[Musicforawhile (OP)]

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).

Yes I was thinking that, that even in something like 7, 16, 21, 33, 39, 42...a mathematician might find a pattern in that.

[phyti39]

The lottery system has no memory, therefore each drawing is like the first ever. This eliminates any causal connection, and enforces a fair system. As mentioned, any sequence has the same probability as any other. Just as the toss of a coin is time independent, so is the lottery.
When someone says multiple occurrences of the same number are rare, they are in reality saying it cannot happen in there lifetime. This is false based on time independent behavior, it can occur anytime.

[Musicforawhile (OP)]

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 numbers
2. Were randomly generated each week
3. 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)

This is assuming you can imagine caring about the tiny chance you have of winning the lottery.

[dlorde]

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 numbers
2. Were randomly generated each week
3. 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.

As already mentioned, the only good reason to select particular numbers is to avoid popular choices, so that if you do win, you're less likely to have to share the winnings with a lot of people.

[Musicforawhile (OP)]

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.

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.

[Musicforawhile (OP)]

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.

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.

[dlorde]

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.

As I said, one intuitively feels that runs in random sequences should change the subsequent probabilities, but this obviously isn't possible if each draw or toss is random. Making this mistake is known as the Gambler's Fallacy because it has tempted so many gamblers to their doom. Once you're aware that your intuition has problems with randomness, you learn to use the maths and ignore your intuition (mathematicians do that anyway). It's not a question of who is watching you, it's a question of making the correct decisions and calculations, and getting the right results.

Runs that seem improbable (e.g. ten consecutive heads or tails) don't get 'corrected' in subsequent tosses, they just become insignificant in the long term (thousands of tosses), so the average result remains about 50:50. This is known as 'regression to the mean'.

It may be of interest that in a number of sports (e.g. basketball, baseball, and others), when individual or team performances have been analysed, 'hot' streaks, when a player or team is said to be 'on form' and scoring consistently (or when they're off-form, having a bad spell), the sequences are often indistinguishable from random variation - that is, the results are often consistent with what you should expect from the random 'luck' of a player or team playing at a consistent level of performance rather than their playing form going up or down.

The same kinds of effects are also seen in other areas, such as in finance with the successes or failures of investors and fund managers, and so-on. It pays to be aware of such possibilities.

[jeffreyH]

I am not a professional physicist, mathematician or otherwise under anyones supervision. It's random and number 3. Not because I guard a reputation but because that is the truth. You can tilt at the windmills all you want. The truth remains the truth.

[percepts]

the odds of you winning the lotto are 1 in 14 million  ( 49!/(6!*(49-6)!)  )

so far there have been 1970 lotto draws so you still have 14 million minus 1970 draws to go before the probability of your 1,2,3,4,5,6 selection appearing once has been reached and even then I think its 50:50 whether it would. There simply have been no where near enough draws for it to be likely that any specific selection of 6 numbers will have appeared. The odds are simply way to small and will remain so until long after you have turned your toes up and your bones have decayed to dust. So don't hold your breath while you're waiting for your numbers to come up.

[evan_au]

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

Let's say we take a keyboard which has about 49 characters (let's say 24 UPPER and lower case, plus space) and then let a child pound on the keyboard.

If they could type a random sequence of 6 characters every 10 seconds, how long  until they type the first 6 letters of "Romeo and Juliet"? (even if you ignored the order in which the letters were typed...)

Answer: There are better things to do with your life!

The odds are similar to winning the lottery, only you have one attempt every 10 seconds instead of every week (and you don't have to pay a few pounds or dollars every time!).

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.

[percepts]

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.

Probability says that if you give enough monkeys a typewriter each and enough time, one of them will eventually reproduce the complete works of Shakespeare. This probability theory has been disproved by virtue of the fact that the internet has failed to produced anything coming anywhere near close.

[alancalverd]

The ability of the human mind to see patterns, or impose apparent order on actual chaos, is amazing. Recognisable images of Jesus and Mohammed appear on slices of toast or in clouds, despite the fact that no living person has seen either bloke in the flesh or even in a contemporary portrait. Listening to Glass or Stockhausen, people often say that they can hear music, and the Raudive Tapes seemed to capture the voices of Hitler or St Francis of Assisi, depending on the listener's preference.

So it would come as no surprise if a monkey won the Booker Prize. It could hardly be more tedious than Anita Brookner, or less meaningful than most of the posts about "consciousness" on this board!   

[syhprum]

I hate speculating about lottery numbers, it would be heart breaking if one wrote down a series of numbers for some reason or other, did not buy a ticket and then found you had written down the winning sequence although normally you would be better off by the price of a ticket.

[burning]

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.

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?

[Musicforawhile (OP)]

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?

True, it was a bit pointless of me to ask. The only answer I truly would accept is that you would think "3" but do "2."

[dlorde]

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

You'd make a lousy gambler. I strongly suggest you stay away from games of chance where money is involved.

[CliffordK]

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. 

http://abcnews.go.com/blogs/business/2013/02/arkansas-couple-wins-lottery-twice-in-one-weekend/
http://www.lotterypost.com/tag/Won_multiple_times
https://www.thelotter.com/blog/2014/10/twice-three-times-lottery-winner/

Most of those individuals winning multiple times also spend A LOT OF MONEY on tickets. 

As far as whether there is a bias towards certain numbers, if the system is truly random, then there should not be. 

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. 

Thus, there are people trying to calculate the statistics for the perfect card.  But, the differences SHOULD BE extremely minimal.  Physical characteristics of the balls might also change over time, so data from 10 years ago may not be applicable today. 

It is best to consider a lottery as a tax.  If the payout is 50%, then if you invest $1,000,000, you should expect to get less than $500,000 back.  But, it is worse than that.  If the payments are spread out over time, then the lost investment income should be significant.  And, taxes also take a chunk out of it. 

So, your $1,000,000 investment starts looking a lot like a $100,000 return.

So, can you "beat the odds"?  If there is a long streak of no winners, the lotteries often reach a point where the expected payout is greater than the odds.  So, for example, it reaches a point where the odds are 1:1,000,000 to win $2,000,000.  Outwardly the odds look favorable.  But, the payouts are often greater than what is needed.  But, also, considering time amortization, and taxes, the actual break even point may be much higher.

[Bill S]

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.

Wouldn't it be true that the occasional multiple winner supports the idea of true randomness?

[alancalverd]

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.

[dlorde]

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.

Outliers are not unexpected in random selections; once a 'run' occurs, regression to the mean can take quite a while, so the outlier persists longer than intuitively expected.