What are the odds of winning the lotto twice?

Bruthal · 10-03-2011 10:35PM

lugha wrote: »

Fair enough. Perhaps it might have being better phrased as "to do it twice in succession" rather than "to do it again"?

Maybe so, but when i said they have already beaten the 8 million to one odds, so to do it again would be 65 billion to 1..., i thought it could be assumed i was referring to having 2 wins.

lugha · 10-03-2011 10:37PM

fergalr wrote: »

The thing is, that's the odds of a single person winning the lotto twice, with two tickets.

If a trillion people each enter 2 lotto draws, then its very likely that one of them will win twice.

So, you have to be careful when you say it does not seem likely to ever happen, because there are more than one person playing the lotto.

This is true. And there is a potential problem with this truth, in a non-lotto scenario, which might be along some day to bite us on the arse.
The probability of an innocent individual having the same DNA profile found at a a crime scene is minuscule. But with a suitably big database, the chances of a "false" match being generated is far from minuscule.

Jesus Wept · 10-03-2011 10:37PM

robbie7730 wrote: »

That does not say anyone won with 2 sinlge tickets does it? Says a woman won twice over 4 months. Still enormous odds. What i was saying was i cant see anyone winning the lotto twice, just playing twice, with 1 row of numbers on each ticket.

Obviously i know it has been won twice, thats the subject of this thread.

Well I wouldn't be surprised and it isn't really very relevant.

Pace2008 wrote: »

Read it yourself, carefully this time:

A double lottery winner isn't defying the odds; it's actually more likely to happen than not, somewhere, at some stage.

What is your point? It happens somewhere in the world often.
It makes the local papers, sometimes the national and is presented as an amazingly unlikely occurrence.
It isn't.

Bruthal · 10-03-2011 10:38PM

Pace2008 wrote: »

Read it yourself, carefully this time:

A double lottery winner isn't defying the odds; it's actually more likely to happen than not, somewhere, at some stage.

Yes but your confusing the point exactly like lugha referred to very well.

Its likely to happen somewhere. But extrordinarily unlikely to happen to any person as an individual. So the odds of it happening to an individual person such as yourself is astronomically small.

Bruthal · 10-03-2011 10:40PM

The-Rigger wrote: »

Well I wouldn't be surprised and it isn't really very relevant.

So the OP asks what is the chance of a person winning the lotto twice. And my point about the odds of winning it twice from 2 tickets is not relevant? Well then, where do we start with calculating the odds then?

And if it is not relevant, why did you post up a link to show an example of it? Which was not really from 2 tickets, but you put it up to that effect.

fergalr · 10-03-2011 10:43PM

lugha wrote: »

This is true. And there is a potential problem with this truth, in a non-lotto scenario, which might be along some day to bite us on the arse.
The probability of an innocent individual having the same DNA profile found at a a crime scene is minuscule. But with a suitably big database, the chances of a "false" match being generated is far from minuscule.

Actually, I have mixed feelings on that particular issue.
In one way, yes, it'll certainly decrease the usefulness of the DNA database, for finding criminals.

On the other hand, currently, a high level of statistical confidence can be taken from a match because the database is small, because it is only populated with criminals.
But this is essentially holding their prior convictions against criminals, as they are (almost) the only ones in the database.
It might be better - from the point of view, of a just, fair, society - to have everyone in the database, and have people properly acknowledge and correct for the flaws in the current system.

Although, given the level of applied statistics thats out there, and the utter lack of stats knowledge among the population - including juries, and probably even judges and some expert witnesses -, I wouldn't hold hope for them doing it correctly.

Jesus Wept · 10-03-2011 10:44PM

Well do you know that the person only did two single lines of the lotto in their life?
I highly doubt it and it wasn't really the point of the thread.

The OP didn't even name the person, just 'some random dub'.
It wasn't even someone they knew so it is not like they were amazed it happened to one particular person, they were amazed that it could happen at all.
And they are incorrect to be amazed by this because it happens quite often.

