Wednesday, October 19, 2005

Powerball mania strikes

Texas used to be a Powerball state, but no longer. We now have MegaMillions, which is an equally good ripoff. They say that the lottery is a tax on people who are bad at math. Apparently people who are bad at math think that spending $1 on a 1 in 146 million shot at what is claimed to be $340 million is a good deal.

Being good at math, let's run the numbers ourselves.

The smaller prizes, ranging from $3 to $200,000 have a total expected value of just under 20 cents. To break even the grand prize must have an expected value of 80 cents. We know that we won't break even, because the whole point of the lottery is to fund the government. The worst odds in privately operated casinos are around 90 cents on the dollar. To match that, the expected value of the Powerball grand prize would have to be 70 cents.

At first glance, the expected value of the grand prize appears to be $340 million / 146 million = $2.33. However, the real value of the grand prize is about half of $340 million. The winner has the option of taking roughly $164 million now, or getting the full $340 million in 30 annual payments. Either way, the present value is less than half of what they advertise. At $164 million, the expected value of a ticket is still in the money: $1.12.

But of course, Uncle Sam will want his cut. By the time he is done with you, a third of the jackpot will be gone. You will be left with $118 million. Now the expected value is $0.81.

This is right at the break even point. And this is as good as the odds ever get. I must point out that for the odds to get this good, 540 million losing tickets were sold over the last 10 weeks. All those people who are bad at math are responsible for the odds being anywhere close to even in this one drawing.

But it is not as good as it looks even now. We have not yet considered that you might have to split that jackpot two or three ways, or more. With 120 million tickets sold for this drawing, the odds are good that there will be multiple winners. If you do happen to win, there is a 56% chance that someone else won too. There is a 31% chance that you will have to split the jackpot 3 ways or more. On average, a winner will get $78 million after taxes. Taking this into account, the expected value of that ticket is just 73 cents, including the 20 cents from the small prizes.

It would be illegal for any private casino to offer odds this bad.

So why does the Lottery Commission tout the $340 million number instead of what it is really worth: $78 million? It's all marketing hype. The bigger number will attract more ticket sales. More ticket sales mean more profit for the Lottery Commission. Every ticket sold, regardless of the results of the drawing, means a 20 cent profit for the Lottery Commission.

Proponents of the lottery say that it helps to fund beneficial government programs, such as education. After all, who could be against better schools? But at what cost? And from whose pocket? The evidence clearly shows that most lottery revenue comes from people who can't afford to play. For many people who are professional wards of the state, dependent on government for their meager existence, the conditioned response is to look to government as the source of all hope. The lottery acts to maintain the cycle of dependency. Similarly, unskilled, uneducated people in low-paying jobs, the same one's who don't have the mathematical ability to know how bad a deal the lottery is, see the lottery as their only chance to escape their paycheck-to-paycheck existence. These are the products of the public education that the lottery provides.

It is true that some people who can afford to play and do recognize that the system is heavily rigged against them still do play for entertainment purposes. It gives the buyer the chance to dream what she would do if she won. An argument can be made that the jackpot is "big enough" even though the expected value is less than the price of the ticket. After all, $118 million split three ways is still enough to change a person's life. However, for most people, the change is not as positive as they imagined. Many squander their money. Most find friends and relatives distancing themselves, or scheming for how to cash in on the sudden wealth. The case of William "Bud" Post is a great example. Bud had been living on a government disability pension. In 1988, Bud won $16.2 million in the Pennsylvania Lottery. The government immediately took $5 million. Soon after winning, a former girlfriend sued and won a third of his winnings. Bud's brother was later convicted of hiring a hit man to kill Bud and take a share of the winnings. Post used up what was left on fancy vehicles and high-dollar toys. He gave loans to relatives and lost money in investment scams. He soon was deep in debt, with the future lottery payments as collateral. Post now lives on a $450/month government disability pension. Some dream, huh? If Post had not been so bad at math, he might not have played in the first place, or he might have planned wisely, budgeted, and invested the money for long-term growth. He could have gotten by on a mere quarter-million dollars a year for the rest of his life.

If someone has the extra money they can afford to lose, I don't object if they choose to spend a few dollars on the lottery for entertainment purposes. Personally, I can find plenty of more entertaining ways to waste my money.

2 comments:

Craig said...

Like I say, the Lottery is a perfect tax on stupid people. The more stupid you are, the more you pay.

Don Dodson said...

Taxing stupid people is a good start, but we really need to find a way to prevent stupid people from voting. It is a well-known fact that stupid people vote Democrat 10 to 1. If Democrats lost the stupid vote, it would be the final nail in their coffin.