Evolutionary Wagering

Tyler Cowen posts a reader's evolutionary hypothesis for why people like to gamble. It sounds plausible enough, although – as with much of evolutionary psychology – there’s no hard evidence. But Tyler’s post provides an excuse for me to present my own evolutionary hypothesis (sans evidence, naturally) about gambling – not why people gamble, but how they gamble.

Take the game of craps. In my head, I know (a) that all throws of the dice are independent; (b) that each outcome is just as likely as it ever was, regardless of how recently it has occurred; (c) that it doesn’t matter who’s throwing the dice; and (d) that a sequence of independent random events will produce streaks and patterns from time to time, but those streaks and patterns don’t tell us anything about the future.

But at the table, it’s incredibly easy to forget all that. When the same number keeps coming up throw after throw and everyone at the table is winning and cheering, or when the old dude in the funny hat somehow craps out every single time, the temptation to believe in real patterns is damn near irresistible. “This is a hot table,” I’ll think to myself, or “That dude in the hat is a loser, don’t bet with him.”

And I’m hardly alone. Ask most anyone who plays craps and hasn’t been trained in probability theory, and they’ll be sure that a skillful gambler can exploit streaks, some people are lucky and some are not, some tables are hot while that others are cold, and so on. But why?

Recognizing true statistical independence generally requires having a large data set. If you don’t believe dice throws are truly independent events, you can throw them a thousand times and see how close the realized frequencies are to the predicted frequencies. But in the environment in which humans evolved, it’s doubtful people had the chance to observe any given event that many times. Small data sets were the norm. Even if it were possible to collect a large number of observations, the need for immediate action probably made it unwise to do so in many cases. The gain from recognizing true patterns – that herd of animals migrates this way every year; this plant flowers immediately after rainfall – most likely swamped the losses from seeing patterns where there weren’t any. As a result, humans possess a powerful tendency to notice patterns even when they aren’t present.

Now back to craps. Say you’re at a table where everyone’s losing, and there’s a spot available at the next table where everyone’s winning. If you falsely conclude that the other table is better, what’s the downside? You’ll move over and face the exact same probability distribution you did to begin with; ex ante, there’s no cost to your false inference. On the other hand, if the other table really were better, you’d be harming yourself by refusing to move.

Similarly, say you notice the old dude in the funny hat always craps out, but the frat boy always hits his point. Whom would you rather have as a “hunting partner”? If you erroneously decide Frat Boy is lucky and Funny Hat is unlucky, you’ll start betting with the former (pass line) and against the latter (don’t pass line). As anyone familiar with craps odds can tell you, the expected value of your bets will remain the same, so you're no worse off. But what if Frat Boy really were luckier? Then failing to change your betting strategy would lower your returns.

Of course, educated people know that tables and people are not really lucky – at least not in ways you can exploit – so switching tables or betting against “losers” is pointless. But that sort of knowledge isn’t built in, whereas the capacity to detect patterns based on scant evidence probably is.