You Will Not Win the Lottery

April 3, 2012

And making money in Vegas is a bad long term life plan. It doesn’t matter what your “strategy” is. These games of chance are built around a simple premise: no matter who you are or what you do, the more you play, the more you will tend to lose money.

Maybe the best way to drive home the ridiculousness of our relationship to the random is with comedy (thank you, Stephen Colbert, for the most mathematically sophisticated analysis I’ve seen on TV in a long time.)

Let’s review some facts about how random events work, which I’m trying to teach to 2nd-3rd graders at the moment, but which I’m pretty sure the majority of adults don’t know.

Fact 1: A random event is not affected by what comes before it.

This means that lottery numbers that have come up before are equally likely to come up again. The numbers that won last week’s lottery are as good a bet to play this week than any other set of numbers.* By the way, it also means that 1, 2, 3, 4, 5, 6 is as good a lottery ticket to pick (sorry, Colbert) as anything else*, so don’t disparage that choice.

Thus, ignore the advice I found on a randomly chosen lotto website: “Look at past winning numbers. If you really enjoy statistics and probability, look for patterns in these lottery tickets, and use that information for the best lottery numbers to pick.” Looking for predictive patterns in random noise is the ultimate fool’s errand.

*Of course, some numbers are better picks in that they are less likely to be picked by other people, so if you do win, you’re not too likely to have to share.

Fact 2: Nothing you do affects the outcome of a random event.

All your superstitions, knocking on wood, crossing your fingers, etc., don’t do anything. There’s a very strong human need to feel like we’re in control of our lives. Well, we’re in control of some things, but not as much as we’d like, and we have absolutely no control over which numbers come up on dice, cards, or spinning balls.

Now, there are ways to bias an event. I may be unable to predict whether it will be sunny or rainy on a given day next year (a random event, for all practical purposes), but my chances of a sunny day will be better in the summer. Random doesn’t necessarily mean even odds. Similarly, my students have experimented with spinning dice rather than rolling them to constrain the outcomes, and some claim that they can get their odds of a certain outcome up to 1/3 instead of 1/6.

Fact 3: Most specific events in the future are fundamentally impossible to predict.

Predicting the future in any precise way is impossible. Predicting weather in the future, predicting the stock market number precisely, predicting which horse will win a certain race, etc.–virtually impossible. Interestingly, if you change the question in the right way, it is possible to make much more accurate predictions. For example, I have no way of knowing whether a given coin toss will be heads or tails; however, if you flip 100,000 times, I’m confident roughly 50,000 of those flips (give or take) will be head. Similarly, I can’t predict the weather in the future, but I can probably get a reasonable read on the climate, and I have no idea what the stock market will do on a given day, but I may be able to give a pretty good assessment of where the economy as a whole is headed (though even though both of these questions are at the right scale, they’re still very difficult to answer).

The difficulty in predicting the future is a relatively new discovery, mathematically, but at this point, it’s been established in the field of chaos theory.

These are lessons I’d like the 2nd-3rd graders in my math circles to understand. I’d like them to let go of their superstitions, and try to understand how randomness really works. There is perhaps no lesson the next generation needs to learn more urgently. And here’s my prediction: those who understand probability and statistics will have huge advantages over those who don’t in the information economy, and those with a hard technical knowledge of both fields will always have job opportunities waiting for them.

I’m heading in a few minutes to meet with a group of kids that has been showing some real finesse for these ideas already. Lately we’ve been designing dice games to be tricky enough to appeal to others even though the games are biased in our favor. In other words, I’m teaching them to think like casinos. If I can succeed, maybe I can keep them from ever patronizing those places, too. Or buying a lottery ticket.

Because, face it, it’s just not a good bet.

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