Bruthal · 10-03-2011 10:56PM

The-Rigger wrote: »

Well do you know that the person only did two single lines of the lotto in their life?
I highly doubt it and it wasn't really the point of the thread.

I never said they only did 2 tickets, i think it can be safely assumed they did far more. The point is, to calculate the odds, we have to start from the fundamental position of 2 tickets. We did that. I said i can safely bet no one has won with 2 tickets. Hardly an earth shattering statement. But you came in with a link supposedly showing someone that had managed it, then tell me its irrevelant.

So you tell us what you think the odds are then, even the link you posted about the woman winning twice had a reference to 2 single tickets even though its very unlikely she only played twice,, any idea why?

The OP didn't even name the person, just 'some random dub'.
It wasn't even someone they knew so it is not like they were amazed it happened to one particular person, they were amazed that it could happen at all.
And they are incorrect to be amazed by this because it happens quite often.

So if your neighbour won it twice, you would just say, a sure its a regular occurance?

Jesus Wept · 10-03-2011 11:06PM

robbie7730 wrote: »

So if your neighbour won it twice, you would just say, a sure its a regular occurance?

I would not be amazed like the droolers out there who think that such occurrences are one offs or unheard of.
I am consistently underwhelmed by the 'amazing' coincidences people point out.

There are many threads you can click into whereby someone will post something, let's say, Clint Eastwood, and some drooler will come along and say 'OMFG, I just watched a movie of his, or OMFG, I had a dream about him last night, toooooo weird'

It's like the birthday problem, people are generally amazed by it and it's a good way to make some money off some knuckle draggers.

Bruthal · 10-03-2011 11:12PM

I think the odds of a person getting 2 tickets, and winning twice is 65,000 billion to one.

So if 2 million people do that, get a ticket for sat and wed, then its 32 million to 1 there would be a double winner out of them all.

So in a year it would be probalby near a million to 1 that we have a double winner if 2 million players get 1 row of numbers for each lotto.

Bruthal · 10-03-2011 11:15PM

The-Rigger wrote: »

I would not be amazed like the droolers out there who think that such occurrences are one offs or unheard of.
I am consistently underwhelmed by the 'amazing' coincidences people point out.

There are many threads you can click into whereby someone will post something, let's say, Clint Eastwood, and some drooler will come along and say 'OMFG, I just watched a movie of his, or OMFG, I had a dream about him last night, toooooo weird'

It's like the birthday problem, people are generally amazed by it and it's a good way to make some money off some knuckle draggers.

Yes these co-incidences do happen. Its just extreme almost impossible odds for an individual. Thats all.

The birthday problem? Family members with the same birthday is it?
Well what amazes me about that one is they work the odds out for 2 people on them shows with 365 x 365, forgetting the fact the parents can aim roughly for the time. The are not going to have a child in jan, feb march etc if they conceive in jan.

Jesus Wept · 10-03-2011 11:19PM

robbie7730 wrote: »

Yes these co-incidences do happen. Its just extreme almost impossible odds for an individual. Thats all.

Yes, of course.
But who gives a **** about the individual (aside from the individual and their loved ones).
It's not like there is only one person on earth.
And it's not like someone started a thread about Jimmy and said, Jimmy is going to do two lines of the lotto and scoop them both, then followed up when he did, ship ship.

It's after timing essentially, omg, some person who is one of the six billion on earth that I don't know or give a crap about won two lotteries, despite that there are millions of lottery draws every year across the globe, amazing, first time ever.

robbie7730 wrote: »

The birthday problem? Family members with the same birthday is it?
Well what amazes me about that one is they work the odds out for 2 people on them shows with 365 x 365, forgetting the fact the parents can aim roughly for the time. The are not going to have a child in jan, feb march etc if they conceive in jan.

