Can someone help me figure out how the lottery gets its numbers?

[xiphias]

So, the Mega Millions jackpot is up to 540 million dollars, and might be raised to 600 million dollars, or, to put it another way, about what's in Mitt Romney's couch cushions.

So, naturally, I've been doing the calculations to see if it's worth playing.

Here's how the game works.

You've got a panel of numbers up top, from 1 to 56, from which you choose 5. Then you've got a panel of numbers on the bottom, from 1 to 46, from which you choose 1. Match them all, win whatever the jackpot is -- it starts from 12 million dollars, and goes up from there, right now being above half a billion dollars.

It seems to me that the odds of winning are therefore 1 in 56*55*54*53*52*46, which is 1 in 21,085,384,320. But the Mega Millions websites all claim that the odds are 1 in 175,711,536, which is exactly 120 times as good.

What are we doing differently? Where are they getting that 120-times improvement in the odds, and which one of us is right?

Edited to add: In any case, if the numbers the lottery web pages give are right, and I've done my math correctly to include all the non-jackpot prizes, the break-even point at which it's worth playing is when the jackpot hits $155,002,177. Not counting taxes, or the odds of more than one person hitting the same number as you, which would leave you splitting the jackpot.

Edited to add again:: Factoring in the fact that the jackpot amount is an annuity, and the cash value is approximately 58% of that, the 25% federal tax, and a 6.25% state tax, the break-even point is $389 million dollars. Going more decimal places than that is pointless, since the cash value is only an approximate percentage of the published jackpot. That still doesn't factor in the chances of hitting the same number as another person and splitting the pool.

Comments

[xiphias.livejournal.com]

Oh, we went over this junior year of high school; it's just that that was over twenty years ago. The information is still there in my head somewhere; it's just retrieving it is tricky.

[ron_newman]

Yep, it's pretty rusty for me as well; I haven't thought about this stuff in years.

[asciikitty.livejournal.com]

whereas I was raised by math teachers, and think about this stuff for breakfast. I'm pretty sure this is a sign of something terrible in me.

[thnidu.livejournal.com]

Oh, I dunno. I'm a research linguist, and my dear wife was an English Lit major and a librarian. She wrote up the following about our kids (I knew I'd written this up, but I had to find it here):

SON got into trouble in AP English because he didn't want to work out of the intro to poetry book. I had to point out to the teacher that he and I had already hashed out assonance and alliteration as I drove him to nursery school one day. Not to mention that he had written a pamphlet on the subject himself for Academic Decathlon. His teacher got his permission to use it for her regular track 9th graders, since there wasn't anything available that explained it as clearly.

Not to mention hearing DAUGHTER on the phone in high school, saying impatiently to a friend, "Of course I know what the Great Vowel Shift is. Everyone does."

I have not yet taken a poll of 15-year-olds to verify this.