Logical thinking and bias blind spots

Here’s a simple arithmetic question:

A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

(the vast majority of people respond quickly and confidently, insisting the ball costs ten cents; this answer is both obvious and wrong — the correct answer is five cents for the ball and a dollar and five cents for the bat)

Here’s another one:

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

(your first response is probably to take a shortcut and to divide the final answer by half, leading you to 24 days. But that’s wrong — the correct solution is 47 days)

While we like to think (hope) that human beings are rational agents, studies such as the bat and ball question from Daniel Kahneman (a Nobel Laureate and professor of psychology at Princeton) can indicate the opposite: when people face an uncertain situation, they don’t carefully evaluate the information or look up relevant statistics. Instead, their decisions depend on a long list of mental shortcuts, which often lead them to make foolish decisions. These shortcuts aren’t a faster way of doing the calculation; they’re a way of skipping it altogether. Asked about the bat and the ball, we bypass our arithmetic and default to the answer that requires the least mental effort. We assume that intelligence is a buffer against bias, but a 2012 study suggests that, in many instances, smarter people are more vulnerable to these thinking errors.

Find out more about bias blind spots, anchoring bias, framing effects and “cognitive sophistication” in this interesting New Yorker article: “Why Smart People Are Stupid“.


  1. Hey Tom,
    There’s a recent bestseller by this guy ‘Thinking fast and slow’ with many of these fascinating counterintuitive puzzles. The book is essentially about the power of our faster intuition (he calls System 1) vs. our logical reasoning (System 2). Evolving such an intuition system might cause as you say foolish errors in the face of such problems, but no doubt conferred some form of selection advantage probably related to speed and tendency overall to get more optimal outcomes from a gut reaction.

  2. Cool article Tom;John‘s response was interesting too

    Tom I think a lot depends on how you setup the question. If you pose a question in such a way that leads the hearer to believe that the question is simple or easy, they will likely look for the simple or easy answer via mental shortcuts. However, if you pose the same question in a different way, in a way that appears complex, technical, or difficult the hearer will likely pay greater attention to the details as well as the final answer. So instead of a bat, ball, and currency, you substituted ‘x’, ‘y’, and whole numbers, then told them they had 15 mins to “calculate” the correct answer you would likely get more correct answers from the same participants..

    John’s response reminded me of how +Armis fosters subconscious game play. Armis is a brain game that was specifically designed to develop critical thinking skills in a very complex environment (land, air, sea; million+ setups, decentralized power, yada, yada, boom, boom). They believe WELL developed critical thinking skills easily transfer to academic endeavors.

    Question, do you believe that rigorous game play of any strategy board game can necessarily result in better grades?

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