The Equivalent Bet Test

THE EQUIVALENT BET TEST

Imagining a bet can generate a qualitative sense of your confidence in a belief. Do you feel happy to take the bet, without hesitating? Do you feel a little bit of doubt? Do you feel truly torn? Your hesitation, or lack thereof, is a proxy for your degree of confidence that your belief is true.

Contemplating a bet can also be used to pin down how sure you are quantitatively, helping you put a number on your degree of confidence. Sometimes I hear an ambitious technological forecast like, “Self-driving cars will be on the market within the year!” My first reaction is often to scoff, “Well, that’s crazy.” But how sure am I that the forecast is wrong?

To answer that question, I imagine facing a choice between two possible bets. I use a technique I adapted from decision-making expert Douglas Hubbard called an “equivalent bet test.”12 Here’s how it works in this case: I can bet on self-driving cars, and get $10,000 if they’re on the market in a year. Alternately, I can take the “ball bet”: I’m given a box containing four balls, one of which is gray. I reach in and pull out one ball, without looking—if it’s gray, I win $10,000.*

Ball bet (1 in 4 chance of winning):	Bet on self-driving cars
Draw from a box with four balls, one of which is gray. If I draw the gray ball, I get $10,000.	If fully self-driving cars are available for purchase in a year, I get $10,000.

Which gamble would I rather take? I hesitate for a moment, but I feel happier with the ball bet. Since the probability of winning the ball bet is 1 in 4 (or 25 percent), the fact that I feel more confident in the ball bet implies that I’m less than 25 percent confident in self-driving cars making it to the market in a year.

Let’s try decreasing the odds of winning the ball bet. Suppose the box contains sixteen balls, only one of which is gray. Now which do I prefer: betting on drawing the gray ball or betting on self-driving cars in a year?

Ball bet (1 in 16 chance of winning):	Bet on self-driving cars
Draw from a box with sixteen balls, one of which is gray. If I draw the gray ball, I get $10,000.	If fully self-driving cars are available for purchase in a year, I get $10,000.

This time, I notice that I prefer my chances on self-driving cars. After all, sometimes technological progress surprises us. Maybe one of the companies working on self-driving technology is actually farther along than they’ve been letting on. It seems unlikely, but I’d still rather gamble on that than on being lucky enough to draw the gray ball. And since the probability of drawing a gray ball is 1 in 16 (or about 6 percent), the fact that I would prefer to bet on self-driving cars implies that I am more than 6 percent confident that self-driving cars will make it to the market in a year.

Okay, let’s adjust the chances of winning the ball bet back upward a little bit, to one in nine. Now which do I prefer?

Ball bet (1 in 9 chance of winning):	Bet on self-driving cars
Draw from a box with nine balls, one of which is gray. If I draw the gray ball, I get $10,000.	If fully self-driving cars are available for purchase in a year, I get $10,000.

Hmm. I’m really torn. Neither seems like a clearly better bet. The bets feel equivalent to me—and since we know that the probability of winning the ball bet is 1 in 9 (or about 11 percent), that implies that I have roughly 11 percent confidence in self-driving cars coming out within a year. I still don’t think the “Self-driving cars will be on the market in a year” forecast is likely to come true, but I’ve gone from a glib “That’s crazy” to a more honest best guess.

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Thought experiments can reveal that judgments are contingent: what seems true, reasonable, fair, or desirable may change when you vary a feature that should have been irrelevant.

The equivalent bet test asks for a related skill: telling the difference between making a claim and actually trying to guess what’s true. Making a claim feels like your press secretary is speaking. It feels pat; neat and tidy. Sometimes hurried, as if you’re trying to put something past yourself. The mental motion is declaring, proclaiming, insisting, or perhaps scoffing.

Trying to guess what’s true feels like being the board of directors, deciding how to bet. There’s at least a second or two when you don’t know what answer you’re going to end up giving. It’s like you’re squinting at the evidence, trying to summarize what you see. The mental motions involved are estimating, predicting, weighing, and deliberating.

Quantifying your uncertainty, getting calibrated, and coming up with hypothetical bets are all valuable skills in their own right. But having the self-awareness to be able to tell whether you’re describing reality honestly, to the best of your abilities, is even more valuable still.