No, it's how many random people you need before they start sharing birthdays. It's in the article I posted but I am familiar with it from a book I read many years ago.

http://en.wikipedia.org/wiki/Birthday_problem

Bruthal · 10-03-2011 11:22PM

The-Rigger wrote: »

No, it's how many random people you need before they start sharing birthdays. It's in the article I posted but I am familiar with it from a book I read many years ago.

http://en.wikipedia.org/wiki/Birthday_problem

I see. So when you have 366 people there must be at least 2 with the same birthday type thing, i remember it now.

But sometimes they have on these beyond chance type programmes where the mother has the same birthday as all the kids, and they show astronomical odds. Its high odds in reality alright, but not at the level they usualy say.

Bruthal · 10-03-2011 11:29PM

keane leaves when the real fightin starts:D

Jesus Wept · 10-03-2011 11:32PM

He's too busy with his dictionary.

im invisible · 11-03-2011 01:58AM

loving this thread, and learning a bit aswell:pac:

robbie7730 wrote: »

I see. So when you have 366 people there must be at least 2 with the same birthday type thing, i remember it now.

NO, if you have 366 people, there is 100% chance that two people will share the same birthday
But, what size would a random group of people have to be to have a 50/50 (not bad odds) chance of two of them sharing a birthday? 183? 91?

there is a 99% chance that two people will share a birthday in a group of 57 people
there is a 75% chance with a group of 32 people
a (greater than) 50/50 chance in a group of 23 people, that two will share a birthday

fergalr · 11-03-2011 02:22AM

im invisible wrote: »

NO, if you have 366 people, there is 100% chance that two people will share the same birthday

Not true...

im invisible · 11-03-2011 02:24AM

ok, 367 (counting that elusive leap year kid)

Mellor · 11-03-2011 02:55AM

J K wrote: »

No, you are 100% wrong. You don't know what literacy means.

wow, you are incredibably pedantic.
Which is even more embarassing seeing as you are wrong.

For a start, numeracy is a noun. He used the adjective literate. So an acceptable adjective would be numerate. But that doesn't make all other words and phrases obsolete. His phrase was fine. It was a potmanteau. Hardly a new concept in english language.

"numerical literacy" was coined in 1959 by the UK Committee on Education, presided over by Sir Geoffrey Crowther.

Even more damning to your pedantry, the the fact that over the atlantic, they favour the term literacy over numeracy.

In the United States, numeracy is also known as Quantitative Literacy, and is familiar to math educators and intellectuals.

By all means discuss the rights and wrongs on the maths and/or gambling theory. But if you are going to chatise his choice of words, at make sure you get it right.

Back to the martingale,
I still say there is nothing wrong with it as a system. This still has yet to be disproven by anyone here. I don't advocate it, prefering the kelly criterion in situations were a bet is staked repeatedly.

lugha · 11-03-2011 09:13AM

Mellor wrote: »

Back to the martingale,
I still say there is nothing wrong with it as a system.

Out of curiosity, do you believe pyramid schemes work (as in everyone who piles in will make money)?
If not, can you outline why not?

keane2097 · 11-03-2011 09:53AM

lugha wrote: »

Out of curiosity, do you believe pyramid schemes work (as in everyone who piles in will make money)?
If not, can you outline why not?

This again is the fratration with this thread.

He's spoken about one system, and your means of disproving what he said about it is to ask him about something completely different.

Why can't you address what he said directly and make a coherent attempt at disproving it?

Why do you have to continually talk around the problem instead of talking about it?

11-03-2011 11:31AM

keane2097 wrote: »

This again is the fratration with this thread

Actually, the frustration with this thread is that you refuse to answer even the simplest questions about your "system", then dismiss any attempts to compare it to hypotheticals without explaining why.

Of course, it all becomes clear when I find out that you actually are trolling. Why you decided to drag it out for 440 posts, I have no idea. I can only hope your "followers" are trolling too.

