as well as the future. Odds are not time-dependant. The odds of a coin toss don't change simply because the coin toss happens in the future, or in the past. Just like it doesn't matter if it happens in Nevada or on the moon. As far as I'm concerned we can be completely certain that the outcome of the coin toss was heads; that doesn't change the fact that the odds of it being heads are only 50%.Are you, maybe, confusing confidence intervals and probability? They're related, obviously, but I don't think they should be conflated. You're committing the Monty Hall fallacy, though.Of course the odds that you've won the lottery are 1 in 146 million, because you still have to match all 6 numbers. The outcome doesn't change the odds. Imagine that, instead of drawing the numbers one at a time, they generated the numbers all at once. Would you really say that the odds of winning those two different lotteries were really different?Or imagine that you forgot to TiVo the drawing, and so you only find out the numbers the next day in the newspaper, regardless of what order the numbers were generated. Does that really change your odds?Of course not. How you find out about the numbers, obviously, has no bearing on the odds of you winning the lottery.In the Monty Hall game, the odds don't go from 1/3 to 1/2 just because Monty opens one of the doors. That's the mistake you're making, here. In the Monty Hall game, the odds that you picked the right door the first time are the same both before and after Monty opens a door - 1/3.Edited by crashfrog, : No reason given.

So you've won. The odds of that happening are 1 in 146 million.If you're asking me "what are the odds of winning, given that you've already won", you're just wasting my time. That's not a question of probabilities; that's a question of "what does nonsense mean?" If you've artificially restricted the sample space to the one outcome that actually happened, then yes, obviously that single outcome represents the totality of the sample space.But at that point you're not doing probabilities; you're generating nonsense and obfuscating mathematics. Yes, I know. That's what I just told you, in fact. Regardless of which door Monty opens, the probability that you were right in your initial guess doesn't change. It was 1/3 before, it was 1/3 after.What are the odds that you've won the lottery? 1 in 146 million, regardless of whether or not you read the numbers one after another, or checked them off all at once, or had some proxy do it for you, or any number of other methods.You buys your ticket and you takes your chances. That chance is one in 146 million.It's really just that simple, Mod, and I can't understand why somebody who claims to know so much about probability would disagree. Um, no, Mod, no I'm not. Are you even reading my posts? In subsequent lotteries? That question doesn't make sense. Tickets are good for only one lottery.It's like asking "what are the odds of winning if you don't even play"? That's a nonsense statement, probabilistically speaking. Not playing isn't an outcome in the sample space. No, of course it doesn't. Your odds were always 1 in 146 million.Look, Mod. Odds don't have anything to do with time. That's why, if I hand you a balanced coin, and I ask you "when I flipped it this morning, what were the odds it came up heads?" you're able to answer the question.And when I ask you what the odds of heads will be the next time you flip it, you can answer that question, too.Even if the very next thing you do is toss the coin into a smelter and never flip it again, you can tell me what the odds of flipping that coin would be any time that it was flipped. In the future, in the past, whenever. Odds aren't time-dependant!

This is probabilistic nonsense.The odds that you have a winning ticket are 1 in 146 million because that's the odds of matching the lottery numbers with your ticket. There's no "depending on whether or not you matched." That's nonsense. It doesn't matter whether the lottery drawing happens in the past or the future; the odds that it wins that drawing are 1 in 146 million. It doesn't matter whether or not you know it's a winning ticket or not - the odds that it wins are 1 in 146 million.The reason people throw away their losing lottery tickets is because they know they don't match the numbers; but the fact that the ticket is in the trash doesn't change the fact that there's a 1 in 146 million chance that it matched the numbers for that lottery drawing.

Fair enough, but the lottery is unconditional probability. There's no communication between lottery players and the lottery draw-er, there's nothing conditional about the numbers except that the first 5 are from the same pool of numbers, and the 6th is from a separate pool. And you don't have the opportunity to change your numbers.The numbers might as well be generated simulatenously; they do it the way they do for dramatic reasons.It doesn't change the odds of you winning. Your odds don't change simply because your friend reads you the numbers in random order, or compares them all at once, or writes a sophisticated computer program, or what have you.Regardless of how you find out the results, your odds of winning are 1 in 146 million.

