Tuesday, August 5, 2008

Guaranteed way to win the Powerball

It's been a while since I've posted a humorous but financial interesting post. Today at lunch, I had an interesting (and financially geeky) debate over how much the Powerball lottery would have to be to make it worthwhile to purchase every possible number combination, thereby guarateeing a Powerball win.

Powerball is won by choosing 5 numbers and the Powerball number correctly. According to the Powerball site, the odds of doing so is 1 in 146,107,962. Since every Powerball ticket costs $1, theoretically, you can spend $146,107,962 or about $146 million to acquire all possible combinations.

But of course, it's not that simple.

Assuming you had $146 million, the jackpot would need to be a lot bigger than that to provide you a return. Remember, due to inflation, the value of $146 million today is not worth the same amount of goods you can buy with $146 million 30 years from now.

So how much would it have to be?
Looking at the website, it appears they assume a 2.38% inflation rate each year. In that case, you would need the jackpot to be worth $296,164,788 just to breakeven. But of course, there is something else to think about.

Remember that money used? That is money after tax. When you win the Powerball, you still need to pay taxes. Assuming a lump sum, and applying the highest tax rate of 35% for all winnings over $357,700, you'll need a jackpot of $456,099,627.

Unfortunately, this situation hasn't occured yet. To date, the largest Powerball winnings was $365 million (link).

Additional Issues
Since it is currently a net negative return on your investment (until the jackpot is larger) to try this method of winning the lottery, I won't delve into other considerations that will require the jackpot to be substantially larger. However, here are some issues we kicked around:

  • Logisitics of storage/retreival of such an amount of lotto tickets. How much would that cost?
  • What if you have to split the winnings?
  • What if you accept an annuity and die early?
  • It's possible an out-sized purchase of 146 million tickets could balloon the overall pot, which could statistically increase the number of people buying tickets, and therefore the number of people splitting the winnings.
Suffice to say, for now, even an investment in sub-prime mortgages seems safter than an outright purchase of all 146 million powerball number combinations.


Eric said...

What if someone else wins? 2 people? 3 people? If there are two winners, which is more likely if the total were to break $500 million, you would need to double it again to break even. In that case, based on your math, you need a jackpot around $1 billion.

Rob said...

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