## Media Fail & Lotteries

Posted by mattusmaximus on January 22, 2011

This past December 17th, I saw a headline in my local paper which stunned me with the level of irresponsibility it displayed. Back then the Powerball lottery was getting a lot of attention because the jackpot was up to a potential $25 million, and when such numbers start getting thrown around, people’s critical thinking skills go right out the window. And it doesn’t help when the media joins the chorus of unreason…

First, there is the fallacy that when the jackpots are high, more people play because they “feel lucky that they’re going to win the BIG one!” Of course, when more people play the lottery it actually *decreases* the odds that any specific person will win, yet this doesn’t stop the gullible from scarfing up the lottery tickets.

Then, there’s this horrible headline:

## Wanna win Powerball? Try these numbers

For 13 years, a red ball with the number “20” printed on it has been whirling around with its numerical counterparts in an enclosed Powerball kettle waiting to potentially make someone a millionaire. That No. 20 red ball has made its way out of the kettle 49 times, the most of any of the numbered balls. No. 20 also is the second most common number on the five white balls that are selected in each Powerball drawing as well, behind 26 and ahead of 32, 16 and 42, a Daily Herald analysis of the numbers shows. …

This headline and the leading paragraphs of the article play directly into the gambler’s fallacy of “lucky numbers” – in reality there are no more or less “lucky” numbers. In fact, the past performance of the lottery is in no way, shape, or form a predictor of the next random drawing of numbers. The article cited above actually does attempt to be at least marginally responsible by interviewing a mathematician, though their discussion is buried in the article…

… While some gamblers may see that information as an edge, mathematicians and oddsmakers say it’s all just luck.

“The numbers and the pingpong balls have no memory,” said Jeff Bergen, a mathematics professor at DePaul University. “So whether a given number has come up once or twice or 10 times or never, it is no more or less likely to come up today than any other number.” …

## 04-11-19-33-43 and 14 as the Powerball

**NOT… ONE.**So much for “lucky numbers.”

You have much better chances of most things than of winning the lottery–getting struck by lightning, dying in a plane or car crash, etc. The odds are astronomically low of winning the big prize. Invest that money instead, and you’d end up with far more in the long-term, even with the low interest rates.

## Chris said

If I offered to pay you $2 if a coin flip turned up heads, but you’d have to pay me $1 if the coin flip turned up tails, would you take the bet?

One thing I remember from my study of economics is the concept of expected return. You compare the costs/benefits of all the possibilities and multiply by their expected percentage outcomes. Such analysis says you take the $2 for $1 bet on the coin flip. But it also concludes that if the expected return on the lottery is greater than $1, then it makes economic sense to pay. I forget the calculation, but when the lottery goes above $250 million, I usually buy a ticket.

As science-oriented guys, we (I teach high school physics too) should respect the need to spend money on unlikely outcomes. By your anti-lottery logic, who cares if we track asteroids, since there’s such a small chance of a big one hitting any particular day or week. As for me, despite the low odds, the benefits of finding one early greatly outweigh the benefits of saving or investing that dollar today.

## mattusmaximus said

I understand the concept of expected return, but I think you are misapplying it in this case because of some flawed assumptions on your part. First, you neglect the fact that when lottery jackpots are larger, more people play the lottery; this means that your expected return is potentially lessened by a great deal because, statistically, with more players there’s a greater chance that more than one person will win the pot. This is especially true regarding situations such as when everyone in an office or workplace goes in on a single set of lottery numbers, etc.

Regardless, I would like to see a specific reference on your $250 million number. As a science-oriented guy, you should know better than to speculate on numbers like that without having a solid reference to back you up.

And, concerning your critique regarding asteroid tracking, you are comparing apples to oranges. That is because the “jackpot” in the case of a killer asteroid striking the Earth goes far beyond impacting (pardon the pun) a single person or group of people, as with the lottery. In fact, such a killer asteroid strike has disturbing implications for pretty much every human on the planet, so this alters the “expected return” calculation quite significantly.

## Chris said

I stand corrected. It was years ago that I calculated the odds of matching the available lottery numbers at 1 in about 200 million, and ever since then I’ve kept that number in my head. (As it turns out, the Jackpot possibilities for Powerball are 1 in 195,249,054 and for MegaMillions they are 1 in 175,711,136 source:http://www.durangobill.com/PowerballOdds.html) However, in all these years, the “multiple winners” calculation never entered my mind. The expected return on $1 is about $0.50.

However, the entertainment value of the dream of winning may just make up for the remaining fifty cents!

You have also made a valid point about asteroids impacts.

Thanks for setting me straight, as I’m willing to have my mind changed in light of better evidence (as any skeptic should).

## ronmurp said

“First, there is the fallacy that when the jackpots are high, more people play because they “feel lucky that they’re going to win the BIG one!””

“Of course, when more people play the lottery it actually decreases the odds that any specific person will win”

Your first statement may or may not be true. Do you have the data? Note, what you are actually claiming is that they play

becausethey “feel lucky…” – i.e.becauseit’s a big one, their chance increases. So, what data do you have on why they play? It may simply be that they know they are no more likely to win than usual, but simply don’t want to miss out on the minute chance of winning the big one.Your second claim is technically correct, but not in the way your first claim seems to imply, and it depends on what you mean by winning: winning it all, or winning but sharing.

The more people play makes no difference to your particular chance of matching the winning numbers, so your odds of ‘winning’ don’t change.

What does change is the likelihood of more people sharing your numbers, and so sharing the big one, should you win it. But what are the odds of this happening? Take the UK lottery, with odds of about 14M-1. If only one more person buys a ticket, the odds are 14M-1 that they’ll pick the same ticket as you – if they pick randomly (whatever that means). Even if the number of players increased by 10%, you’re still looking at 1.4M-1 for any one of them to pick your number.

So, your odds of winning are the same; but the odds of winning, AND winning it all aren’t necessarily that different, depending on how many extra players there are.

But if you and many other people have fixed numbers, as many do, then you may have an unknown but fixed chance of sharing, should you win, even for low jackpots. A larger jackpot may then actually increase what you win, since a one week rollover doubles the prize, but, depending on number selections, may make no practical change to the number of people sharing.

## mattusmaximus said

All good criticisms. I apologize for not being more specific in my blog post regarding the question of winning but sharing.