I wonder what's the probability of winning something in that sweepstakes.
For a game copy? Very, very small. Garbage conjectural statistics incoming
It's very difficult to make any firm numbers because we won't know how many people are playing, but this is what I came up with.
Assuming about 1/3 of all American players enter it (I'm estimating about 3-4 milllion based off of Black and White lifetime sales of about 12Mil, it will probably be on the lower end of that estimate due to the 3DS's smaller install base.) And assuming that absolutely every one uses all 24 entries and therefore has an equal number of entries:
192/72,000,000 or 2 ten thousandths of a percent per draw.
Of course not absolutely everyone is going to use all 24 entries so I'll lop off about 6 entries on average.
192/54,000,000 or 3.5 ten thousandths of a percent per draw.
If you do all 4 contest periods you might even get into the thousandths of a percent!
This is all wild conjecture and it's entirely possible your chances might actually be much better than that, so don't get too disheartened. It's not like you lose anything from trying.
EDIT: Did the cumulative prob for the optimistic value, it's 1/100th of a percent for a game.
