lrn2 Utility of Money.
The lottery isn't a ripoff (or is at least less of a ripoff than people think) because a big amount of money is actually worth disproportionately more to a person than a small amount of money. For example, money is only worth as much as what you can buy with it. With $1, you can buy a king-sized Snickers bar. With $100,000, you can buy a Corvette ZR1. Most people would rather have the car than 100,000 candy bars, so the "value" u($100,000) of a hundred thousand dollars is more than 100,000 times the value u($1) of one dollar.
So if u(X) represents a person's utility function, then the expected gain in buying a $1 lottery ticket is (using numbers from
http://powerball.com/powerball/pb_prizes.asp and writing X for the grand prize amount)
1/61.74 * u(3) + 1/123.48 * u(4) + 1/787.17 * u(7) + 1/359.06 * u(7) + 1/13644.24 * u(100) + 1/19030.12 * u(100) + 1/723144.64 * u(10000) + 1/5138133 * u(200000) + 1/195,249,054 * u(X)
If the ticket purchaser has a linear utility function, u(x) = ax+b, this gives an expected value of
0.17471 a+0.0284783 b+(aX)/195249054
or a break-even point of
X = -3.41119*10^7+1.95249*10^8/a-(5.56036*10^6 b)/a
In the case a = 1, b = 0 (i.e. $100,000 *is* worth exactly 100,000 times as much as $1), this becomes $161,000,000.
Of course, with taxes and stuff, you'd probably have to double that.
tl;dr: If the powerball jackpot is in the $400 million range or higher, a ticket is actually a good investment, technically.