What are the odds of winning the lotto twice?

thenutflush · 15-02-2011 10:21PM

^ Seems to be true!

http://www.tribune.ie/article/2003/may/11/lotto-surgeons-winning-streak-continues/

J K · 15-02-2011 10:22PM

alastair wrote: »

You do.

No you don't.

15-02-2011 10:25PM

sparkthatbled wrote: »

I remember hearing what might have been one of those 'friend of a friend told me' stories with no substance. It went that a doctor living in Donnybrook who entered the lottery for the hell of it won the jackpot twice (it being the days when the jackpot was rarely above 2mil). Dunno if it's true but it sure angries up the blood when you're paying off a €500 credit card bill in instalments!

That's who I was referring to in my previous post

fergalr · 15-02-2011 10:33PM

xoxyx wrote: »

The odds of winning the Lotto twice are the same as winning the Lotto once.

You probably know this, but exactly what you wrote, isn't true.

Of course, the odds of winning the lotto the second time, per entry, were the same as the odds of winning it the first time.

But: The odds of winning it twice, before winning it the first time, are very much less than the odds of winning it once.

Its like rolling 6 on a 6-sided fair die (you know, one of the dice you use to play monopoly or whatever).

If you throw one die, your chance of throwing 6 is 1 in 6.
That's a probability of 0.1666...

If you throw two dice, your chance of throwing 6 both times is 1 in 36.
That's a probability of about 0.0277...

0.02 is much less than 0.1666

However!
If you have just thrown a 6, and you try throw another 6, your chance of doing so is 1 in 6 again - again, probability of 0.1666

Now, there are some assumptions here.
If you always buy as many lotto tickets as you can afford to, obviously, having won it once, you are much more likely to win it a second time - because you can buy more tickets!

xoxyx wrote: »

The chances of a certain set of numbers coming up is the same every week. The fact of a person having those numbers doesn't come into it!

Same way as the odds of throwing a red number 3 at roulette once, doesn't affect the odds of that same number coming up again on the next throw.

It's a random occurrence every time. Past plays don't come into it!

fabbydabby · 15-02-2011 11:10PM

Fergair is correct. Probability of this event happening twice = the probability of it happening once, squared.

To use the die example (1/6)^2 = 1/36

However if you have already won the lotto, the chances of you winning it again are the same as they always would be for anyone.

Captain Darling · 15-02-2011 11:26PM

orourkeda wrote: »

remote

8145060 to 1 to do it once.

So there is a chance?

Poor Uncle Tom · 15-02-2011 11:27PM

Twice...Pffft....I've won the Nigerian lottery 6 times this month alone and shares in the Spanish lottery at least a dozen times since Christmas.

Savage Tyrant · 15-02-2011 11:37PM

The mother of a friend won over 3 million on the lotto about 6 years ago.... She hasn't won it a second time but she does spend 350 euro a WEEK on lotto tickets. Pretty disgusting actually.

u140acro3xs7dm · 15-02-2011 11:48PM

I think what we should do as they do in other countries is every time there is a roll over have an extra draw. So if it no one wins for 4 weeks there would be 4 draws on that night for 1 or 2 million each or whatever the jackpot is. that way you change 4 peoples lives rather than 1. Saying that i would be so pissed off if i had to share with others.

Iwannahurl · 16-02-2011 12:18AM

fabbydabby wrote: »

Fergair is correct. Probability of this event happening twice = the probability of it happening once, squared.

To use the die example (1/6)^2 = 1/36

However if you have already won the lotto, the chances of you winning it again are the same as they always would be for anyone.

This kind of thing is a statistical favourite and a nice head-wrecker that gets you thinking about coincidences and surprising events.

As always with calculating probabilities, probably the trickiest part is deciding exactly what question you are posing.

Is the question "what is the probability that a specific person buying a single ticket for two separate draws will win both times"?

Or is it "what is the probability that some person, out of all the people who buy Lotto tickets, will win the lottery twice in a lifetime"?

The specific individual playing twice and winning twice is a very different mathematical beast from the someone somewhere some day eventually winning twice.

If it's the first one, then the chances are indeed astronomically small but not very relevant.

The second is a bit more real, and in fact far more likely than we might think, because large numbers of people buy lots of tickets every week for every draw for years on end. I would suggest that what people are really wondering about is the possibility of anyone ever winning twice.

Check out these articles referring to a story in the New York Times about a woman who won the New Jersey lottery twice in the mid to late 1980s. The NYT said it was a "1 in 17 trillion chance", which was strictly correct but only for a very specific condition. Two statisticians from Purdue University came up with a very different answer. Read on...

