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Don't Take a Single Bet, Take Many Instead: Why Taking Many Small Risks is Better Than Playing It Safe

Everyone has to decide how much risk to take in life. Whether it’s buying insurance, approaching someone interesting at a bar, or investing in a new project, the way we handle uncertainty can determine our outcomes. But should you lean toward taking more risks, or is it smarter to play it safe?

In this article, we’ll explore the science of risk-taking, show why playing many small "positive bets" is a winning strategy, and highlight why fearing a single loss might be holding you back.

What Is Risk and How Do We Evaluate It?

At its core, risk is the uncertainty of an outcome. It’s frightening because negative outcomes, like losing money or experiencing harm, can have significant consequences. For example, if your house burns down, the resulting damage could affect your life dramatically. The uncertainty—combined with the potential cost—makes such risks hard to bear.

However, we can evaluate risk rationally using the following framework:

\[ \text{Expected cost of risk} = \text{Probability of occurrence} \times \text{Potential damage} \]

Let’s say the probability of your house burning down in a year is 0.25%, and the damage would amount to $500,000. Then, the expected yearly loss is:

\[ 0.25\% \times 500,000 = 1,250 \, \text{dollars}. \]

If your insurance policy costs $2,500 per year, is it worth it? That depends on two factors:
1. Can you afford the loss? If the loss would ruin you financially, then insurance may be necessary.
2. Are you paying too much for peace of mind? Insurance companies charge more than the expected loss to profit—your "rational" cost-benefit tradeoff often tilts against you.

Why People Are Risk-Averse (and What It Costs Them)

Studies show that people are naturally risk-averse. Most individuals are willing to pay far more to eliminate uncertainty than is rationally justifiable. Insurance companies thrive on this: they sell peace of mind, not value.

This behaviour can be explained using Prospect Theory, which was developed by Daniel Kahneman and Amos Tversky in 1979: Losing money "hurts" disproportionately more compared to the pleasure of gaining the same amount.

This psychological effect makes buying insurance appealing—even when it’s mathematically unfavorable. However, overpaying to avoid risk can significantly limit your long-term wealth and opportunities.

Why Taking One Risk Is Scary—But Taking Many Isn’t

Imagine this bet:
"Heads or Tails: Heads you win $20, Tails you lose $10."

At first glance, the idea of losing $10 might feel uncomfortable—even though the expected value (EV) of the bet is clearly positive:

\[ \text{EV} = (0.5 \times 20) + (0.5 \times -10) = 10 - 5 = 5. \]

Now, consider playing this bet 1,000 times. Would you take it? Here’s why you absolutely should:

Expected Value Grows Linearly:
\[ \text{Total EV} = 5 \times 1000 = 5,000. \] After 1,000 bets, you expect to earn $5,000.

Variance Shrinks Relative to Gains:
While individual bets carry risk, the law of large numbers ensures that outcomes stabilize over time. We can calculate the standard deviation to measure uncertainty:

So, your final result after 1,000 bets will likely fall within:

\[ 5,000 \pm 474.34 \, (\text{between } 4,525.66 \text{ and } 5,474.34). \]

The chance of losing money is extremely low, but it is not exactly zero. The probability of losing money would require the outcome to fall more than 10 standard deviations below the mean, a highly unlikely event with a probability in the order of \( 10^{-24} \).

The Power of Many Positive Risks

The lesson here is simple: don’t focus on the outcome of one bet. If you have the opportunity to take many small risks with a positive expected value, you’re almost guaranteed to win in the long run. This is how businesses thrive, investments grow, and individuals build wealth.

Life is a game of repeated risks. While one failure may feel devastating, it rarely matters when spread across dozens or hundreds of opportunities.

But What About the "Good Feeling" of Playing It Safe?

Economists often overlook an important aspect of risk: the emotional comfort of avoiding it. Insurance, for instance, not only reduces financial risk but also brings peace of mind. And sometimes, that peace of mind is worth the cost.

However, you should still ask yourself:

Is Losing a Bet Really That Bad?

Here’s a thought experiment: imagine playing a video game like GTA with unlimited cheats. It might be fun at first, but eventually, the game becomes boring. Why? Because overcoming challenges and taking risks is what makes the experience meaningful.

Similarly, in life, "losing" is often not as bad as we fear:

  1. Failures Build Resilience: Bad experiences teach us lessons and make us stronger.
  2. Challenges Give Life Meaning: Struggling to overcome obstacles can bring fulfillment and satisfaction.

Final Thoughts: Embrace the Law of Large Numbers

Your life likely won’t end tomorrow, and you’ll have hundreds or thousands of chances to take risks. By embracing opportunities with positive expected value—whether in relationships, career, or investments—you stack the odds in your favor.

So don’t let the fear of one loss hold you back. Take many small bets, let the law of large numbers work its magic, and watch your outcomes grow. Life rewards those who dare to play.

Key Takeaways:

  1. Avoid overpaying to eliminate risk (like overpriced insurance).
  2. One isolated risk feels scary—but many positive risks are your ticket to success.
  3. Failures and challenges are part of the game. They make life interesting and worthwhile.

Take the bet. Then take another. And another. It’s the surest path to long-term victory.