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If there is an equal chance of any number in the lottery being drawn then why do you never get a combination like 1,2,3,4,5,6 or 9, 12, 15, 18, 21. Even 1,2,3,4,12,36 would probably not happen.

Please don't explain with equations, I am not a mathematician.

So let me ask you...what is the probability of 5, 12, 24, 37, 41, 46 coming up in consecutive weeks??? Is it more or less likely to see a completely different set of numbers coming up after the initial drawing of 5, 12, 24, 37, 41, 46?

PmbPhy said they were special numbers...what does that mean? Can you explain?'

And as for the same numbers that came up last week coming up the next week being the same...you've got to be kidding right? Is there an equal chance of those same numbers coming up again week after week?? This is why I hate probability. Real life doesn't work this way.

What is the likelihood that that same set of numbers comes up every week until we finally get hit by a huge asteroid and the planet and our lottery machines are destroyed? You can't tell me its the same likelihood as having a mixed/more different drawing of numbers each week??

Another thought..if you look at all the lottery draws, more of the winning numbers have no pattern than do have a pattern.

Another thought..if you look at all the lottery draws, more of the winning numbers have no pattern than do have a pattern. The Maryland draw was quite unusual but it's not the norm...so it seems it's more likely that the numbers wont be in a sequence than will be, if you look at all the draws that have happened. So therefore it is more likely that the winning numbers won't have any pattern.

10,068,347,520 to 1 chance of any selection appearing

of course the Maryland draw isn't the norm

Impossible lottery combinations

You can ignore any odds that your numbers will come up two weeks in a row ...

Quote from: evan_au on 09/11/2014 03:17:16You can ignore any odds that your numbers will come up two weeks in a row ... The odds that someone who only buys one lottery ticket per week winning first prize on the UK national lottery on two consecutive weeks is approximately 1 in 200,000,000,000,000 whether they use the same numbers each week or different ones.

You are fixating on the order that the selection of numbers are presented in as if they mean something. _{1} to X_{49}.

The numbers could come out of the draw like:5, 2, 1, 4, 6, 3The pattern is there once you re-arrange them, unless I'm missing what you're saying.

I think despite all your kind efforts, I just don't have the kind of mind that can accept this sort of thing. In my life, I am involved with art, literature and music and am very much led by my intuition.

I do understood that certain things in the universe are counter-intuitive like Einstein's theory where time slows down when you approach the speed of light. Is that right?

Thing is, they're just numbers. You decide what particular combinations are significant to you (you seem to find simple sequences of adjacent numbers significant) and whether they count if they're jumbled (you seem to think not). A mathematician could probably find some kind of pattern in a lot more combinations than you can, and almost every combination could be significant to someone on the planet (birthdays, phone numbers, house numbers, etc).

Ok, if someone said they would buy you a lottery ticket for the next ten years, one each week. Would you prefer to choose a set of numbers that:1. Had already been the winning numbers2. Were randomly generated each week3. You really wouldn't care whether it was 1 or 2 as the probability is the same (not because you just don't care about the lottery)

3 - it makes no difference whether the numbers have come up before or are randomly generated. Intuitively, one feels it should make a difference, just as one feels that after tossing a coin 10 heads in a row you're more likely to get tails. Intuition is wrong about this.

Quote from: dlorde on 09/11/2014 20:42:063 - it makes no difference whether the numbers have come up before or are randomly generated. Intuitively, one feels it should make a difference, just as one feels that after tossing a coin 10 heads in a row you're more likely to get tails. Intuition is wrong about this. My mind can't accept this, not at the moment anyway. And I think that if all the mathematicians here weren't under the gaze of their colleagues, academic supervisors, and potential academic funders then you would all go for Number 2. But you don't want to be seen as woolly-headed and led by your instinct rather than your rationality. In the same way I am sure many scientists wouldn't want to admit their secret agnosticism or prayers to god.

My mind can't accept this, not at the moment anyway. And I think that if all the mathematicians here weren't under the gaze of their colleagues, academic supervisors, and potential academic funders then you would all go for Number 2. But you don't want to be seen as woolly headed and led by your instinct rather than your rationality.

I am involved with art, literature and music and am very much led by my intuition

Writing a comprehensible story is hard, which is why we don't teach kids the "random bashing on the keyboard" method for producing great literature, no matter how much your intuition tells you that it should produce text that follows a pattern.

Quote from: dlorde on 09/11/2014 20:42:063 - it makes no difference whether the numbers have come up before or are randomly generated. Intuitively, one feels it should make a difference, just as one feels that after tossing a coin 10 heads in a row you're more likely to get tails. Intuition is wrong about this. My mind can't accept this, not at the moment anyway. And I think that if all the mathematicians here weren't under the gaze of their colleagues, academic supervisors, and potential academic funders then you would all go for Number 2. But you don't want to be seen as woolly headed and led by your instinct rather than your rationality. In the same way I am sure many scientists wouldn't want to admit their secret agnosticism or prayers to god.

If you're not going to believe us if we say "3," then what is the point of asking the question in the first place?

The only answer I truly would accept is that you would think "3" but do "2."

There have in fact been a few people who have won major lotteries twice, or even more, although many of the multiple wins are smaller lotteries with under $1 Million in prize money.

For something like selecting balls from a cage. Perhaps even a few milligrams difference in the weight of the balls, or a few cubic millimeters in volume would make a difference. Or, perhaps the lottery commission has a verification phase in which all balls are ordered before dumping into the cage, and for some reason they don't get fully mixed.

In a mindboggling waste of public resources, the UK lottery balls are weighed, measured and assessed for sphericity by the National Physical Laboratory, and the results are analysed for randomness by the Office for National Statistics. Despite all of which, number 20 seems to be an outlier.

If there is a long streak of no winners, the lotteries often reach a point where the expected payout is greater than the odds.

In an infinite universe, an infinite lottery becomes possible, and therefore inevitable...

Now the probability that the monkeys would randomly not produce any numbers that included a 9 is extremely small, but there are an infinite number of ways that it could be done...

If the lottery pays out at a finite rate or in a finite period though, these paradoxes can be eliminated. A million dollar lottery that draws every week would have a finite pool of tickets and ticket holders as well as finite buy-in and payout for each cycle, so even though the process repeats infinitely, the infinity isn't involved in any one game.

I have often criticized the "infinite monkeys" type arguments that imply that an infinite sample size must contain all possible outcomes. I guess some of this comes down to definitions (which infinity, how does one define non-zero probability etc.)

I doubt that an infinite lottery is possible whether the universe is infinite or not (except in the sense that chiralSPO suggests).

I'm also not sure whether everything possible must necessarily happen in an infinite universe - I think it depends on the event and what kind of an infinite universe it is. Also, if you have to wait an infinitely long time for something to happen, does it actually happen?

But, putting aside my doubts, it would take an infinitely long time to organise each stage (e.g. print the tickets, or get the applications, or whatever), and that must come before the draw, so would it ever get drawn?

It's no different in principle from the whole numbers (e.g. all the lottery players) being countably infinite, and the multiples of 1 million (e.g. one in a million are winners) also being countably infinite.