Bruthal · 11-03-2011 11:39AM

im invisible wrote: »

loving this thread, and learning a bit aswell:pac:

NO, if you have 366 people, there is 100% chance that two people will share the same birthday

Well i dont know why you said NO when quoting me, i said this

when you have 366 people there must be at least 2 with the same birthday

Looks very similar to you saying

if you have 366 people, there is 100% chance that two people will share the same birthday

But i think you changed slightly what you originally said, in saying someone would be guaranteed to have the same birthday as anyone you pick from the group. And forgot to remove the NO bit.

Bruthal · 11-03-2011 11:59AM

fergalr wrote: »

The thing is, that's the odds of a single person winning the lotto twice, with two tickets.

If a trillion people each enter 2 lotto draws, then its very likely that one of them will win twice.

So, you have to be careful when you say it does not seem likely to ever happen, because there are more than one person playing the lotto.

When i said its unlikely to happen, i said it in reference to winning having only bought 2 tickets ever. Even 2 tickets one after another having played regularly seems unlikely.

They would have to do it on their first 2 ever tickets to win twice on only 2 tickets to have beaten the odds mentioned before. Once they dont win it on very first attempt, they now cant win with only 2 tickets ever bought. So it still seems very unlikely.

If a trillion people bought 2 tickets for irish lotto, the odds against a double winner are 65 to 1 if our odds of winning twice are the odds of once squared.

lugha · 11-03-2011 01:05PM

keane2097 wrote: »

This again is the fratration with this thread.

He's spoken about one system, and your means of disproving what he said about it is to ask him about something completely different.

Why can't you address what he said directly and make a coherent attempt at disproving it?

Why do you have to continually talk around the problem instead of talking about it?

It is a fairly standard way of trying to highlight the flaw in someone’s reasoning. i.e. Show them a somewhat similar scenario where the may possible see the flaw and they may then appreciate the problem with the original.

Pyramid schemes and the Martingale system suffer from the same fundamental flaw, finite resources. Pyramid schemes eventually run out of “investors”, Martingale gamblers eventually run out of money. Also common to both schemes in the fact that some people will make money (most in the case of the MG system in fact).

The flaw in the Martingale system seems clear to me (Though I am well aware that probability can be subtle, and errors are easy to make. So feel free to highlight any errors in my calculation.

)

Consider a simply version where all bets are even money, where you have a total of €32 to bet and your original wager is €1.

If he wins on the first bet, he is up €1.
If he wins on the second he will win €2 but having lost €1 on the first bet, his net gain is €1.
If he wins on the third he will win €4 but will have lost €1 + €2, again giving a net gain of €1.
And so on. Thus when he wins, whenever that it, he wins €1 net only.

If he loses the first 5 bets, he will be down 1 + 2 + 4 + 8 + 16 = €31 and of course, he cannot “go again” as he has limited resources.

With even money bets, there is one chance in 32 than he will encounter such a 5 bet losing streak. Thus, one time in 32 he will lose €31 and 31 times out of 32 he will win €1.

Which means his expected long run winnings is [31(€1) – 1(€31)] / 32 =exactly zero!

And I don’t think this calculation depends on the resource limit I specify, or even on the assumption of even money bets. I would be pretty confident that the net gain of zero would be the case in all scenarios.

Thus somebody playing this game once will almost certainly win (96.9% chance. Presumably, this is why some seem to believe “it works in practice”?) but someone who plays this game repeatedly can only expect to break even.

And of course as any bookmaker will only give shorter odds than are warranted, in practice, a repeat player can expect to lose.

Bruthal · 11-03-2011 01:28PM

lugha wrote: »

Yes. That would be correct. 8 million squared to win 2 from 2 single tickets, but before the first draw takes place.

Burt earlier you said:

Shirley you cant be serious, and dont call me Burt:D

Fremen · 11-03-2011 05:09PM

Mellor wrote: »

Back to the martingale,
I still say there is nothing wrong with it as a system. This still has yet to be disproven by anyone here. I don't advocate it, prefering the kelly criterion in situations were a bet is staked repeatedly.

