I wrote in this space a couple of years ago about the unlikelihood of winning the Powerball or other large lotteries.
I ended that column by leaving open the following big question: "How does anyone win, if the probability is so small?" The occurrence of recent winners of big jackpots reminded me that this question should be answered.
First, let's do a quick review. The probability of winning the Powerball Jackpot is about 1 in 175 million. Mega Millions is worse -- about 1 in 259 million. In the previous post, I noted that 175 million one-dollar bills, laid end-to-end, would make two laps around the lower 48 states. Envision yourself walking around that thousands-of-miles-long-stretch of dollar bills, having just one chance to pick the "lucky dollar bill." Your chances of picking that one lucky bill are the same as your chance of winning the big lottery jackpot. That is, it isn't going to happen!
But, you say, it happened to Harold Diamond, an 80-year-old resident of Wurtsboro, New York, in the Mega Millions lottery last November. That's true! So, if you are Harold Diamond, you can tell me I'm wrong. But for the rest of you, in the words of Inigo Montoya, "Let me explain -- no, there is too much -- let me sum up." (If you want a really fine and complete explanation, you should read David Hand's book titled, The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day).
In short, it is highly likely that someone will win the big lottery drawing you have so hopefully entered. This probability is the result of a large number of people playing the lottery -- the same factor that contributes to the large amounts of money in the jackpot. The fact it is highly likely that someone wins changes nothing about your chance of winning.
To understand this, you need to recognize that rare occurrences happen all the time. For instance:
- The winning numbers in the February 4th Powerball drawing were 24, 36, 51, 52, 56, with 22 as the Powerball. The occurrence of those specific six numbers was a rare event -- it had only a 1 in 175 million chance of happening. But it was a certainty that some set of six numbers was going to be selected during that drawing.
- According to the National Oceanic and Atmospheric Administration (NOAA), lightning strikes the lower 48 states 20 million times a year on average -- an average of a bit more than once every two seconds. Yet most places -- and most of us -- haven't been struck by lightning (even while we were trekking around the country trying to pick up the lucky dollar bill!).
- There are millions of blades of grass on a golf course, so the chance your golf shot lands on a particular blade of grass is minute. But your golf shot is going to land on some blade of grass (assuming you avoided the water, sand traps, cart path, highway beyond the course, etc.).
That seems clear enough, but here is what gets missed in this: The certainty of something happening doesn't increase the chances that it will happen to you. For example:
- Bet on your golf ball landing somewhere, but just don't place a bet on it landing in a particular spot -- especially if you play as poorly as I do.
- Lightning strikes people all too frequently, but it isn't going to happen to you -- especially if you practice basic storm safety and, for heaven's sake, don't try to hit that blade of grass with a golf ball and a lightning rod (for instance, a four iron) during a thunderstorm.
- And, when it comes to the lottery, sooner or later someone is going to win that humungous jackpot. The fact that someone will win it -- the indisputable fact that Harold Diamond won it -- doesn't change anything about your chances.
Of course, the cold rationality of probability is overwhelmed by our optimistic psychology. The reason lotteries make a big deal of who the winners are is to encourage you, and millions of other people just like you, to believe that because Harold won, you could, too.
Sorry, friend. It just isn't going to happen. The next time you buy that Powerball ticket don't be surprised that someone won the jackpot -- and certainly don't be surprised it isn't you!