Can you out-Vizzini your partner or friend in a Battle of Wits?
Try this interactive experiment, based on economics research, with your significant other, close friend, or coworker.
Then learn more about the game-theory principles it demonstrates.
By SHAUN GALLAGHER
In the film The Princess Bride, based on William Goldman's novel of the same name, the mysterious, swashbuckling Man in Black challenges the egomaniacal villain Vizzini to a Battle of Wits.
The Man in Black explains the rules: into one of two goblets, he has placed deadly poison. All Vizzini needs to do is choose a goblet to drink; the Man in Black will drink the other one, and then one of them will die.
Vizzini explains his decision-making process to his opponent.
"All I have to do," he announces with bravado, "is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet, or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I'm not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool. You would have counted on it! So I can clearly not choose the wine in front of me!"
Your own personal Battle of Wits
Below, you will have an opportunity to engage in a similar Battle of Wits with your partner or friend.
This particular battle is adapted from a 2012 study by two economics professors, and after the battle is over, you and your opponent will get to learn a little bit more about what the professors were studying and what conclusions they drew.
To begin, select an adversary. It could be your significant other, your close friend, or your coworker — but it should be someone whose methods of thinking and decision making you are at least somewhat familiar with.
Next, click on the "Begin the Battle of Wits" link below. You will be asked to answer a few questions — it should take you 1 to 3 minutes.
Then, you will be given a personalized URL to provide to your adversary. Pass along that link to your adversary and encourage them to fill out their answers to the questions it asks. (It should take them 1 to 3 minutes as well).
After your adversary submits their answers, they'll receive a new personalized URL that they can share with you. It will provide the results of the Battle of Wits along with more information about the game-theory principles it demonstrates.
Your first name:
Your adversary's first name:
We are:
Your own personal Battle of Wits
Below, you will have an opportunity to engage in a similar Battle of Wits with your partner or friend, who selected you as their worthy adversary.
This particular battle is adapted from a 2012 study by two economics professors, and after the battle is over, you and your opponent will get to learn a little bit more about what the professors were studying and what conclusions they drew.
They already completed the first part of this experiment. Now, it's up to you to finish it.
Click on the "Begin the Battle of Wits" link below. You will be asked to answer a few questions — it should take you 1 to 3 minutes.
After you submit your answers, you'll receive a personalized URL that you can share with your partner or friend. It will provide the results of the Battle of Wits along with more information about the game-theory principles it demonstrates.
You and your adversary are going to play a brief game in which the goal is to win as many points as possible.
Each of you gets to request a number of points between 11 and 20, and you are each guaranteed to receive the number of points you request.
But if your request happens to be 1 point less than your adversary's request, you'll receive a 20-point bonus.
How many points do you request?
Why did you choose this value? (Provide a sentence or two.)
Once you have answered both questions, click "Get Shareable Link" to generate a personalized URL. Share that URL with your adversary so they can complete their portion of the experiment.
When your adversary finishes, they will get a results URL that you can both view to see the results of the Battle of Wits and learn a little more about the science behind it.
Once you have answered both questions, click "Get Results Link" to generate a personalized URL. Share that URL with your adversary so that you can both review the results of the Battle of Wits and learn a little more about the science behind it.
The Hypothesis
Each of you is very likely to have chosen either 17, 18, or 19 points, and to have explained your choice methodically, e.g. "My partner probably thinks I'll choose 20, so she'll choose 19, so I'll choose 18."
However, if you happen to have chosen a point value below 17, you probably did not explain it methodically, but rather as a best guess, without elaborating on your reasons for why you think it is the best choice.
The Results
Hypothesis confirmed!
Hypothesis (partially) confirmed!
You defied the hypothesis!
The Science
This type of competition is called a "one-shot" game, because you only have one chance to win. Unlike a repeated game, you have no opportunity to pick up on your opponent's strategy through gameplay. You have to rely on what you already know about how they think.
In games like these, not everyone uses the same depth of strategy.
Some people make choices that don't rely on strategy. They try to maximize their chances of winning without trying to figure out what the other person will do. In game theory, these choices are called "level-0" choices, because they involve zero beliefs about what the other person will choose.
Other people use "level-k" strategies, where k is a number greater than zero.
For example, if you make a "level-1" choice, you assume the other player's choice will be level-0. And if you make a "level-2" choice, you assume that the other player's choice will be level-1, and so on.
In the 2012 study on which this Battle of Wits is based, participants played a game very similar to the one you just played with your adversary.
The study found that only 6 percent of participants chose the level-0 strategy, which would be a request of 20 points. A strong majority of the participants, 74 percent, chose either 17, 18, or 19 points.
When the study's authors looked at the explanations the participants gave for their choices, they found that almost invariably, participants who chose an amount less than 17 points did not think it through methodically. They didn't use level-k reasoning; instead they made a best guess. In contrast, just about everyone who chose 17, 18, or 19 points used level-k reasoning to explain their choice methodically.
The Takeaway
If you're in a romantic relationship, you might want to use these results as a jumping-off point for a conversation about how well (or how poorly) you are able to predict your partner's choices, and about whether that bothers or excites you. Perhaps you like being able to complete each other's sentences, or maybe you find it more thrilling that you never quite know what your partner is going to say next!
But in the end, the most important takeaway is one illustrated by Vizzini himself:
It's not the size of your k that earns you the victory. It's whether your opponent's value is k minus 1.
