I would never play a lottery that permitted winners to remain anonymous. Too much corruption and shady behaviour in the lottery world. Credible lotteries publish winners' names to prove that a) real people are winning the money, and b) they're not employees of the lottery corporation.
I also think it's a bit of a scam that they dole out the winnings over 3 decades, or substantially reduce it if you actually want your winnings now. And finally, it's shameful that the government takes a quarter of the money in taxes, when they've already gotten a huge piece of the pie in taking their "cut" of the pot, before the numbers are even drawn.
In those respects, I actually like the lotteries here in Ontario. If the jackpot is $20 million, you win $20 million, not a $12 million "lump sum." You bring your ticket to the head office and they cut you a cheque for $20 million, in full. And lottery winnings are completely untaxed in Canada. So you get the full $20 million, and you keep every penny. They also publish the names and photos of winners, so it's credible.
All that said, if I had a convenient way to buy a Powerball ticket, I probably would. But it's a 45 minute drive to the border from where I am currently, and I don't really care that much.