First of all, I did not realize this was a scratch ticket. I thought it was the regular lotto where you have to match the numbers. Obviously scratch cards are a bit different because who knows how they’re distributed? So 2 winning tickets happened to go to this woman’s town. That increases the odds of her winning significantly. But, disregarding that…

“That means we need 419 million people to buy 100 tickets.”

No, it doesn’t. To get those 1/419 million odds, you’d need one person to buy 100 tickets, or 10 people to buy 10 each, 100 people to buy one each, etc.

I understand where you’re coming from, but I’m not sure thats right.

think of it this way, if I flip a coin there’s a 1/2 chance of it being heads. fair enough. but if I flipped 2 coins, the chance of both being heads is only 1/4. of course, if I flipped a coin and got heads, then the chance of the other also being heads is 1/2.

in the same way, the chance of winning the lottery twice is not the same as winning it once. of course, if you did win once, then the chance of winning it again is the same as winning it once. but, when you consider that most people don’t even win once…

another point, they say that the odds of winning twice are something like 1 in 30 for a four month period, that would mean that someone would be expected to win twice every 10 years. yet, over 10 years, most people still haven’t won even once. am I the only one who sees that that doesn’t fit?

but, there is yet another way to think of it (note: my ability with maths and statistics is somewhat limited. so I’m really sorry if I totally screwed something up here >.> ). the odds of winning once are 1.44 million-to-1. now, I don’t know how many different people win the lottery. but, over 10 years, I’d imagine it would only be about 500 people (please correct me if you have a better number. mines kinda just a guess) I’ll be very nice and say that those 500~ people combined buy a total of 1000 tickets per lottery (since, as someone said, some of those people will buy more than one ticket).
so, come next lottery, the chance of the winner being someone that also won in the last 10 years is about 1.44 million-to-1000 (1.4 thousand-to-1). now, this may sound more friendly, but it means that it would take about 1.4 thousand lotteries before someone could be expected to win twice. I don’t know how this lottery works, but assuming there is one winner a week, it would take about 27 years for someone to be expected to win twice. that actually sounds somewhat possible…
but of course, knowing me, I probably did make some huge mistake somewhere. and my brains starting to hurt too much for me double check some of this working and writing >.

http://tinyurl.com/3coxmv

“The odds of winning just once are 1.44 million-to-1, according to state lottery officials. The odds of winning twice vary, depending on how many tickets are scratched. Lehigh University professor Bob Storer placed the odds of winning twice at 419 million-to-1, if 100 tickets are played.”

The calculation is correct, but it’s a pain in the ass to do, because they are large numbers. The formula we use will be http://en.wikipedia.org/wiki/Binomial_distribution , which is:

Combination(100, 2) * (1 / 1440000) ^ 2 * (1439999 / 1440000) ^ 98

Calculate that out. It’s about 1 in 419 million :-P.

That means we need 419 million people to buy 100 tickets. And one of them will win twice. There are 12 million people in Pennsylvania. So we would need each person in PA to buy 3491 tickets. At $20 each.

It’s absolutely ridiculous. It’s very easy to not do the calculation and say, “Yeah I suppose a person winning twice is bound to happen”. No, it’s not bound to happen. Do the calculation.

“The key word here is ’someone’. Those are the odds that, out of MILLIONS of people that consistantly play the lottery, the odds that any random one of them will win twice is 1 in 30 over a four month period. Of course the odds of any specific person doing it are wildly small, but out of all those people, it’s bound to happen to someone.”

And that is basically the idea I was presenting in my first post about how each ticket holds a 50(recalculated) million to one chance of being a winner. Buy more, it goes down. Calculated as a group of tickets between a group of people, it goes down more. But buy one single ticket and the odds are still going to be 50 million to one.

The key word here is ’someone’. Those are the odds that, out of MILLIONS of people that consistantly play the lottery, the odds that any random one of them will win twice is 1 in 30 over a four month period. Of course the odds of any specific person doing it are wildly small, but out of all those people, it’s bound to happen to someone.

Just like, for the non-creationist people, what are the odds that the planet we happen to live on would have just the right combination of temperature, atmosphere, gravity, etc. Obviously these odds are not very good, we’ve yet to find anywhere else with these characteristics. But that doesn’t matter because if it didn’t happen, we wouldn’t be able to think about it. There may be a billion places not like here, but we are the lucky ones. Similarly, there are millions of people that never win, but there’s a few that happen to win more than once.

Large numbers are really an interesting thing. Some other things to think about are car accidents. What are the odds that any specific time you go driving, you’ll crash. Pretty low right? Yet millions of people get into car accidents, some get into more than one, and some do it quite often. Of course this isn’t entirely the same because part of it is driving skill, but same idea.

The bottom line is, if our understanding of randomness, probability, and large numbers did not work, then Lottories and those amazingly rich insurance companies would not be able to function. Insurance companies base their whole business model on calclulations based on these laws.

Computer psuedo-random numbers are a different story. No, those are indeed not random, but that’s because computers are entirely determanistic. All things being said, they put on a pretty good illusion.