# Lottery Math – If You Play You Should Know Your Odds

Pop Quiz

Here’s a little pop quiz for you, my friends. Sorry, it’s a math quiz. But don’t worry, it’s easy and this is a math blog, after all. Little Johnny, a fifth grader, came home from school one day, visibly upset. His mommy asked what was wrong. Little Johnny told her that he lost out on a treat that his teacher had. He explained to his mommy that his teacher had just one treat, but there were ten students in the class. So each of the students put their names into a hat. Then the teacher randomly chose one name to receive the treat. The rest of the class got nothing. Little Johnny didn’t get the treat. He was upset.

To comfort him, mommy told Little Johnny that the odds of him getting the treat were against him from the start; his odds were a mere 1-in-___ (Fill in the blank).

Little Johnny didn’t appreciate his mommy spewing out odds as if she was a bookie. Seriously, is that all about, mommy? However, being a simple fifth grade math question, he knew the answer (as should you).

Pop Quiz #2

The next day, Little Johnny’s teacher had another treat to give away. Luckily for Johnny, though, five of his classmates were home sick with the chicken pox. Now there were only five of them and one treat. The teacher told the class to write their names on two separate pieces of paper and put them both into a hat. That meant that there would be ten pieces of paper in the hat, with each of the five student’s names twice. Little Johnny, knowing what his mommy told him about odds, already knew that his chances were much improved from the previous day. He knew that his odds improved to 1-in-___ (Fill in the blank again). Nice, little Johnny!

I’ll let you in on the answers to both pop quizzes in a bit. First, let me talk about lottery math. I’m not here to promote playing the lottery. With that said, many people do play it, with dreams of becoming instantly rich one day. It’s kind of like an entertainment expense. For a dollar or two, you get to daydream about being a millionaire.

If you play the lottery and daydream about winning millions, you should know your odds. With that said, if you’re a marketing rep for a lottery, you better know the odds. I say this because I once had an argument with a marketing rep for a major lottery.

Now, every lottery has the odds of winning posted on their website. No problem there. The problem is figuring out the odds of winning if you buy multiple tickets. For example, say the odds of winning a particular lottery are 1-in-10-million. Now say you bought two tickets. What would your odds of winning be? This is the argument I had with this particular marketing rep. I told her that my odds of winning, with two tickets, would be 1-in-5-million. She forcefully replied “No, it would be 2-in-10-million.” I replied that she was 100% correct, but so was I. 1-in-5-million is the same as 2-in-10-million. It’s basic fifth grade math. Even little Johnny would know that. This marketing rep was too hard-headed to understand the error in her ways. I couldn’t win. Arghhh!

What’s The Problem With Big Numbers?

Did you get the answers to the pop quiz right? The odds of winning the first prize (Where each of the ten kids got 1 ballot) were 1-in-10. The odds of winning the second prize (Where each of the five kids got 2 ballots) were 1-in-5. The first quiz was easy – 10 kids with one ballot each. The second quiz was just slightly harder, but still easy – There were five kids with two ballots each, so one of those five kids was going to win. That’s easy to visualize when there’s such a small number of kids.

The problem with big numbers is that it’s harder to visualize, but the math is still the same. Take our lottery with 1-in-10-million odds of winning. That means that there are 10 million different combinations of numbers to choose. If you still don’t get how buying two tickets would improve your odds to 1-in-5-million, visualize it like this. Say 5 million people each buy two tickets (For argument’s sake, we have to say that every ticket bought had unique numbers). That would mean that those 5 million people would have bought all of the combinations. one of those five million people would then win it, or 1-in-5-million. See, my math is correct – You just have to visualize it. That’s the beauty of math, it’s constant, whether or not it’s a big number like the lottery or a small number like little Johnny’s contest was.

Last Pop Quiz

You want to win the American Powerball jackpot because that’s just crazy money (Or the Philippines 6/49 – That’s good too). The odds of winning with just a single ticket are approximately 1-in-175-million. If you bought one hundred tickets, what would your odds of winning be. Don’t worry, I’ll give you the answer – 1-in-1.75-million. Don’t believe me? Pfft, that’s just basic grade 5 math. Go ask a math teacher about it.

A  post by Tino Sundin, a lottery blogger.