Academic said:
As lisab said, its a tax on people who are bad at math and statistics.
The monetary value of playing a game of chance is easy to calculate, for each instance of playing the game you multiply the amount you could win by the probability of winning and the amount you could lose by the probability of losing.
<math skipped> There is no financial reason to play such a game, so you shouldn't think to play it for the chance of winning rather than the fun of playing.
No offense, but this is what happens when you couple excessive knowledge of mathematics with insufficient understanding of the real world: you're able to make incorrect conclusions from correct data. It is people like these who made the Great Financial Meltdown of 2008 possible.
Yes, the expectation value of payout of one lottery ticket (less the price of ticket) is typically negative.
HOWEVER, the expectation value is deeply irrelevant, unless you intend to invest the amount of money that is at least remotely close to inverse chance of winning a jackpot.
Odds of winning California Super Lotto are 1 in 41,416,353. One ticket is $1. Therefore, if you were to spend, say, $400,000,000 on tickets over your lifetime, you'd be able to use the expectation value to predict your expected winnings (-0.71 * 400,000,000) and, with some more advanced probability theory, to put some sigmas around that.
On the other hand, if you're only going to buy 1000 tickets over your lifetime, the expectation value does not tell you squat.
Instead, you should estimate your expected lifetime earnings, estimate relative desirability of different end-of-life financial outcomes, and then use probability theory to ask yourself "what strategy gives me the best expectation of outcome?"
For most people, the optimal strategy is to spend as much money on the lottery as they can without otherwise constraining themselves financially (maybe, 1% of after-tax earnings?), because that maximizes their chances of retiring rich (say, with $10,000,000 or more by the age of 65).