I like to play the lottery.
There, I’ve said it. Go ahead and make your snarky comments now. There are a lotta reasons they’re misconceived. But I’ll get to that in a moment.
I like the word lottery too, though that’s not why I play the lottery. I like it a lot, because it’s fluttery and lettery and a little bit buttery, and because it gives us a key to an old and influential concept.
The concept is of choosing a person for some purpose by “random” chance. I put “random” in scare quotes because what we treat as random is really just whatever has causes and mechanisms inaccessible to us and, consequently, outcomes unpredictable to us. When ancient people wrote names on pieces of wood – each one a lot (Old English hlot) – and shook them in a jar and saw which fell out first, the rules of physics governing what fell out first were the same ones that apply everywhere. Today we could in theory with perfect data and a precisely calibrated machine cause a specific lot to fall out as we wish. The same goes for coin tosses, balls from lottery machines, and so on. Even random functions in computers are actually based on identifiable input and processes. It’s just like the ball-in-cup game: if you can pay close enough attention, it’s not random.
But that’s a lot to ask for. Quite literally. Say, wonder how lot came to be used for land, auctions, and indefinite plurals? Originally, your lot was what determined for you what you got when goods or property were assigned; then it spread to the thing you got. Which would be property of some kind. Or a set of property, as in an auction. And from that, a lot of other things. And when you “accept your lot in life,” the lot is not your property, it’s your “random” drawing. (There is no known connection between this lot and the Biblical Lot whose wife was turned to a pillar of salt in a suspiciously Eurydice-like moment.)
More things than just pieces of wood in earthen jars can be used for “random” outcomes now, of course. Coins are very popular for Boolean stochastics. And coins illustrate nicely two fallacies about probability.
The first is well enough known. If a coin has come up heads three times in a row, what are the odds of its coming up heads the fourth time? One in two, of course; a fair coin has an equal chance of coming up either side in any toss with no regard to prior results (provided the tosser is not so adept as to control the outcome).
The second is sometimes overlooked. If a coin has come up heads 15 times in a row, what are the odds of its coming up heads the 16th time? In this case, given that only one time in 32,768 will a fair coin toss come up heads 15 times in a row, we may ask ourselves whether there isn’t a much greater than 1/32,768 chance that the toss is not fair. It seems reasonable, frankly, to imagine that the coin is unevenly weighted or the tosser especially skilled. So I would go with heads again, unless it seemed like that was just what the person flipping the coin was waiting for me to do.
But, now, lottery. People like to joke that the lottery is just a tax on people who are bad at math. As it happens, I’m quite good at math, and I know that the odds of winning the big prize (easily looked up anyway) are vanishingly small (heck, they post them online). So why would I play it?
Simple. In Ontario (where I live), the lottery is run by the government, and the profit from the lottery goes towards arts and hospitals and community projects and similar things, things that really deserve support. So I’m happy to see some money go to them, and it’s a lot cheaper than a charity dinner (if you go to a $200-a-plate charity dinner, not all of that money goes to the charity, after all). And there are prizes other than the big prize. Every so often I will win a free ticket or $5 or $10 or, now and then, $50. Once I won over $100. Do I run a net loss? Of course I do! Really, it wouldn’t make money if people didn’t. But I find it amusing. I get more fun out of a $5 lottery ticket than I would out of a $5 sugary coffee drink. It buys a piece of a fantasy. It’s like probability porn. Do you really think people who look at smut think they have any real chance of getting it on with the men and women they see there? Pfft. Same with lotteries: ticket buyers generally know their chances of winning are inconsiderable. I know that instant millionaire is not likely my lot in life. So what.
There’s one more thing that many people don’t understand about lotteries: what odds are and aren’t relevant. I once looked (for some reason) at one of those little checkout-stand impulse-purchase booklets on things to do to win the lottery (sorry, did you have something in your mouth? take a moment to clean your screen), and it gave advice that showed a basic failure to understand the nature of the thing. It said that you should make sure to distribute your numbers fairly evenly because the odds of them all clustering within, say, the set of numbers that can represent birthdays is on the low side.
Well, yes, that’s true, but it’s irrelevant. You’re not betting on the distribution of the numbers. You’re betting on six or seven specific numbers. Which means that you’re betting on six or seven specific balls in the machine (that’s what they use to draw the numbers). Each of those balls has no idea of what number is on any of the other balls, nor, in fact, even of what number is on it. You may as well be betting on which six random strangers out of a crowd of 49 will scratch their noses first. Or on which 6 specific paint colours out of 49 will be chosen first by a crowd of deranged colour-blind interior decorators. In the world of the balls, 8 is not between 7 and 9; it is just a ball with a two-looped ink shape on it, bouncing around with all those other balls. Unless you realize that, you don’t get what’s going on. 1 2 3 4 5 6 has exactly the same odds of coming up as 1 5 17 24 33 46.
But also, until you realize that those balls are actual physical objects with subtle irregularities, objects that are replaced every so often when they seem to come up too often or not often enough, you also are overlooking potentially relevant information. Just remember that the subtle increase or decrease in the odds may require a lot of play to net you any benefit.
The biggest hazard in games of chance, in fact, is not utter naïveté. It is cockiness. It’s thinking you’re smarter than all those suckers. Once you get cocky, you’re an easier mark. Cockiness results in failure to accurately assess what is and isn’t relevant.
Consider a roulette wheel. It is spun by a croupier, a human who has certain tendencies in when to set the ball rolling and how hard to push the ball and so on. If you think you see a recurring pattern in the numbers, you may be wrong, but then again, you may not. One time I watched a person spinning a cogwheel at the Canadian National Exhibition and realized that the stopping spot tended to be a predictable distance around from where the person pushed it from. I used this to double up my money. And then I moved on. Remember: it’s not really random. But it’s not always completely predictable, because there are too many factors involved.
And one of those factors is humans. Humans can sometimes be moderately predictable – there’s money to be made from that, and more in sales than in gambling – but can also in ways be sufficiently irregular to be as good as random. When so many people can’t manage to construct a five-point bulleted list with syntactic parallelism, you have to reckon that the way they do anything else will also be unreliable. Better to bet on bouncing balls. Although you know you can’t know well enough how they will bounce.
But I know this: When I buy a lottery ticket, part of it goes to something worthwhile. And the rest goes to fantasy. And it’s cheaper than most fantasies and not as brief as many. And that’s saying… well, if not a whole lot, then at least half a lot. It may not be my lot in life to win a lot in the lottery, but so what? It still draws me.