No, I'm not. I'm talking about the probability of the event at all points in time.The probability doesn't change before the event, or after the event, or whenever (unless of course you change the conditions of the event, like rolling a dice instead of flipping a coin - you know what I mean). I can tell you what the odds of getting a heads result on a coin flip are (given a fair coin), regardless of when you plan to flip the coin. Regardless of when the event happened - the future, the past - I can tell you what the odds of the outcomes are. I mean - according to how probability works, the statement has no meaning. But that's clearly not true. I can tell you the probabilities surrounding a coin flip, even if you already flipped the coin. You can always figure probabilities after the fact, as long as you can determine the sample space.A fair coin is 1/2 heads, 1/2 tails. That's the same for every flip - whether or not the flip has happened yet. Even if you flip the coin and it comes up tails, and you're standing right there looking at it, there's only a 1/2 chance of the coin came up tails. It did, but that doesn't make it any more likely.The fact that only one outcome can actually happen doesn't change the probabilities of other outcomes. Probability isn't about telling you what's going to happen, or what did happen; it's about telling you about the relationship between desired outcomes and all outcomes.Edited by crashfrog, : No reason given.

I still don't see how it does. You don't ever have an opportunity to act on that information; the question of whether or not you're going to win happens when you pick your numbers and the lotto people pick the winning ones. There's never an opportunity to act on the information, unless you're cheating somehow - cheating, in fact, would be the only way to raise your odds above 1 in 146 million besides buying more tickets.And I know this is so because the only way anybody has ever figured out how to reliably "game" the lottery is to buy more tickets - to buy so many tickets, in fact, that you've purchased one of every combination of numbers. No one has ever increased their odds of winning the lottery by having their friend read the numbers to them, or TiVoing the drawing and watching it in reverse, or what have you.There's only one way to game the lottery and that's to cover all the possibilities. (I'm not a gambler - is that what they mean by "covering the spread"? I've heard that term.) If changing the way you learn about the lotto numbers increased your odds of winning as remarkably as you misrepresent it, we'd see people doing that as a strategy. It was 1 in 146 million, just like it was for everybody else. You boughts your ticket and you took your chances. You lost. That doesn't mean you had no possibility of winning; just that you didn't. The odds didn't change just because you lost. No, they're the same as they were before. It doesn't matter that the drawing happened in the past and now you know what the result is. It was 1 in 145 million.You're displaying the exact same fallacious thinking that causes people to credit God when they win the lottery - that, somehow, winning is so unlikely that if it happened to you, it had to happen to you; it couldn't have happened to anybody else. But that's nonsense. The other outcomes don't disappear from the sample space just because they didn't happen. That's not what probability is about.It's about the relationship of desired outcomes to all outcomes, and that doesn't change just because one of those outcomes is what actually happened.And, contrary to your assertion, changing the way you learn about the outcome doesn't change how many of those outcomes are desired. There's only one desired outcome in this case - the one where your numbers are the ones that match. Changing how you find out about the numbers after the fact doesn't increase the number of those possible outcomes that lead to a big cash payout for you. Heads is one outcome out of a sample space of two, so the probability is the same as it was before you flipped it - 1/2. How many different ways do I have to say this before it sticks?Look, prove me wrong, empirically. Buy a lottery ticket tonight, and then have your friend read you the numbers in whatever way you think will maximize your odds of winning. When you win, you can fly me out to Manchester and I'll buy us a pitcher of Newcastle and tell you I was wrong.

I don't see how reading and comparing numbers is a function of probability. That's just a function of using your eyes.Look, if I'm wrong, then there's somebody out there making a killing in the lottery - or at a casino, or somewhere - by having their friend read the numbers/cards to them instead of just looking at them directly. But I'm familiar with a considerable number of ways to cheat games of chance - which I think should be completely legal, since they're already cheating you in return - and this, to my knowledge, is not one of them.

Too simple, in fact, to be relevant to probability. It's just nonsense dressed up in probabilistic language. "Given that you are you, what are the odds that you are you"? and the like. I don't see where that's stipulated in Mod's example. He's telling me that your odds of winning go up as your friend reads the numbers to you compared to if you look at the numbers all at once.So, let's see it happen. Somebody go win the lottery by buying a ticket and then, rather than watching the results on the news, having their friend read them the numbers the next day.I agree it only works if your friend reads you the numbers as you buy the ticket, but your issue is with Mod in that regard, not with me.

Yes, I understand.My rebuttal is that the question of whether or not you have the winning ticket given that you have the winning ticket is not a probabilistic function; it's linguistic legerdemain.And it's a pretty considerable waste of time. Why are we even still talking about this?