P(Winning Lottery) > 0… but Just a Little
I know a fair bit about the probability of winning the lottery.
State-run lotteries are a tax on the mathematically challenged.
Given the odds of winning, then you might wonder why I occasionally buy scratch-off lottery tickets. Lord knows, my wife often wonders aloud about it. Believe it or not, there are three reasons that I buy these tickets:
- First, I’m from a rural town in the-middle-of-nowhere Pennsylvania. The rural poor are infamous consumers of lottery tickets. Consequently, I believe that buying lottery tickets is part of my genetic code.
- Second, it’s a guilty pleasure that is easier to indulge than buying PowerBall or Daily Number tickets. When you buy one of those, there is a human interaction, and I imagine that the clerk selling me the ticket is thinking, “Loser! Don’t you know how low your odds of winning are?” For the scratch-off tickets, you insert your money in a vending machine, and the tickets are dispensed. Sure, you may get a disapproving eye from a passer-by, but at least there’s no formal exchange with another human.
- Third, and most importantly, I know a bit about probability, but I also know a little about the intersection of math and psychology. As it relates to the lottery, the idea is fairly simple — make every third or fourth ticket a winner, and people who buy scratch-off tickets will win often enough that they’ll keep coming back for more. Truth is, the winning tickets usually have a prize equal to the price of the ticket or twice the price of the ticket. For instance, if the tickets cost $5, then the winning tickets usually have a pay-out of $5 or $10. When four tickets are sold for $5 each, the state collects $20 and only pays out $5 or $10. Good work if you can get it, eh?
This last point is actually the one that hooks me in. If I buy four tickets at a time, I can almost guarantee that one of them will be a winner. Consequently, I’ll only be giving $10 or $15 to the state instead of $20. (What a bargain, right? I walked into the store with $20, and I get to leave with $5 or $10. Who could pass that up?) But on the off chance that there are two winners in this group of four, or if one of the tickets is a big winner with a prize of more than double the price, well, then, this could work out all right for me.
Yes, I am fully aware that my argument is irrational and that I am slightly delusional. Recognizing my irrationality and delusion, I don’t buy scratch-off tickets very often; but, I do buy them occasionally.
So, why am I telling you all this? Because this morning, I bought four scratch-off tickets at the local supermarket.
First Ticket: It had a “5 Times” logo next to $10. That means I won $50.
“Wow!” I thought. “I’m already ahead $30.” And then, of course, I realized how unlikely it was that the other three would be winners.
Second Ticket: I matched not one, not two, but three of my numbers to the winning numbers for $5 each. That means $15 in winnings on the second ticket.
“Holy schnikeys!” I said out loud, though probably too soft for anyone else to hear. (I hope.)
Third Ticket: I matched two numbers for $5 each. That means another $10.
Fourth Ticket: Nada.
But, whatever. I was up $55, so who cares about that stupid fourth ticket?
I collected my winnings, and I walked across the street to Panera and ordered a chai tea latte and a bagel. I handed my MyPanera card to the clerk — indicentally, I hate the recent trend of naming something as MySomething, because then it’s really awkward when I want to refer to the MySomething that belongs to me by calling it my MySomething; but, I digress — and he told me that I had earned a free bagel. “You can have this one for free, if you want,” he said. Well, hell yeah!
A few hours later, I went to lunch with a new professional acquaintance. Even though I had asked her if she wanted to meet for lunch, she picked up the tab!
Can you believe it? Fifty-five dollars in lottery winnings, a free bagel, and a free lunch. Financially speaking, this could have been the luckiest day of my life. (Well, except for the day when I learned that an essay I’d written had won a honeymoon in Oaxaca for my wife and me. But that’s a story for another day.)
Yep, the chances of one good thing happening in a day are low. But the chances of three good things happening in a day? Infinitessimal! Guess I’m just blessed.
My former boss, Jim Rubillo, knows a thing or two about probability and statistics, too. Somehow, his favorite line seems appropriate for this post.
If you don’t believe in the power of random sampling, then the next time your doctor requests a blood sample, tell her to take it all!