Thursday, July 07, 2005

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.

6 comments:

MLS said...

You don't really bet the Don't Pass, do you? That's not cool. Just take the Any Craps to hedge the come-out when it's the old dude's turn.

Gil said...

I don't know about the evolutionary part, but you're definitely right about people's tendency to infer patterns even when they aren't really there.

In general, I think good pattern recognition is an important aspect of intelligence, because sometimes apparent patterns actually can lead you to good theories, or good predictions. But, this sort of induction is invalid (apparent patterns might not repeat), and we should criticize and test theories before adopting them (and betting on them!). Many people skip that step.

They also tend to discount contradictory evidence, and have very selective memories about what their experience is.

Many craps players will tell you about how the dice "almost always" come up 7 after someone says "seven" or the dice are changed, or they hit someone's hand or a stack of chips. It's just not true, and that's not their experience (it really comes up 1/6th of the time under all of these conditions), but they honestly believe that it is.

Also, I think it's just more fun to act as if there are hot and cold runs, so people are more inclined to believe it. Betting on independent, individual throws is just not as interesting. The game already helps to chunk them into series (by establishing a point, etc.), and riding a hot streak of passes is something people can notice and get into.

I'm a pretty intellectual player, but I like to increase my bets during a "winning streak" and go back to my minimum bet after a loss. Mostly this helps money management (by avoiding ruin after a small number of throws), but it's also because it's fun to think about how much I could make with a sufficiently long winning streak. But, I know that no betting strategy will increase my expected outcome.

About "Don't Pass" betting...I admit that I avoid it too, even though the odds are slightly better on that side. I think it's because I'm an introvert and playing craps is a chance for me to socialize and have fun with total strangers. Betting "Don't" would inhibit that.

Glen Whitman said...

MLS -- I rarely bet the Don't Pass, but I will on occasion. The etiquette is that you can't cheer openly when you win. Don't Pass bets must be made discreetly. As for this "Any Craps" hedge, wouldn't that just as obviously be a bet "with the casino" as the Don't Pass? (And yes, I realize that all bets are really against the casino, but you know what I mean.)

Gil -- the difference in the house edge between Pass and Don't Pass is negligibly small, about 1/100 of one percent, or a penny on every $100 bet. That's so small I don't even think about it.

Blar said...

You're right that people see patterns when there aren't any there, and this shows up in gambling. Your evolutionary account, that the gains of correctly identifying a pattern outweighed the losses of seeing a pattern when there was none in evolutionary times, is part of the story, but it's not the whole story.

Part of the issue is with cognitive limitations, rather than adaptations. For instance, people remember when someone says "seven" and then a 7 comes up, but they don't remember as well the times when someone says "seven" and no 7 comes up. Since people assess probabilities partly based on the preponderence of examples that turn up in their memories, this will bias their judgments of likelihood. The full explanation ought to combine a bunch of other factors, like the illusion of control and people's overapplication of the idea of "like goes with like" (e.g. you roll the dice softly to get a low number).

I think that you're wrong that these biases are harmless when it comes to gambling. If people did not think that they could go on hot streaks, see patterns, identify lucky tables and people, and do other things to increase their chances of winning, then they would gamble a lot less and therefore lose a lot less. I'm reminded of both Dostoevsky's The Gambler and the movie Pi, both of which involve people who are obsessed with uncoding a complicated pattern to make a lot of money, when the "pattern" is really completely unpredictable to them.

Jadagul said...

This is a nitpick that doesn't really affect your main point, but there are actually people who, for whatever reason, throw some numbers more than others. I know of one guy who threw a lot of nines, and so was doing well; the casino sent people out to switch dice, to weigh the dice, to watch him throw, and couldn't figure out. Apparently he was a bit confused as well as to why he tended to throw nines, but he knew he did (and it was a real enough effect for the casino to investigate).

Gil said...

Glen,

Just out of curiosity, since you don't even think about the miniscule odds advantage, but you still bet "Don't Pass" on occasion...

For what reasons do you ever decide to bet that way?