Think you're no good at Chess?   Not a strategic thinker?   You're better at it than you may think.

When we make any decisions related to how we think someone else will act,  we must use reason to infer the other's next moves to decide what we must do. This recursive reasoning ability in humans has been thought to be somewhat limited but new research says people can engage in much higher levels of recursive reasoning than was previously thought. 

Decision-making is part of day-to-day life, but when it involves competition, the complexity grows exponentially. Think of the scene in "The Princess Bride" (in Science 2.0's top 10 movies of all time) when Vizzini and the Man in Black argue over which of two wine cups is poisoned - "The battle of wits has begun. It ends when you decide and we both drink, and find out who is right . . . and who is dead", Vizzini explains.   In games such as chess, "thinking ahead" and trying to anticipate your opponent's moves is what distinguishes a casual player from a Grand Master.

When people typically make decisions, especially in competitive situations, they try to choose the path that has the most advantageous outcome, and while sometimes the best path is obvious, often it's less clear, especially in games or military conflict. 

"The question we asked was this: What level of reasoning do human beings engage in when they aren't master chess players?" said University of Georgia psychologist Adam Goodie. "Previous findings had been extremely pessimistic, suggesting that people were about equally likely merely to acknowledge the immediate preferences of an opponent as they were to go beyond that to higher levels of reasoning. If they do go to a higher level, it seemed that they only thought one step ahead."

In order to find out how deeply people really go in working out how many "moves ahead" they can make, Goodie and his colleagues set up an experiment in which large samples of student participants (136 in one trial, 232 in another) played against a programmed computer, though they were told it was another participant in another room. 

Called the "3-2-1-4 Game" the experiment was laid out on four spaces in a square with numbers on them in that sequence, starting with 3. The students were told they and their invisible opponent, the computer, would walk around the spaces together, starting together and stopping together, alternating on who decides whether to stop where they are or to continue moving forward. The complicating factor was that each would have a different probability of winning money depending on where they finished—with the students winning more on the highest possible number and the opponent winning more on the lowest. 

"The ideal solution is to think ahead to what will happen if you get all the way around to 1," said Goodie, "and you have to choose whether to stay there or move to 4."

Contrary to previous literature, those in the experiment had no trouble with the game, ramping up from what is called "first-level reasoning" to "second-level reasoning" easily and consistently.  After discovering that participants had little trouble with the four spaces, the researchers made the game even more complicated by adding five stops in the order 3-2-4-5-1, with the same rules applying. 

"To our surprise, participants had just as little trouble learning the game and playing it at the highest possible level," said Goodie.

In another film from the 1980s, "WarGames", humans who appear unable to decide whether or not to launch nuclear missiles are replaced by a computer with chaotic and potentially disastrous results. The new research shows, as the film hints, that maybe people could have done the job all along.

Citation: Adam S. Goodie, Prashant Doshi, Diana L. Young, 'Levels of theory-of-mind reasoning in competitive games', Journal of Behavioral Decision Making, first published online 17 OCT 2010, DOI: 10.1002/bdm.717