The law of truly large numbers says that with a large enough sample many odd coincidences are likely to happen.

For example, you might be in awe of the person who won the lottery twice, thinking that the odds of anyone winning twice are astronomical. The New York Times ran a story about a woman who won the New Jersey lottery twice, calling her chances "1 in 17 trillion." However, statisticians Stephen Samuels and George McCabe of Purdue University calculated the odds of someone winning the lottery twice to be something like 1 in 30 for a four month period and better than even odds over a seven year period. Why? Because players don't buy one ticket for each of two lotteries, they buy multiple tickets every week (Diaconis and Mosteller).

1-in-a-Trillion Coincidence, You Say? Not Really, Experts Find

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CrazyRabbit · 16-02-2011 01:46AM

If you flip a coin, you've a 50/50 chance of it being 'tails'.
If you flip the coin again, there's still a 50/50 chance of it being 'tails'....again. Luck doesn't play into it, and the odds never change so long as the initial conditions remain.

Doesn't matter how many times you win, the odds are exactly the same each time.

Of course, if you won a few million on the lotto, you could buy more tickets for each subsequent draw, thus increasing your chances of winning.

alastair · 16-02-2011 02:05AM

fabbydabby wrote: »

Fergair is correct. Probability of this event happening twice = the probability of it happening once, squared.

To use the die example (1/6)^2 = 1/36

However if you have already won the lotto, the chances of you winning it again are the same as they always would be for anyone.

The chance of you winning every time you play is always the same - independently defined by the terms of the draw - it just happens that you're extremely likely to lose each time, and the more you play, the more the probability of you losing asserts itself.

J K · 16-02-2011 02:13AM

CrazyRabbit wrote: »

If you flip the coin again, there's still a 50/50 chance of it being 'tails'....again.

Before you flip the coin the first time. You want to calculate the probability of both flips being heads. The answer is 25%. So you're wrong it is not 50/50.

J K · 16-02-2011 02:16AM

alastair wrote: »

The chance of you winning every time you play is always the same - independently defined by the terms of the draw - it just happens that you're extremely likely to lose each time, and the more you play, the more the probability of you losing asserts itself.

Let's say you were going to play the lotto next week - one line, and then one line again the week after.
What are the statistical chances of you winning both jackpots. Not the same as winning either the first alone or the second alone.

upandcumming · 16-02-2011 03:28AM

8145060 to 1 to do it first.
Same again the second time.

Nothingbetter2d · 16-02-2011 03:29AM

what are the odd of being as lucky as this woman 4 fecking times the jammy git

http://www.thaindian.com/newsportal/world/texas-woman-wins-lottery-for-the-fourth-time_100391731.html

Iwannahurl · 16-02-2011 12:11PM

tommy21 wrote: »

Just heard on newstalk that some lucky dub had picked up a cool half mil after winning 2.5mill a few years ago. I can't help but feel a little bitter...

What are the odds of this?!

The OP didn't ask any question about the flipping of coins or the throwing of dice.

IMO he is asking what is the probability (or odds, whatever) of some person winning the lotto twice within a time period of several years.

To estimate the real-world probabilities of such an occurrence you need to factor in real-world conditions, in this case the fact that large numbers of people play the lottery and that there are two draws every week (more if you want to include Lotto Plus).

It all depends how you frame the question. Are you asking "what was the probability that both of those particular tickets would win" or are you asking "what is the probability that some lucky person will win the Lotto twice in the space of a few years"?

When Evelyn Marie Adams won the New Jersey lottery for the second time back in the 1980s, the New York Times called it a 1 in 17 trillion longshot.

They were giving the right answer to the wrong question though. Here's a 2009 article in the Wall Street Journal that explains why "some lucky Dub" winning twice in the space of a few years might not be such an unlikely occurrence after all: Odds Are, Stunning Coincidences Can Be Expected.

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Duggy747 · 16-02-2011 12:15PM

The odds of me winning the lotto = zero.

Everytime I get a lotto ticket I can hear it laughing at me for having such foolish notions.

Doesn't help that the toaster won't stop bullying me, either.

dolphin city · 16-02-2011 12:19PM

tommy21 wrote: »

Just heard on newstalk that some lucky dub had picked up a cool half mil after winning 2.5mill a few years ago. I can't help but feel a little bitter...

What are the odds of this?!

same as it is first time round

each draw is different so the odds will be the same for each draw.

