The Probability of Manufacturing Success

I came across a short clip recently discussing the difference between being lucky and getting lucky.

At first glance, it sounds like standard social media fluff. But it got me thinking about whether “manufacturing luck” actually holds up mathematically.

The Math: Cumulative Probability

Suppose you try something where your odds of succeeding on any single attempt are just 10% ($p = 0.10$).

Each attempt has no memory. If you fail twice, your odds on the third attempt are still just 10%. That is the nature of independent events—past failures do not entitle you to future wins.

The math changes, however, when you look at cumulative probability across multiple attempts:

The probability of hitting at least one success across n attempts is simply the inverse:

How the probability shifts as you increase attempts (n):

• 1 Attempt: 10.0%
• 5 Attempts: 40.9%
• 10 Attempts: 65.1%
• 20 Attempts: 87.8%

Even if no individual attempt gets any easier, taking 20 shots turns a 10% long shot into an 88% statistical likelihood of at least one win.

On paper, this is why people say you can “manufacture” luck through volume. But translating this formula to the real world requires understanding its assumptions.

The Hidden Assumptions

The formula is neat, but it only works if several strict conditions hold:

1. The Survival Problem (Gambler’s Ruin)

The math assumes you can afford 20 attempts. In reality, attempts are rarely free.

If an attempt costs very little—sending a cold email, publishing an article, applying for a job—you can easily afford 20 or 50 trials. But if a failed attempt wipes out your capital, sanity, or runway, you never reach $n = 20$.

The math only works if the cost of failure is low enough that you survive long enough to let probability play out.

2. Events Aren’t Truly Independent (Which Can Help or Hurt)

Roulette wheels are independent. Humans are not.

• The upside (Learning): If you pay attention, each failure teaches you something. Your pitch gets sharper, your product gets better, and your network expands. In practice, $p$ increases with each try ($p_{10} > p_1$). This makes cumulative success happen faster than the formula predicts.
• The downside (Correlation & Macro): If you pitch firms in the same tight circle, a bad impression can spread. Or if a recession hits, all 20 of your “independent” opportunities can fail at once from the same systemic shock.

3. Payoffs Are Asymmetric

The binomial formula treats success as binary: 0 or 1.

In investing and business, payoffs follow a power law. You don’t just care about the probability of getting one win; you care about the magnitude of that win. One $100\times$ outcome compensates for dozens of zeroes.

What This Means in Practice

“Manufacturing luck” is not about blindly repeating the same action 20 times and hoping for a different result.

It comes down to three things:

1. Keep failure cheap: Structure your attempts so no single failure knocks you out of the game.
2. Iterate, don’t just repeat: Use the feedback from each failure to raise your baseline probability ($p$).
3. Stay in the game long enough: Let cumulative probability do the heavy lifting.

Control the downside, learn from each shot, and take enough attempts to let the math work.

Disclaimer: The ideas presented in this post are solely my personal perspective and have not been substantiated by any verifiable evidence. Please form your own opinions on such matters.