Depending on your assumptions, there are mathematical proofs that the martingale system doesn't work. It's probably possible to explain the proofs in layman's terms, but it would be quite difficult, and it would require a fair amount of effort on the part of the layman. I'm not sure I'm up to the task.

Maybe you'll allow me to use some hand-waving and another thought experiment. If we can make a convincing argument that the house still makes money regardless of whether people are using the martingale system or not, it will follow that the players are losing money on average.

What if everyone in the world used the martingale system at a single roulette table? Suppose about half the players bet on red, and half the players bet on black. If black comes up, the house pays the winners with what it took from the losers. Same with red.

Half the world walks away from the table with more money in their pocket, the other half keep playing. They've now doubled their stake so the same amount of money is still at the table. Let's say half of them pick red and half pick black. Again, the house pays the winners with what it takes from the losers, so the house pays nothing.

We can repeat this a large number of times, since we have assumed that there are a very large number of people playing.

The thing is, after a large number of spins, a green will eventually show up, and the house makes a profit. Remember that the house was paying the winners with the losers' money all along, so it paid out nothing, but eventually made money itself.

It follows that the house won "on average", so the players lost "on average".

That's not a proof, but it's a heuristic. Maybe it will go some way towards convincing you.

Note that the kelly criterion says you should bet 0 unless the odds are in your favour. Even if it's a fair game with no house edge, kelly tells you to bet 0.

11-03-2011 05:20PM

Fremen wrote: »

Depending on your assumptions, there are mathematical proofs that the martingale system doesn't work...

Don't bother, keane2097, Mellor and The-Rigger are all trolling

123balltv · 11-03-2011 05:26PM

euromillions tonight 80 million wish me luck
I had a family member who won the lotto years ago maybe winning twice
within families happens

fergalr · 11-03-2011 07:54PM

Fremen wrote: »

Depending on your assumptions, there are mathematical proofs that the martingale system doesn't work. It's probably possible to explain the proofs in layman's terms, but it would be quite difficult, and it would require a fair amount of effort on the part of the layman. I'm not sure I'm up to the task.

Maybe you'll allow me to use some hand-waving and another thought experiment. If we can make a convincing argument that the house still makes money regardless of whether people are using the martingale system or not, it will follow that the players are losing money on average.

What if everyone in the world used the martingale system at a single roulette table? Suppose about half the players bet on red, and half the players bet on black. If black comes up, the house pays the winners with what it took from the losers. Same with red.

Half the world walks away from the table with more money in their pocket, the other half keep playing. They've now doubled their stake so the same amount of money is still at the table. Let's say half of them pick red and half pick black. Again, the house pays the winners with what it takes from the losers, so the house pays nothing.

We can repeat this a large number of times, since we have assumed that there are a very large number of people playing.

The thing is, after a large number of spins, a green will eventually show up, and the house makes a profit. Remember that the house was paying the winners with the losers' money all along, so it paid out nothing, but eventually made money itself.

It follows that the house won "on average", so the players lost "on average".

That's not a proof, but it's a heuristic. Maybe it will go some way towards convincing you.

Note that the kelly criterion says you should bet 0 unless the odds are in your favour. Even if it's a fair game with no house edge, kelly tells you to bet 0.

I think that's a very nice, intuitive explanation.

I've tried to explain this to people before, but ended up going down the route of needing exponential amounts of money to cover the unlikely series of losses; most people don't have the intuition to reason about this, and the appeal collapses - Fremen's explanation is much better.

Has much work been done on using the martingale, or other similar systems, in a game where the player has negative expectation, but has a non linear utility curve for money? (Eg, as an extreme example, maybe I've got 10 euro, need a 20 euro ticket urgently, and a game of roulette is available to me - should I make one bet (thats what I'd assume?), or several?) I'd imagine the correct strategy changes depending on the shape of the utility curve I have?

What are the odds of winning the lotto twice?

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