This is just a random thought that was bouncing around in my head last night, so dont read too much into it.
Accepting that in an infinite universe everything that can happen, will happen, what are the odds of one individual person winning your national lottery (pick a country) having never actually bought a lottery ticket?
Anybody want to take a stab at it?
It depends on both the odds of winning, and the ticket purchase frequency distribution per capita over time for that lottery, and how often the lottery has occurred. With that information, a very precise answer could be given, without it, nothing really can be given.
I’m not sure I undestand the question, but this page might help.
The first thing that pops into my mind is that we need to know, on average, how many lottery tickets are given out as gifts. Any other ways to win without buying one?
How do you arrive at “a very precise answer” when you have to account for the factor of a person who has never bought a lottery ticket somehow winning the lottery? While it’s easy to calculate odds for those who DO purchase tickets, this seems like something that’s quite difficult to assign probability to.
On a somewhat related note, check out this link at cockeyed.com – it’s a California lottery simulator. Pick your numbers, set it to play them twice a week for ten years, and see how much money you make. It really drives the point home that the lottery is a tax on people who are bad at math.
Zero. If a person never buys a ticket, the chances of them winning are zero.
Do you mean “having never actually bought a lottery ticket before?” The answer is the same odds as for any other winning ticket. The numbers come up randomly, they don’t know whether you’ve bought any tickets in the past or not.
People who pick the same numbers every week are shortening their odds, but at a microscopic rate; you’d have to play the same numbers every week for millions of years to be assured of a win.
By co-incidence, I just spent $10 on lottery entries right before checking the SD. My theory is that by the power of woo, I am now totally guaranteed that my numbers will come up this time. Thanks, buck.
Zero, obviously - if you really meant to ask what you said, and setting aside such possibilities as someone who did not enter the lottery being given the prize due to some sort of error (that, could happen, but they would not really have won, and the odds of it happening are surely unquantifiable).
This does not make any difference, because legitimately winning any nation’s lottery without having bought a ticket is not something that can happen: no lottery’s rules are going to allow for it. It is thus a logical impossibility. It violates the rules of the lottery, as surely as 1 plus one equaling three violates the rules of arithmetic, and will never happen even in an infinite universe.
Really? I thought the probability was exactly the same whether you play the same numbers every time or if you pick random numbers every time. After all, you can play the same numbers forever, but you’re NEVER “assured of a win”.
Previous results have no bearing on the next drawing, so the odds are always exactly the same for any given set of numbers…meaning you can’t ever say “after x years, those numbers HAVE to come up”. You can do the math and say that after x years they SHOULD come up, but that’s not the same.
Huh? It most certainly is not zero, the fact that a person can be given a lottery ticket as a gift is enough to ensure that, even apart from other possible reasons for having a lottery ticket, such as being part of a company funded syndicate, where you are contractually entitled to a share without ever physically paying a pound and getting a ticket.
I disagree. What if as part of a promotion, the lottery organisers play a ticket for everybody on the electoral register whose name starts with L. Thats a lottery win without buying a ticket. What if a phone company buys lottery tickets, then gives them away free with a new mobile phone, that could be winning the lottery without buying a ticket.
It is possible to win the lottery without buying a ticket, and since in an infinite universe everything must happen, I was just curious as to what the odds may be.
No, lotteries are a chance for people who like spouting tedious homilies to indulge themselves. They’re also:
1: a chance for some of us to harmlessly daydream, and
2: a tiny but real chance at riches
Most people who buy lottery tickets don’t seriously believe they’re actually going to win, they’re enjoying a little thrill of possibility. Yes, the chance of any particular set of numbers coming up are tiny, but they do come up every week. Somebody always does win big.
I’ve personally met someone who won millions on a lottery. I’ve personally met a couple of other people who won tens of thousands. The only people who are guaranteed to not win are the people who are too clever to gamble.
I buy lottery tickets every now and then, probably 6 or 7 a year on average. That constitutes a use of my disposable income that pleases me, causes no problems for anyone else, and is no more foolish than spending my money on beer or seeing a band. I’m left with “nothing” at the end of those experiences, too, but I enjoy them, in the same way that I enjoy the chance to fantasise about what I’ll be spending my millions on.
People who genuinely believe they’re going to win are losers, sure, but most of us lottery ticket buyers are not as stupid as you seem to believe. And you’re sure going to look silly if my numbers do come up.
That’s too easy: in a truly infinite universe, the odds against anything are zero.
If everything that could possibly happen does happen, then everything is inevitable, therefore there are no odds against anything.
Please note that this is not true. For one thing, “infinite” is not synonymous with “contains everything”; for another, there are some things that can happen that, if they do happen, they preclude other things from happening. For a more thorough discussion, see this old thread: “Anything that can happen, will happen, given enough time.” – Really?
