How do you win 2 lotteries?

[X]

From the creationism page

What are the odds of winning twice in a row? Well, it's pretty damned ugly, but of course, you already knew that The number of possible combinations for this week's draw is 14 million. For every one of those combinations, there are 14 million possible combinations for next week's draw. This means that the probability of someone sitting down and picking the next two weeks' winning numbers is one in two hundred trillion.

Now, this is where it gets interesting. The odds of picking two consecutive winning numbers are just 1 in 200 trillion, so it obviously isn't likely to happen. But let's think about this for a minute- what if we aren't talking about just one person? Suppose we're talking about 10 million people (everyone in the province of Ontario) all playing simultaneously? What are their combined odds of winning the lottery twice in a row? Well, suppose all 10 million people play. One would think that the odds would improve by 10 million times, from 1 in 200 trillion to 1 in 20 million, but that's still very poor, isn't it? In other words, it would appear that the odds are 20 million to 1 against the entire population of Ontario ever winning two lotteries in a row!

The above analysis seems to make sense, but wait ... the people of Ontario have won the lottery twice in a row, lots of times. In fact, they've won it three, four, and five times in a row many times in the past (for which the probabilities would seem to be staggeringly low). How can this be? How can real life thumb its nose at probability theory? Well, the problem is that the above probability analysis is oversimplistic and therefore wrong, for the simple reason that it treats two separate sequential events as if they were a single combined event.

Suppose we model it correctly, as two separate events. The odds of 10 million players winning each separate lottery are 10 million in 14 million, or roughly 71%. If we combine the probabilities for the two events (as opposed to combining the events themselves), we find that their odds of winning two lotteries in a row are greater than 50%. Not so surprising that it happens all the time, eh?

What would be the right way to determine the probability of winning 2 lotteries in a row (seperate sequential events)?

[Zoink]

I've never heard of anyone winning two consecutive lotteries. Its definitely not 3-5 times in Ontario. My bologni-detector says to check the validity of the claim. I'd need to see actual names and news links for me to believe that. I've heard of people winning the lottery twice (vague stories), but that would be with years in between, perhaps different lotteries, and for the entire world.

If the odds of winning are 1 in 14 million, the odds of winning twice is 1 in 200 trillion as stated.

However let's say that everyone buys 2 tickets each draw. That's 1 in 50 trillion chance of winning twice.

Let's say you buy for 50 consecutive draws in a year, so that's 1 in 1 trillion chance of winning of you winning in a year.

Let's say 1 million people do this. That's 1 in 1 million chance of occurring in a year.

Let's say this is for the last 20 years, so that’s 1 in 50,000 chance of it occurring in the last 20 years.

.. however, who in the world goes out to buy another lottery ticket after winning millions? You'd have to factor in the chance someone would buy another ticket. If its 1 in 100, then the odds are increased.

[X]

Not any one person winning twice, ANYONE from Ontario winning twice.

Like Person A, who lives in Ontario, and Person B, who also lives in Ontario.

.. however, who in the world goes out to buy another lottery ticket after winning millions?

You never know... some people are pretty crazy.

[Zac Naloen]

could have bought it before realising he'd won, some people don't check their numbers until the middle of the week...

[Zoink]

EDIT

But let's think about this for a minute- what if we aren't talking about just one person?

I misread. The analysis is not talking about a single person, therefore the numers are correct, there is a 51% chance of the lotto being won sequentially.

Individually, you'd have to do something like I did. You might make different assumptions.

[X]

EDIT

I misread. The analysis is not talking about a single person, therefore the numers are correct, there is a 51% chance of the lotto being won sequentially.

Individually, you'd have to do something like I did. You might make different assumptions.

Yes, but how did you get 51% from?
What is the process for figuring it out?

[Zoink]

You never know... some people are pretty crazy.

Evidently so: I did a search and somebody in Chile won two cars consecutively using the same numbers, there was a 1 in 2 million individual chance of winning the car. You would think that after winning the car, she'd figure she didn't need another?

[Zoink]

Yes, but how did you get 51% from?
What is the process for figuring it out?

From the text, assumptions:

1 in 14 million chance of winning.

