The much, much bigger question is why anyone would play the lottery. It is quite simply a tax on those that can’t to math. Really.
Ever been to a football stadium? Well, if not, picture any very large seating capacity structure. Doesn’t matter. Let’s say the stadium holds 100,000 seats (most hold much fewer). Now picture, on each and EVERY seat, 14 music CDs. Now, for $1, you get to go in and pick just two CDs. If one of them matches the name written down by the guy running this, you win! If not, “next!” This is for a 1 in 14,000,000 chance of winning! Big Game is far worse! Big Game is 1 in 76,000,000. (Picture 76 CDs on each and every seat… and that is in a 100,000 seat stadium! Most stadiums would be 50,000, meaning you need 152 CDs on EVERY seat).
So how you take a trip to NYC. You open a phone book listing EVERY SINGLE PERSON IN THE GREATER NYC area. And then some. Find a name. Pick a second name. Stop the next person on the street and ask if they are either of those two names. No? Next! Again, that is for 1 in 14,000,000. 1 in 76,000,000 would be more like NYC, Boston, LA, Chicago and more… COMBINED. Probably like the entire West Coast of the US.
If you came across either of these games at a fair, you wouldn’t play. You’d laugh at those that did.
Your chances are, to 7 (!) decimal places, 0.
As for cash or annuity, well, I guess the question is whether you think you can invest smarter than the people running the lottery.
Payout for Big Game right now is $325,000,000 jackpot or $170,950,00 cash. Assume 40% tax. Jackpot would be $195 million. Cash would be $102 million. Doing the math, it is obvious the lottery officials expect to earn 8.25% on the money. If you can beat that, go with cash. If you can’t, annuity is the way to go.
More directly to the OP, which is: why do they care? More than likely it has to do with figuring the jackpot total. The upfront cost of a cash payout is obviously much higer than an annuity payout. Figure in the probabilities based on how many picked which, and you can get a good idea how much cash they are going to need for the next payout. As others pointed out, people can switch, but there again I’m sure those odds are figured into all this. It really doesn’t matter, though.