June 6, 2013 at 4:37 PM ET
Before lottery regret and mathematical misunderstanding puts another dent in civility everywhere, know this: It's OK to let a senior citizen step in front of you when buying a ticket. Please, continue being polite to older folks.
When Gloria MacKenzie purchased her $590 million lottery ticket in Florida last month, a much younger woman allowed her to cut in line, according to published reports. Many of those indicated that the woman's random act of kindness cost her $590 million. It didn't.
Before lottery ticket buyers start boxing out little old ladies at convenience stores everywhere, let's examine this issue from a mathematics point of view. Could letting someone cut in line at the lottery counter hurt your odds of winning? To use the language of statistics, let’s call this the "risk of being nice."
It would feel strange — wistful, certainly — to learn that someone purchased the winning lottery ticket at your store. (It coulda been me!) It would probably plunge you into full-fledged regret to learn the winner was right in front of you, had taken your place in line, and had purchased the same kind of Quick Pick machine-generated lottery ticket you did. (It shoulda been me!) But random acts of kindness are indeed safe, because random numbers don't work that way.
Random means random
Some lottery ticket buyers arrive with a pre-determined set of numbers in their heads — their children's birth dates, perhaps — and purchase tickets with those fixed numbers. Others let the lottery machine generate numbers, called "Quick Pick" in many states.
Even so, Quick Pick numbers could theoretically be generated in batches of, say, 10 million at time, by a central computer, and then doled out to local machines. Or maybe they could be generated 25 at a time in convenience stores, then handed out. If either were true, your place in line certainly would matter.
But it’s not true. Computers are particularly good at generating random numbers, which have been important to computing since the very beginning. Random numbers are needed any time a programmer wants to surprise a user, such as in video games. Even the most basic computing machines have a built-in ability to create fairly random numbers, often utilizing their internal clocks to make them even more random. So every millisecond matters to a random number generator.
In other words, there is no "risk of being nice." Stopping to sneeze before buying a Quick Pick ticket could just as easily cost someone a winning number as trading places in line.
What's more, every number generated is independent of every number before it. There are no numbers ticked off a master list, leaving you with more limited possibilities. If the odds are 1 in 100,000,001 when you step in line, your odds remain 1 in 100,000,001 when you let someone else step in front of you.
Naturally, lottery administrators don't advertise precisely how their machines work — random number generators aren't perfect, and lotto machines are a constant target for attackers — so we must engage in a little speculation. But plenty of descriptions can be found that suggest that this is the way they work. For example, here's a description from the Texas Lottery's FAQ.
"The Quick Pick random number generator for our online games has no built-in memory. Once a set of numbers is picked in one play, the random number process starts fresh for the next play. The fact that a number is picked in one play has no influence on the chances of it getting picked in following plays. Each set of numbers generated by the Quick Pick feature is unrelated to any other Quick Pick selection."
(You can almost feel the frustrated mathematician behind this repetitive explanation, no?)
Of course, other factors make the "risk of being nice" flawed logic. People were buying lottery tickets at locations all around the country. In the time it would take to push a little old lady out of line, thousands of people in other locations would "step in front of you."
Powerball isn't a raffle
One can conjure up a game of chance where the "cost of being nice" could be real. A church raffle that sold tickets with sequential numbers might seem to qualify. Imagine you let a senior cut in line, and he bought winning ticket number 1065, leaving you with a worthless 1066 ticket. Of course, if the winning number was truly picked at random, that wouldn't matter, either, but it certainly would "feel" bad. (Note: feelings and mathematics rarely get along very well).
On the other hand, imagine a church raffle with a finite number of tickets, where this little old man bought five, and you could only buy four tickets because the supply was exhausted. By limiting your chances of winning, you have a true "risk of being nice."
Sadly, Powerball has an unlimited supply of tickets for fools with money, so that scenario doesn’t apply.
Lotteries have often been called a tax on the mathematically disinclined, so it's no surprise that math logic can be in short supply when discussing lotteries. After all, anyone using logic would take their investment in lottery tickets and put it to good use — betting on this weekend's Belmont Stakes, for example.
But here's a happy thought. Because both the winning numbers and the Quick Pick numbers are randomly generated, the "reward of being nice" is of equal value to the "risk." That is, you are equally likely to end up with a winning ticket because you let someone step in front of you. Think about that the next time you consider being polite ... doing so could win you $590 million!