10 million people buy a ticket.

Therefore the chance of the lottery being won is:

10,000,000/14,000,000 = 0.71 or 71%

There is a similar chance the second time, so the chance of it happening twice is the multiple of the two:

0.71*0.71 = 0.51 or 51%

[CaptainChewbacca]

This is why I hated statistics when I took it.

It defies logic. At least, I think it does.

[Sea Skimmer]

Evidently so: I did a search and somebody in Chile won two cars consecutively using the same numbers, there was a 1 in 2 million individual chance of winning the car. You would think that after winning the car, she'd figure she didn't need another?

Humans aren't greedy since when?

[Rye]

This is why I hated statistics when I took it.

It defies logic. At least, I think it does.

I know what you mean, i never quite understood it. Well, the way i see it, is specific outcomes are difficult to get. For example If we think of all the healthy sperm that were produced to have a chance at what became you, then 1 in 100 million (per se) did it, plus all the variables for the human egg and sex cycle....multiply that by thousands of generations, statistically, you're -very- unlikely, as a specific outcome. But the chance that a child is born is much larger, although still quite low.

[AdmiralKanos]

This is why I hated statistics when I took it.

It defies logic. At least, I think it does.

It is completely logical. What part of it defies logic? It's really nothing more than glorified card counting.

[beyond hope]

This is why I hated statistics when I took it.

It defies logic. At least, I think it does.

It's the statistical abusers (you know, the "4 out of 3 prefer Acme brand!" types) who defy logic.

[Shrykull]

[quote="X"]From the creationism page

[quote]
What are the odds of winning twice in a row? Well, it's pretty damned ugly, but of course, you already knew that The number of possible combinations for this week's draw is 14 million. For every one of those combinations, there are 14 million possible combinations for next week's draw. This means that the probability of someone sitting down and picking the next two weeks' winning numbers is one in two hundred trillion.

I was wondering when I read the probabilty page, why can't someone who can afford to buy tickets with every combination do so? If the price of them is lower than the jackpot and no one else wins you'll gain money.

[salm]

From the creationism page

<snip>

I was wondering when I read the probabilty page, why can't someone who can afford to buy tickets with every combination do so? If the price of them is lower than the jackpot and no one else wins you'll gain money.

they only pay out half of the money earned by selling lottery tickets. so you´d actually lose half of your money.

[Edi]

There was one guy in Finland some 10 years ago who won two consecutive mega-jackpots, one 20 million and one 18 million or thereabouts, which would translate into roughly €6 million and change now. Needless to say, he decided to promptly retire.

Odds of winning any given week are somewhere around 1 in 15 million and change, and he didn't win two consecutive lotteries, but the consecutive big pots that had accumulated when nobody had gotten the correct numbers. The odds of that happening are pretty slim, even when you play systems instead of the one-shot rows.

Edi

[Shrykull]

From the creationism page
they only pay out half of the money earned by selling lottery tickets. so you´d actually lose half of your money.

But isn't the jackpot they announce on tv or whatever media (that becomes real well known when the jackpot is high) the amount you'll get? Which already half the amount of money of the tickets purchased. So, still if it's 15 million and it would cost you say 6 million to get every ticket combination, wouldn't it be worth it?

[Edi]

But isn't the jackpot they announce on tv or whatever media (that becomes real well known when the jackpot is high) the amount you'll get? Which already half the amount of money of the tickets purchased. So, still if it's 15 million and it would cost you say 6 million to get every ticket combination, wouldn't it be worth it?

Lotteries are money-making operations. Therefore the cost of getting all the winning combinations in a system where you get to select your own numbers is always higher than the jackpot, unless it gets insanely high. In a 7 out of 39 number system, the jackpot would have to get somewhere beyond €10 million before trying out all the somewhat over 15 million combos all at once netted you anything, because at €0.60 a pop, you'd have to spend €9 million and something just to cover the cost.

Edi

[Shrykull]

But isn't the jackpot they announce on tv or whatever media (that becomes real well known when the jackpot is high) the amount you'll get? Which already half the amount of money of the tickets purchased. So, still if it's 15 million and it would cost you say 6 million to get every ticket combination, wouldn't it be worth it?

