Magnitude vs. Frequency: Why Rare Events Matter More Than You Think

Let's walk through a simple bet.

I’ve secretly picked a number between 1 and 1000. You must randomly guess a number within that range. If the number you pick does not match mine, you win $1. Pretty nice!

But—if your number does match mine, you lose $10,000.

Would you take this bet?

Although you could possibly lose a huge amount of money, the chances of that happening are tiny! After all, you have a 999/1,000 chance of walking away with a dollar. Seems like a good idea, right?

But with a little math (everyone’s favorite subject), we realize a harder truth:

If you play this game enough times, your expected value is a loss of around $9 per game.

Suddenly, it feels like an irrational decision to play. And reasonably skilled gamblers would have come to that conclusion intuitively.

What This Silly Game Teaches Us

This might be a lighthearted example, but how often does this logic apply to real life?

Financial markets: "The housing market is solid and safe."
Day-to-day behavior: "I don’t need to wear a seatbelt in the back of a car."

All it takes is one improbable event—like the 2008 recession or a tragic accident—to shake those beliefs and prove that our perceived security was never truly secure.

Mistaking Probability for Expectation

As humans, we often confuse probability with expectation. We subconsciously equate how often something happens with how much it matters.

This happens for two key reasons:

We round high probabilities up to 100% certainty.
It’s easier for our brains to treat 99% as a sure thing. Visualizing a 50/50 coin toss is much simpler than imagining a 1-in-1,000 chance.
We’re taught with symmetry in an asymmetric world.
Most basic education in stats, econ, or business revolves around clean, symmetrical examples: coin tosses, perfect markets, ideal conditions. Reality is messier and more skewed.

Frequency ≠ Magnitude

We must make a clear distinction between how often something happens and how big the outcome is when it does.

Even if the probability of an event is small, the impact of that event could be massive—far more than anything we’d anticipated.

Using This Distinction to Your Advantage

So far, we’ve looked at negative impacts of improbable events. But there’s a flip side: huge potential in rare upside.

You've probably already engaged with this idea, even if unintentionally:

Applying to dozens of jobs
Buying lottery tickets
Hoping to meet the right person

These are asymmetric bets: high failure rate, potentially high reward.

High-Stakes Winners

Some people build entire careers around these bets:

Angel investors and VCs fund startups expecting most to fail. But one Unicorn—a company valued over $1B—can pay for all the others.
Gamblers, sports managers, and market investors look for variance. They often lose, but when they win, they win big.

The Billion-Dollar Thought Experiment

Astro Teller, head of Google X (aka the "Captain of Moonshots"), asks a provocative question:

If you could choose between being 100% certain of making $1 million, or having a 1% chance of making $1 billion—what would you pick?

With our gained intuition, we see the 1% chance at $1B is actually the better bet. Magnitude trumps frequency.

So, What Should You Ask Yourself?

The most important question is:

Is the cost of losing small enough compared to the value I gain if I win?

If yes, the bet may be worth it.

Here are a few guidelines when making these asymmetric bets:

1. Can I replicate this scenario easily?

If you're going after something unlikely, don't rely on one shot. Increase your chances by increasing attempts.

Want more sales? Have more prospective clients.
Dream job? Apply broadly.
Startup investing? Diversify.

2. How often can I afford to lose?

It's not just about how much losing costs—it's about how often you can afford to lose.

Calling a client takes 5 minutes? That gives you 60 shots in 5 hours.
Job applications? You can send out hundreds in a month.
Small investments? You can spread your risk across dozens.

3. How many times do I need to win?

The best answer is: very few.

If your success requires too many wins to break even, it’s probably not worth it. But if one win can change everything, then it’s worth placing many small bets.

Ask any early investor in Twitter or Uber.

Final Thoughts

There’s a world of difference between how often something happens and how much it matters when it does.

Outcomes are rarely linear. The decisions we make—financial, personal, or professional—should reflect that.

So always ask yourself:

If I lose, do I lose small? If I win, do I win big?