Tuesday, November 27, 2012

How to Play the Lottery, If You're Gonna Play It at All

Readers of this blog may remember that I played the lottery once before - back when the MegaMillions lottery jackpot reached an all-time high, and my back-of-the-envelope calculations showed that the expected value of a lottery ticket was actually greater than the price of the ticket, thanks to the huge jackpot.

Well, the Powerball lottery jackpot has reached similar heights, with an estimated payout of $500 million ($327.4 million cash value) - I haven't done the math, but I figured I'd play the lottery one more time, as I'd definitely like to be a multimillionaire with no effort.

So, here is the Angry Bureaucrat's guide to playing the lottery:
  1. Don't play the lottery. You're not going to win. I forget where I heard this, but I overheard some wise statistician who was asked how to maximize one's chances of winning the lottery. He thought about it, and he said to buy a ticket on the day the drawing was happening, because the odds of you dying on a given day was higher than the chance of winning the lottery, so buying the ticket on the day of the drawing increased the odds of you being alive to claim your winnings, if you win.
  2. If, in spite of #1, you're going to buy a lottery ticket anyway (like I did), buy 1, exactly 1, and only 1 ticket. The reason for only buying one ticket is this - if you buy one ticket, you're infinitely increasing your odds of winning (i.e. your chance of winning the jackpot goes from 0% to more than 0% - to 0.00000057%, to be exact). However, each additional ticket only increases your chance of winning the jackpot by another 0.00000057% - such a small amount that the additional increase in probability of winning isn't worth the cost of the additional ticket.
So - to summarize: Don't play the lottery. If you do, going from 0 to 1 ticket infinitely increases your chances of winning. Going from 1 to more than 1 ticket doesn't increase your chance of winning, statistically speaking. Therefore, only buy 1 ticket.

Hope this helps, and bad luck to all of you playing tomorrow ;)