Lotteries are money-making operations. Therefore the cost of getting all the winning combinations in a system where you get to select your own numbers is always higher than the jackpot, unless it gets insanely high. In a 7 out of 39 number system, the jackpot would have to get somewhere beyond €10 million before trying out all the somewhat over 15 million combos all at once netted you anything, because at €0.60 a pop, you'd have to spend €9 million and something just to cover the cost.

Edi

Let's just say you could cover the cost where can you get that many tickets? Not at a mom and pop convienience store, and online it would take too long to fill each one out, is there someone you can simply just tell, "I want a ticket for every combination"

[Darth Wong]

Let's just say you could cover the cost where can you get that many tickets? Not at a mom and pop convienience store, and online it would take too long to fill each one out, is there someone you can simply just tell, "I want a ticket for every combination"

I believe there are ways to buy blocks of tickets; in our local lottery you can buy wildcard tickets, where one of six numbers is a wildcard (needless to say, these tickets are quiet expensive).

However, it's a stupid idea. What if 4 people win? Then the prize gets divided up and you end up losing a shitload of money and feeling like an idiot.

[Edi]

Let's just say you could cover the cost where can you get that many tickets? Not at a mom and pop convienience store, and online it would take too long to fill each one out, is there someone you can simply just tell, "I want a ticket for every combination"

I believe there are ways to buy blocks of tickets; in our local lottery you can buy wildcard tickets, where one of six numbers is a wildcard (needless to say, these tickets are quiet expensive).

However, it's a stupid idea. What if 4 people win? Then the prize gets divided up and you end up losing a shitload of money and feeling like an idiot.

Indeed. This is something I forgot to mention. It happens pretty frequently too, as our system (the abovementioned 7+3 extra out of 39 ) has wildcard systems where you can get a various number of wildcard numbers, and people play them. Last time there was a big jackpot, around €3.6 million or so, there were three or four winners.

Edi

[Metatwaddle]

Where I'm from, we have this thing called the Powerball which has about 1 in 80 million odds. A couple of years ago, the jackpot got really high - $250 million or so. I thought about whether it could possibly be beneficial to buy every ticket combination, and here's what I came up with:
If the lottery gives half of the ticket sales to the winner and half to the government or whatever, then by the time I have purchased 80 million tickets at $1 each (having taken out a loan from the bank), the jackpot is $290 million. But the key factor (at least here) is that they pay the jackpot in annuity, paying over 25 years or 40 years or something like that. Depending on how fast I pay off my $80 million loan, I will probably rack up a shitload of interest to pay. Would I still gain in the end? Maybe. Had I not entered the lottery, would I have retired by the time I stop getting annuity? Possibly. 25 years - probably not; 40 years - maybe. But even if you can pay off your loan without racking enough too much interest, and even if you don't have to split the jackpot with anyone else... well, try going into a bank and asking them if you can get an $80 million loan...

So I retain my opinion that the lottery is merely "a tax on people who are bad at math."

[Zoink]

I thought about whether it could possibly be beneficial to buy every ticket combination,

Also factor in time. Between the time the tickets are on sale and the draw, is there enough time to purchase 80 million tickets. Even at the rate of 1 ticket per second thats 925 days, or about 2 1/2 years. You usually only have a week.

[Shrykull]

Let's just say you could cover the cost where can you get that many tickets? Not at a mom and pop convienience store, and online it would take too long to fill each one out, is there someone you can simply just tell, "I want a ticket for every combination"

I believe there are ways to buy blocks of tickets; in our local lottery you can buy wildcard tickets, where one of six numbers is a wildcard (needless to say, these tickets are quiet expensive).

However, it's a stupid idea. What if 4 people win? Then the prize gets divided up and you end up losing a shitload of money and feeling like an idiot.

the wildcard tickets probably keep the jackpot low to since they are more likely to win.

[Darth Wong]

the wildcard tickets probably keep the jackpot low to since they are more likely to win.

Nope, they're very expensive, in direct proportion to the odds. The lottery corp's not stupid.