# Do the math, please

May 23, 2005 4:13 AM

Math has always come rather easy to me, even complex math. When I bought my first home, the real estate agent kept pulling out her little book and calculator to figure out what our payments would be. Long before she would give us the answer, I’d have the answer to within \$10 a month, using nothing more than my noodle.

When with my friends, they’ll frequently look at me when they need some quick math, whether it’s figuring out the square footage of a room, how to split a check at a restaurant or calculate their hourly wage given their annual salary.

The other night I was at a party. We were celebrating the birth of a friend’s son. The conversation turned to how he was born on Friday the 13th. Some folks wondered how often his birthday would actually wind up being on a Friday the 13th. Without missing a beat, I said that it would occur, on average, once in seven years. Though this seemed pretty obvious to me, I spent the next 15 minutes defending my answers to some rather intelligent people, ranging from lawyers to software engineers to accountants.

The most common challenge to my answer was that, without leap years, my answer would be correct. Without a leap year, if May 13 is a Friday this year, it will be a Saturday next year. But, when a leap year occurs, it will skip two days and thus, it may skip from Thursday to Saturday and skip over Friday. So, the answer cannot be one in seven. It must be less often because it may SKIP a Friday.

Then another person started writing down examples. If it’s a Friday in the year 2000, then it will be Saturday in 2001, Sunday in 2002 and so forth. This person showed how sometimes it was a Friday once in 7 years and sometimes twice in 7 years, so it must occur more often than once in 7 years. When I showed this person how it was possible that, in a given 7 year period, it was never on a Friday, the response was a perplexed, "Oh!"

When the dust settled, I looked at my friends and asked if they would all agree that the likelihood that the 13th (or any other day of the month) was any particular day of the week was the same? That is, that it was just as likely to be a Monday or a Tuesday or a Sunday?

The response all around was in the affirmative. I further went on to say that the answer was thus based on simple algebra. If the likelihood of any given day is the same and the probability that the 13th showed up on SOME day of the week had to equal 1, then we simply needed to solve for a simple algebraic equation of 7x = 1 and thus x = 1/7. At this point, I’m not sure if I truly convinced my friends, or merely left them without any further arguments.

So, what does this have to do with gambling? Well, two important things can be learned from this little story. The first is that even incorrect arguments can lay doubts in one’s head. As I listened to my friends’ alternative theories, I began to wonder if I was correct, despite how incredibly simple the math really was.

Where gambling is concerned, there have been many people who have proposed theories that are simply not mathematically sound, yet have managed to generate a lot of followers because they "sound good."

The second important thing that can be learned from my math tale is that even very intelligent people can miss the boat on some pretty simple probabilities. Imagine what happens when they are faced with some of the complex ones that can be found in the casinos!

Despite all the arguments, the simple reality is that May 13 will be a Friday on average one in seven years. Period. The math is simpler, but it really is no different than the math that dictates that we hold a high pair over a 4-card flush in jacks or better, or that you should discard a full house with three aces in Double Double Bonus to go for the quad aces.

The math tells us what the smart play is. It doesn’t tell us that we can set our watch by it. Just as it may be 10 or 12 years between two Fridays being May 13, it will also be five or six years between them at other times.

But at the end of the century, it will be very close to one in seven. At the end of the millennium it will be that much closer to one in seven. The good news is that, where video poker is concerned, the long run is a lot shorter than centuries apart.

Just remember, compelling arguments don’t have to be correct ones.

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