Jackpot!

The Mega Millions jackpot, as of Friday, December 16th, sits at $135 million. This is an astounding amount of money. Even the annuity option (26 annual payments of $5 million) seems like an awful lot of money. I've worked post-college for 9 years and I've made roughly $350,000 over that time. Over the next 30 years I'd have to have an average salary of about $150,000 annually in order to make $5 million before I retire. I don't think my boss is giving me that kind of raise next year.

The lottery is all about odds, one of the overarching concepts discussed in probability theory and statistics. Odds are calculated as relative probabilities: what is the chance that X will happen against the chance that X will not happen? Don't confuse odds with gambling odds, which relate to the payment of a specific event occurring, such as a 3:2 payout in blackjack or paying 1,000 credits for getting all 7s on a slot machine.

The classic example of odds is to flip a coin. The odds of that coin landing tail up are 1:1, or "even odds". In other words, there is an equal chance of it landing tails up or heads up. But keep in mind that odds still exist in the world of mathematics, and not real life. If you flip a coin ten times don't expect a result of five heads and five tails. You'd probably get four heads and six tails, or vice versa, or maybe even greater variances. Flip it a hundred times and you get closer to a 1:1 output. Flip it a thousand times and you've got too much time on your hands.

All state-run and national lotteries are required to make their odds public knowledge. The odds of winning the Mega Millions jackpot is 1:175,711,536. Those odds seem astronomical, but when you consider that there are about 310 million people in the United States, and roughly half of them are 18 or older, then logic would suggest that you would likely have a jackpot winner at every drawing (especially if you consider that most lottery purchasers buy more than one ticket for a drawing).

So why doesn't it happen? For the same reason flipping your coin ten times did not give you exactly five heads and five tails.

Probability is not constrained to any sort of pattern. You could flip your coin ten times and it could land on heads all ten times. Someone else could pick up that same coin, flip it ten times, and he gets all tails. Someone could, conceivably, buy lottery tickets for the next 75 drawings and win something all 75 times, and you could do the same and win nothing. In other words: just because X happens one time, doesn't mean that X won't happen the very next time.

Should you play the lottery? Any statistician would say "no way", but I disagree.

I remember, back in high school, the drudgery of applying for various academic scholarships. The application, itself, was relatively easy, but the essays drove me nuts. I had applied for a dozen scholarships and, as a result, had to write a dozen different essays, meticulously explaining why I want to go to college or what I want to do in life. I put much more effort into those essays than any paper I wrote for high school. Why? Because every scholarship offered the chance at thousands of dollars off of a college education, and that chance -- no matter how slim -- was worth the effort.

Playing the lottery requires virtually no effort, but it does require money. For most of us, a $2.00 sacrifice every drawing (there's two a week for Mega Millions) is probably a pretty small sacrifice, even if the odds are astronomically small.

My final word of advice: don't overdo it. Playing 5 or 10 or 100 tickets in every drawing does, statistically, increase your chances, but by how much? Instead of 1:175 million for a single ticket you're now at 1:35 million if you buy 5 tickets. That may seem like a huge leap in your favor, but it's still incredibly slim. Putting it in perspective: the odds of dying in a plane crash are 1:11 million.

Personally, I'll throw $2.00 away when the jackpot creeps over $100 million. The odds are against me, but 1:175 million is still better than 0:175 million.