Little Bit of Bullshit

(click to enlarge)

Quite apart from the fact that ads suggesting that the lottery might be a good way to get rich¹ are wildly unethical (imagine ads for alcohol with copy like, "Escape all your problems...find true happiness!"), these particular ads border on false advertisement.² First there are the claims that all you need is a little bit of luck, that there are 100,000 winners a day, and that the chances of winning are 1 in 9. Here, taken from the N.Y. Lottery's official web site, is what those claims mean:

(What exactly is a "ball baby"?)

So there's a 1 in 575,757 chance that you'll win almost $58,000, a 1 in 3,387 chance that you'll win $508, a 1 in 103 chance that you'll win $26 (wow, exciting!), and a 1 in 9 chance that you'll win...another chance to play. In other words, what they mean when they say you've got a 1 in 9 chance of winning is that you have a 1 in 9 chance of not losing yet.

Now, I'm no mathemagician (and I invite my mathemagician friend to comment on this very blog post with some proper mathemagic—check back below to see whether he's done it!), but I have carefully examined this blog post and feel confident about the accuracy of the following analysis, even though it's incredibly let's just say rickety and inelegant:

1. If only the $58,000 first prize were in play, then the expected value of a $1 investment in TAKE 5 would be 10¢.³
2. If only the $508 second prize were in play, then the expected value of $1 would be 15¢.
3. If only the $26 third prize were in play, then the expected value of $1 would be 25¢.
4. If only the fourth prize were in play, then the expected value of $1 would be 11¢ if you got your $1 back (which, as I point out in bold above, is not in fact what's going on).

The problem with the above is of course that all four prizes are in play, and I'm not sure then how to figure out the overall expected value—but it can't possibly be more than all four added together. So let's just say (Dr. Math?) that the expected value of a $1 investment in TAKE 5 is ≤61¢. Given that the expected value of a $1 bet on a single number in roulette is 94.6¢, you begin to get a sense of how ridiculous it is to present this game as having good odds.

On top of all this, the big problem with the 1 in 9 odds (in #4 above) is that what you have a 1 in 9 chance of doing is (again) not increasing your money, not even keeping your money, but not losing your money yet. One way to look at it is that they give you your $1 back but then you are required to play again—but if you can't cash out, then the game is not over, and if the game is not over, you cannot meaningfully be said to have won. So that 1 in 9 claim is essentially false.

Meanwhile, the slogan "All You Need Is a Little Bit of Luck" is classic advertising evil because it's nearly impossible to disprove: what is "a little bit," after all? (I wouldn't even be surprised if the secret added value of having that irritating little mascot is that, if it ever really came down to it, the N.Y. Lottery could claim that "Little Bit of Luck" is ultimately only a name and not even a proper claim!) "Hey there, undergraduate Theater Studies major! With a little bit of luck, you'll become the most famous actor of your generation! What, you say that'll take a lot of luck? Well, to me $100 is a lot of money, but to you, when you get rich & famous, $100 will be like 1 Italian lire⁴—just a little bit of money! A little and a lot are relative, baby!!!"

And none of this yet is even what I find the most offensive about these ads.

Not only is it misleading at best to say that all you need is a little bit of luck, but also they've left out the important information—all you need for what? They've set it up so that they can say (as indeed they already have⁵) that all you need to get to play the lottery again is a little bit of luck. But what lifts these ads from the merely slimy all the way up to the outright mendacious⁶ is copy like what you see in the ad at the top of this post: "With 100,000 winners a day, who says you can't live large in New York?"

(I've used this image before.)

O.K.: "live large" is a joke about their stupid little mascot. But "live large in New York" means something very specific, and it is not a coincidence that it's in an ad for the lottery. Yes? New York is expensive: this ad is saying that it only takes a little bit of luck to live large in New York. In other words, it is very clearly suggesting that TAKE 5 might be a reasonable way to increase your personal fortune. And even forgetting that the most you could make from a game of TAKE 5 is around $50,000 (which in Houston would be $20,000, which if a family of four in Houston were making that in a year, that family would be living below the poverty line), even imagining, in other words, that winning the first prize in TAKE 5 would mean that you could "live large" in New York in any meaningful sense—even then, we've already established that if you had to choose between investing every last penny of your money in TAKE 5 and investing it in the number 6 on the roulette table, the number 6 would be the better choice!⁷

I'm tired and surely making minor mathematical and logical mistakes here. But the point stands: (a) plenty of people out there, addicts or no, look to the lottery as a way to make money, (b) in fact the expected value of a $1 investment in this particular version of the lottery is something like 61¢, and (c) here we have ads whose entire message is that this particular version of the lottery is easy to win. Given that governments should penalize businesses that mislead the public...I want to see tiny, disproportionate heads roll!

¹ Or—given the seriousness of gambling addiction—really any lottery ads at all.

² In fact a Staten Island woman has sued, although I must say that her particular objection seems unnecessarily weak and easy for the Man to deflect.

³ To put it another way, if you played again and again and again and again, you could expect eventually (i.e., if you didn't have to worry about eventually running out of money) to lose 9/10 of your money.

⁴ "What, you say the lire has been replaced by the euro and isn't worth anything anymore? Well then I guess you've proved my point!!!!" (As I recall from my visit to Italy in the late 1990s, a lire was worth about 1/7,000 of a dollar. I may be wrong about this...it might have been more like 1/7,000,000,000.)

⁵ "The clear message is that the 1-in-9 odds definitely includes [sic] winning a free play" (same article as in the second footnote).

⁶ Up and down: also relative, baby!!!!

⁷ To be clear, this is if you "invested" that money by betting on 6 again and again and again—which is fair because "investing" any amount of money in TAKE 5 would have to mean buying a large number of TAKE 5 tickets and therefore, in effect, playing TAKE 5 again and again and again (I am not going to bother checking the Lottery's web site and will just assume that no single TAKE 5 ticket costs thousands of dollars).