Our brains are remarkable organs, capable of incredible feats of logic, memory, and creativity. However, they are also prone to certain cognitive biases and shortcuts that can deceive us into not thinking critically. My favourite examples of how your brain can mislead you are the coin flip, the Ellsberg paradox, and the birthday problem.
The Coin Flip: What Are the Real Odds?
When flipping a coin, most people intuitively believe there is a 50% chance of landing on heads and a 50% chance of landing on tails. This belief holds that if the coin is fair, it has an equal probability of landing on either side. However, the assumption that all coins are fair is where our brain deceives us.
Consider a biased coin, where one side is heavier or shaped differently. The odds are no longer 50/50, yet our brain defaults to this simple heuristic. Without examining the coin or knowing its history, we blindly trust our initial assumption. This is a classic example of how our brain opts for a convenient, though potentially incorrect, simplification over deeper analysis.
The Ellsberg Paradox: Preferring the Known
The Ellsberg paradox highlights our aversion to ambiguity and preference for the known over the unknown. Imagine you are presented with two urns. Urn A contains 50 red balls and 50 black balls. Urn B contains 100 balls in an unknown ratio of red to black. You are asked to choose an urn and then draw a ball, winning money if you draw a red ball.
Most people prefer Urn A because they know the exact probabilities (50% red, 50% black). However, choosing Urn B could offer better odds if the ratio is more favourable. The paradox shows that our brains often avoid uncertainty and prefer the security of known probabilities, even when a potentially better option exists.
The Birthday Problem: Surprising Odds
The birthday problem is a classic example of how our brains struggle with probability. Imagine a room with 23 people. What are the chances that two people in the room share the same birthday? Intuitively, most people think the probability is low. However, the actual probability is about 50%.
This counterintuitive result arises because our brains underestimate the number of possible pairings in the group. With 23 people, there are 253 pairs, each with a 1/365 chance of matching birthdays (ignoring leap years). The brain’s default assumption of low probability stems from focusing on individual comparisons rather than the collective probability of all pairings.
How to manage your brain
Your brain is wired to take cognitive shortcuts, often leading you to oversimplified or incorrect conclusions. Recognizing these biases can help us make more informed decisions:
- Question assumptions: Just because something seems straightforward (like a coin flip) doesn’t mean it is.
- Embrace ambiguity: Sometimes, the unknown can offer better outcomes than sticking with the familiar.
- Consider collective probabilities: Consider the bigger picture rather than isolated comparisons in scenarios like the birthday problem.
By being aware of these mental traps, you can train yourself to think more critically and avoid being deceived by your brain.
