Here’s Powerball’s “hot or not” chart: http://www.powerball.com/powerball/pb_frequency.asp
It seems to be a popular feature with the customers.
Besides that, they want to have drawings with no winners. Then they can roll the unwon jackpot into the next drawing and increase the payout. The higher the jackpot, the more people enter, as demonstrated in the current frenzy.
But surely you’ve seen a TV lottery drawing with ping pong balls, “and the next number up is…”
Interesting, if not well-known: It’s not always fair, or random..
Yesterday, I heard on the radio that so many tickets have been sold for tonight’s Powerball drawing, that they expect 85% of all possible number combinations will be covered.
Extremely difficult, but not impossible. Very likely unprofitable.
In order to cover all 292,201,338 combinations, you’d need a small army of people working for you. Suppose each one of your employees spent 40 hours in a week just buying tickets by filling in those bubbles with a #2 pencil, carefully following a pre-printed list of combinations assigned to this one person. At one ticket per minute, that’s 2400 tickets per 40-hour week. So you’d need 121,751 employees. If you paid them $8 per hour, the labor would cost you $39,000,000 plus payroll taxes. And this doesn’t include overhead like the time spent hiring all those people, coordinating their work loads, hiring an accounting firm to write their paychecks, paying for office supplies. And you’d need some backups for the inevitable employees calling in sick.
Suppose the jackpot was 1.8 billion and tickets cost $2. You’d need $584,402,676 for the tickets, plus about $40,000,000 to pay your employees and maybe another $10,000,000 for overhead. If your team was fortunate enough to be the only one with a winning ticket, then you could end up with a profit of $1.165 billion, which is a nice ROI. But it’s far more likely that you’d end up splitting the prize with other people. If there were 400 million tickets sold to other people (plus the 292 million your team bought), the most likely outcomes would be either 2 or 3 winners. If it’s two, your company ends up with $265 million. But if it’s three, your company loses $34.4 million. And if it’s it’s more than three… you could end up losing hundreds of millions.
Oh, and good luck trying to find more than 100,000 people who are willing to do such a dull and boring job for just $8 per hour, knowing in advance that next week they’ll be unemployed again, and trust them not to keep any tickets for themselves.
Which means we’ve probably underestimated the number of tickets sold. Instead of 400 million tickets bought by other people, let’s figure it to be 800 million. Now the most likely outcome is that the jackpot gets split five ways (your company plus four other winners). In this scenario, your company loses $274.4 million.
But there are also TV lottery drawings that look like this, where each number comes out of a separate machine. Here duplication is possible–and indeed, it happens in the Daily 4 number in this clip.
To those of us who don’t pay much attention to lotteries, exactly how PowerBall works is not necessarily intuitive. Apart from occasionally buying a scratch-off ticket, I’ve never played any type of lottery. It’s kind of interesting to learn the various ins and outs.
It turns out that only 371 million tickets were sold, much less than I estimated.
But I forgot to account for the fact that when they say that the jackpot is 1.5 billion IT’S NOT REALLY 1.5 BILLION. Let me explain. Let’s play a game. We’re going to bet on a coin flip. You have to pay me $15 before we flip the coin. If it comes up heads, I keep your $15 and you get nothing. If it comes up tails, I keep your $15 and I pay you $30. Sounds fair so far, right? It’s 50-50 odds and I’m offering you double-or-nothing. But here’s the catch. If you win, I won’t give you the $15 all at once; I’m only going to give you $1 a year for 30 years. However, I’ll also give you the option to take a lump sump of $18.60 right now. What do you think of the game now? Does it still sound fair?
Put it another way… Right now you can go to a bank and buy yourself an annuity. If you want an annuity that pays $1,000 per year for the next 30 years, that will only cost you $18,600 right now. So tell me, how much is that annuity worth? It’s worth $18,600. Anyone who claims that it’s worth $30,000 is fudging the truth. When the lottery says the jackpot is $1.5 billion, what they REALLY mean is that all the winners (three of them in this case) will each get annuities that pay $16,666,667 per year for the next 30 years. How much is that annuity worth right now? $310 million. In accounting terms, that’s called the Present Value.
So now let’s readjust the numbers I posted earlier. You need $634.4 million to buy the tickets and pay your expenses. If they say the jackpot is $1.5 billion then that means p is really 62% of $1.5 billion, which is $930 million. And if you end up with three winners (which is what happened), then your company takes in only $310 million and you’ve actually lost $324.4 million. That’s a terrible return. Even if there’d only been two winners, you company would have gotten just $465 million after spending $634.4 million, for a net loss of $169.4 million. The only way to make a profit here would be if your company had the only winning ticket. The chances of that happening were roughly 1 out of 10.
I can’t believe I forgot to account for the difference between Future Value and Present Value. Sorry about that.
Don’t forget to also account for the fact that not every dollar collected from ticket sales goes into the jackpot. A bit chunk goes to the states participating in the lottery.