I didn’t mean to insult you or any other lottery players. I was just using that well-worn phrase while trying to explain that when I played the 10-year lottery simulator on the link I posted, the results are even more depressingly terrible than I thought they would be. I totally understand the thrill of playing the lottery (and fantasizing about what to do with the money) and hoping to win – when the jackpot is really, really big (like once every few years, when everyone is talking about it), I’ll buy one or two of them, even if I might feel silly afterward for doing it. It’s fun.
Of course, even if I play a LOT, the odds are I’m going to come out in the red, and not in a small, blackjack sort of way, but a big way (the potential prize is equally big, of course). As long as the player understands that and doesn’t treat it like an investment opportunity, it’s all in good fun.
I’m sure you can see where the phrase comes from, though…after all, regardless of the fun involved, you’re paying for schools and whatever else lottery money is used for on a long-shot hope of winning a prize. I don’t think people like you, who buy 6 or 7 tickets a year, are the type of person that the phrase was coined to describe. Go into a gas station the night of the drawing and hang out for awhile and you’ll see some of those people.
I’m not sure this is true in Thailand; let me explain why.
As shown in this news story, the winning 6-digit number was 113311, an odd-looking number not due to chance but due to a cheating method. That was nine years ago. IIRC, a similar incident occurred about 6 years ago. (I think the government may have refused to pay on those tickets, though they didn’t reimburse losses of underground lottery operators, e.g. my brother-in-law. 
)
Anyway, I’m afraid that when my number, e.g. 447777 comes in, the government will demand a redraw, even without evidence of cheating.
(The reason I play such numbers is very simple. I like to be friendly with the ticket agents, but don’t like wasting money on lottery, so when they offer me a triple number I say, No no, I only play quadruples! Now they save their quadruple-number tickets for me, and of course I have to buy them! :smack: )
SpeedwayRyan - no problem, I just find that “tax on people who are bad at math” line irritating.
I’m not too bad at math, and I do understand probability pretty well. I’m also happy to contribute some extra tax money towards the welfare of society on the off chance of winning big. And I find that most people who buy lottery tickets feel much the same way about it. The problem gamblers are a pretty small percentage of lottery ticket buyers.
If that is the sort of thing you had in your (very unclear) OP, then your question is clearly unanswerable as we have no way of quantifying how likely it is (over all eternity) that people would give tickets as gifts, or change lottery rules so that non-buyers can win,or whatever. (You might be able to empirically determine how often such things tend to happen over some some finite time span - if you had a sufficiently huge research grant - but there is no guarantee that those frequencies would apply over all infinity.)
Arguably it true that in an infinite universe all possible things, including extremely unlikely ones, must happen. Impossible aren’t going to happen even in infinity.
So you dont know. Thanks for the snarky reply anyway. I’m not sure which of the three lines in the OP were unclear, but if you feel that the answer is “We cant know so why bother trying” then more power to you.
From the OP, “Accepting that in an infinite universe everything that can happen, will happen”.
Thanks once again.
For everybody else, yes, I know this isnt something easily quantifiable. I was simply curious how you would go about answering a question like this, and what the answer might be. From the replies so far, it seems the first step is to establish first the possible ways in which you can win a lottery having not bought a ticket, and then the odds of each of those scenarios actually happening. Correct?
As long as we’re thinking outside the box here, the draft lottery that the US ran during the Vietnam War did not require participants to have bought a ticket. One’s odds of winning presumably depended upon certain quantifiable factors (as well as one’s definition of “winning”).
If we assume that anything that can happen will happen then there are no odds to calculate. We have already assumed that the odds are 100% in favor of it happening.
Now if we dispense with the “inifinite universe” we could try to come up with a number for a given period of time by looking at the number of non-bought tickets played in a given year (likely difficult to quantify) and the probability of winning per ticket.
In an infinite universe in which anything that can happen, will happen, there is an infinite number of possible ways you could end up with a ticket you didn’t buy. This really isn’t qauntifiable unless you add some constraints.
Not that it’s my reply, but the response was an honest attempt to answer why an answer may not even be possible.
It’s not just that these numbers aren’t easily quantifiable but also that the situation, as proposed, is ill-defined.
For example, positing this is such a universe, there’s a non-zero probability that I will be given a lottery ticket as a gift 5 days from now. There’s also a non-zero probability that the ticket is a winner. So, in this universe, I’m guaranteed to be a winner because there’s a non-zero probability of the event?
From my understanding of the OP, this type of situation isn’t one covered by the OP. But it does fall into the range of possible starting assumptions from the OP.
On review, this is pretty much what a lot of the other posters are saying.