Imagine you’re playing a coin-toss game with a biased coin. It will land on heads for 70 percent of the tosses and on tails for 30 percent.

(I am not suggesting that any noble MinnPost reader would cheat at a game of chance. This is just a theoretical exercise.)

Before reading on, avert your eyes from the rest of this article and decide your strategy. How often would you bet on heads?

OK. Read on.

Bad choices

A statistician would advise you to pick the higher probability option — in this case, heads — for every toss.

But even when they’re told the coin is “loaded,” people who’ve done this exercise in psychology studies tend to choose heads only about 70 percent of the time.

Why?

“They think that they can do better than just 70 percent, that some order in the world will allow them to do better than they could do by just choosing heads,” said Shawn Green, a University of Minnesota psychologist.

There is some rationality, even in wrong-headed gambling decisions, according to a new study by Green and colleagues published in this week’s “Early Edition” of the Proceedings of the National Academy of Sciences.

We humans love to assign order to our chaotic universe. Often, we can if we understand the basic structures underlying problems we encounter. So it is rational to search for a structure that can inform our strategies.

“The overarching idea is that there is typically structure in the world, and it makes sense that when we make decisions, we try to understand the structure in order to exploit it,” said Green, who is a post-doctoral fellow in the College of Liberal Arts’ Department of Psychology and Center for Cognitive Sciences.

Jelly beans and apples

In one simple and common kind of structure, the outcome that just occurred tells you something about what is likely to happen next. Say you like black jelly beans, and someone tells you that two of the three jelly beans left in a jar are black. On the first draw you get a red one. No doubt about this one. Draw again.

Say you wanted to pick apples, and you could choose one of two nearby orchards. You go to orchard A, and the trees are loaded with the crunchy, sweet varieties you love to eat. You load your basket and go home happy.

The next week, you set out to pick more apples. It would make sense to go back to orchard A, where you now know there was an abundance of great apples.

Where people go astray is in trying to assign some sort of sequential order to independent events, which characterize many of our common gambling games like flipping coins, rolling dice and spinning wheels.

Take a coin toss with a fair coin. You pick heads. You toss five times and tails come up every time. Heads really must be due — right? Not with any more likelihood than was true on the first toss, the second, etc. These tosses are independent, and each side has a 50 percent chance of coming up in any one toss.

Nevertheless, people will act as if those previous flips influence the next one, Green said.

Understand it, exploit it

The research examines the roots of a seemingly irrational human decision strategy that occurs in so-called binary choice tasks. It’s a problem that has perplexed researchers in economics, psychology and neuroscience for decades.

And it helps explain causes of seemingly irrational human decision-making.

Normally, it is very reasonable to assume you are dealing with an underlying structure and that it can be exploited if you understand it, Green said.

“It becomes a sensible thing,” Green said. “Most of the time in the world there is this temporal structure...And in the real world things tend to change slowly.”

It also is reasonable to try to make predictions about the best choices for the future, and in order to do that you have to discover the governing structure.

That can take some casting about.

In that sense, these independent events are unreasonable because the structure we are seeking isn’t there. So gamblers often compensate by inventing structures.

That’s why we mess up in games like coin flips. And we assume the gambler with a three-game winning streak is “hot” and likely to win the next game too.

Doing the right thing

When research subjects were given the context and understood that outcomes were independent, they shifted their choices and did the “right” thing.

“This demonstrates that given the right world model, humans are more than capable of easily learning to make optimal decisions,” Green said.