Good point. I'll amend my rant to reflect that I'm talking about the US lotteries.

Yes, it's an annuity over 30 years. Currently the jackpot is advertised as $248 million, and the lump sum is advertised as $112 million. You won't get either of those because of taxes, so your actual take home is less than $70 million. Some might argue that you shouldn't exclude taxes, but in this case the house is the government. If a casino advertised favorable odds, but then kept some of your winnings, those wouldn't be the actual odds.

It all sounds like pipe dreaming about more money than anyone needs, but there is a very real fraud. The true value of the jackpot is important because it determines the expected value of a bet. The chances of winning the Powerball jackpot are exceptionally small, but people play because $2 worth of hope is worth it if you get to spend the afternoon imagining what you would name your boat.

To calculate expected value, you take the odds of winning times the value of the win. If a casino offered a coin flip game with pure 50/50 odds, and paid double your bet, then a $1 bet would be worth $2 half the time. Your expected value of that bet would then be $2 x 50% = $1. This would be a perfectly fair game. None of the casino games or sports bets are ever perfectly fair, because the unfairness is where all the profits come from.

Compare it to roulette, where you can bet on red or black, even or odd, and those bets typically pay double. Sounds fair, until you notice that the wheel has 0 and 00 spaces which are neither red nor black, not even or odd. So your odds of winning a bet on red is only 47.37%, so your $1 bet has an expected value of $0.9474.

The difference between your bet and the expected value is called the house edge, and it's how casinos make money. Over the long run, each dollar bet on red or black, even or odd earns the casino a little more than 5 cents. That 5 cents on each dollar keeps the lights on and the buffet cheap. Gaming regulations limit the house edge on games, and regulators monitor the slot machines to ensure they pay off frequently enough to be close enough to fair. Casinos caught with games that are very unfair are fined, because gamblers don't make rational decisions and a large house edge is considered predatory. Most of the money comes in through slots because it's easiest to obscure the house edge and distract gamblers from recognizing how unfair each game is.

Interesting tangent, card counting teams can shift the house edge in blackjack from roughly 2% to -1%, and they managed to make fortunes selling books and making movies about that tiny shift in expected value. Successful teams could earn a few hundred thousand dollars if they are clever and well funded. Card counting is not illegal, but a casino will break your kneecaps if you win because you were counting cards, and we're still only talking about changing your odds by less than a single percent.

For the lotto, the expected value includes all of the lower prizes, but those payouts are very far from fair. Getting the powerball correct has a 1 in 38 chance of happening, but only pays double your money. None of the lower prizes pay anywhere close to the odds of winning. The expected value on a $2 ticket for the lower prizes is only $0.32, for a ridiculous house edge of 84%. Of course, the jackpot is supposed to be the big draw and pays out the most. And since it's a progressive jackpot, it gets bigger and bigger until someone wins. Most people wait for big jackpots to buy tickets, because they sort of understand that the expected value of a big jackpot offsets the very low odds of winning.

1 in 292 million. That's your chance of winning the powerball jackpot.

Now, you might think that a jackpot of $292 million would more or less even the odds, and we're almost there, right? Certainly we're in the casino house edge territory.

Except a ticket costs $2. To make the game roughly fair, the jackpot would need to pay $490 million.

Which still sounds like a ridiculous amount of real money, but jackpots get that big pretty often, right? Seems like every few months, when you start seeing it on the news and people are lining up for the big $500 million jackpot tickets.

And this is where the fraud comes in. Because it's not a $500 million jackpot. It's an advertised $500 million jackpot. To actually get paid $490 million on a jackpot win, the advertised jackpot would need to be $1.7 billion. It's only ever gotten that high twice.

And the kicker? The expected value never reaches the full $2! Because guess what? At that level, the number of tickets sold increase the chances of there being multiple winners. Bigger jackpots sell more tickets, and you actually end up with a better chance of splitting the jackpot 2 or 3 ways than you have of winning outright. The house can never lose, because the game has never been even remotely close to fair.

Remember the card counting potential 1% shift in your favor that would get your legs broken at the casino? Advertising annuity payments creates a house edge disparity of more than 350% between what the advertised jackpot and the actual value of the jackpot. That's 350% more profit just from the fraud. That's not even the mathematical house edge built into the game. That's just money they make from lying to people about the size of the jackpot. 350% shift in the advantage, in a game that was already unfair.