The Palindrome

The Palindrome

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The Palindrome
The Palindrome
Your Brain is Wrong About Probability

Your Brain is Wrong About Probability

The universe doesn't remember your last coin toss

Tivadar Danka's avatar
Tivadar Danka
Jul 01, 2025
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The Palindrome
The Palindrome
Your Brain is Wrong About Probability
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I precisely remember the first time probability finally clicked for me.

During the summer break of my undergrad first year, I had a brief crush on poker, spending most of my days either grinding the online microstakes no-limit Texas hold 'em tables or endlessly consuming poker theory books.

Poker is a beautiful game, and most of the lessons I have learned from it have had a significant impact on my life.

Only fight battles you are favored to win.

Winning one hand is luck. Winning a thousand is skill.

Losing doesn't mean that you made a bad decision. Winning doesn't mean that you made a good one.

To this day, I explain the concept of expected value with pot odds in poker. Someday I'll write a massive essay on the life-changing ideas that my short stint at the online casinos taught me, but right now, I want to talk to you about probability.

Let me tell you: our intuition about probability is fundamentally flawed, resulting in mostly comical, sometimes tragic situations.

This post is about three of them:

  • that misunderstanding probability can lead us to financial ruin,

  • that probabilities don't scale linearly,

  • and what can happen will happen eventually.

Speaking of poker: gamblers on a losing streak tend to keep on playing, as they perceive that their bad luck should increase the chance of winning.

Here's why this is wrong.

The gambler’s ruin

Let's play a simple game!

The dealer tosses a fair coin. If it comes up tails, you win $1. Heads, you lose $1.

Suppose that you lost ten times in a row. Does it increase the likelihood of winning the next round? Take your time to think it through; I'll even leave a couple of blank lines to keep you from spoilers.

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