Iwannahurl · 16-02-2011 12:21PM

Nothingbetter2d wrote: »

what are the odd of being as lucky as this woman 4 fecking times the jammy git

http://www.thaindian.com/newsportal/world/texas-woman-wins-lottery-for-the-fourth-time_100391731.html

"The store sells around a thousand lottery tickets each day, and will now be eligible for another ten thousand dollar bonus for selling a winning ticket. It is the second such bonus won by the store, for a ticket bought by the same person."

http://www.thaindian.com/newsportal/world/texas-woman-wins-lottery-for-the-fourth-time_100391731.html

AnonoBoy · 16-02-2011 01:07PM

adamski8 wrote: »

To estimate the real-world probabilities of such an occurrence you need to factor in real-world conditions, in this case the fact that large numbers of people play the lottery and that there are two draws every week (more if you want to include Lotto Plus).
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How many people play the lottery doesn't affect your particular chances of winning it. It does affect your chances of being a sole winner but not of you actually having the six numbers.

kfallon · 16-02-2011 01:09PM

He may have won it twice but ask yourself this.....is he happy???

:rolleyes:

Course he fooking is, he's absolutely deli'red

Iwannahurl · 16-02-2011 04:41PM

This.

Fremen wrote: »

Well, you need to phrase the question a bit more precisely than that.

If I ask "what is the probability that *I* will win the lotto twice in a row", it's easy enough to show that it's the square of the probability of winning it once.
(the odds of me rolling a die and getting 6 are 1/6. The odds of that happening twice in a row are 1/36).

If you ask "what is the probability that someone in Ireland will win the lotto twice over ten years", the calculation is not nearly as straightforward, and you need to make some assumptions to simplify the calculation.

As a ballpark figure, suppose there are a thousand jackpot winners who still buy two lines a week. In any given week, the odds that one of them will win are about one in three thousand (assuming the lotto is still 42 numbers choose 6 like when I was a kid).

Under these slightly flaky assumptions, after about 39 years, it's 50:50 for a jackpot winner to win twice

( to see this, solve (2999/3000)^x = 1/2. Turns out x = 39 or thereabouts)

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Fremen · 16-02-2011 05:18PM

The last line should read (to see this, solve (2999/3000)^x = 1/2. Turns out x = 2079 or thereabouts). Divided by 52 weeks in a year, it gives about 40 years rather than thirty nine. I just ignored everything after the decimal point when I looked at it earlier.

Iwannahurl · 16-02-2011 05:24PM

This is a key point being missed by other posters in this thread: "suppose there are a thousand jackpot winners who still buy two lines a week".

Now that you mention it, how many jackpot winners are there anyway?

Iwannahurl · 17-02-2011 12:44AM

For the mathematically inclined, here's a paper that addresses the Lottery Double Winner question. The relevant section, Example 2.23, is on pages 18-19 of the PDF file, 42-43 in the original document pagination.

Jesus Wept · 17-02-2011 12:54AM

Wibbs wrote: »

Apparently not that remote. I recall reading somewhere before that you've a slightly higher chance of winning the lotto if you've won it before. I know someone who won it twice myself. Not huge money, but a couple of 100 thou(I know that's loads, but not, "Im buying a small island in the far east, building my own rockets and if that cnut Bond shows up, I'm shooting him in the face on sight" money)

This is true, it's called experience.

keane2097 · 17-02-2011 01:20AM

The-Rigger wrote: »

This is true, it's called experience.

Confirmed.

You're obv going to be in a better position to win the second time now that you know what it takes to win it once.

phantom_lord · 17-02-2011 01:23AM

chances are people who've won the lotto are just better at picking the numbers.

I wonder if we could get a stable of previous lotto winners and start staking them?

Mellor · 17-02-2011 01:36AM

Wibbs wrote: »

Apparently not that remote. I recall reading somewhere before that you've a slightly higher chance of winning the lotto if you've won it before. I know someone who won it twice myself. Not huge money, but a couple of 100 thou(I know that's loads, but not, "Im buying a small island in the far east, building my own rockets and if that cnut Bond shows up, I'm shooting him in the face on sight" money)

[insert bonus ball facepalm pic]

Blisterman wrote: »

Lets see if I can remember my leaving cert probablity..
As every line he buys increases his odds of winning,

It's 66342002403600 divided by the number of entries bought in total.

Say he bought 1,000 lines in his years of playing the lotto, it's 1 in 66,342,002,403.6/1 For one person or just over sixty billion to one.

That's just the odds for an individual. As about a million people play the lotto, the odds of this ever happening reduces to about 60 thousand to one.

Still impressively rare.

Sadly you can't remember your probability, and got this all wrong.

What are the odds of winning the lotto twice?

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