Gambling Math Gone Wrong: Why It Doesn't Apply to Investing - 2021-02-27

Li Yongle, a popular math educator, explained the math behind gambling, demonstrating how prolonged play inevitably leads to financial ruin. His formula for calculating the probability of winning is P(A) = 1 - (B-A) / B, where A is your initial capital and B is your target amount.


No

Money (A) / win (B)

P(A) = 1 - (B -A) / B

1

100 / 120

= 1 - (120 - 100) / 120 = 5/6

2

100 / 200

= 1 - (200 - 100) / 200 = 50%

3

100 / 1000

= 1 - ( 1000 - 100) / 1000 = 10%

4

100 / infinite

= 1 - ( finite - 100 ) / infinite = impossible


Let's break it down with a $100 starting point:

  • Target $120 (a $20 profit): P(A) = 1 - (120 - 100) / 120 = 5/6 (seems pretty good!)

  • Target $200 (doubling your money): P(A) = 1 - (200 - 100) / 200 = 50%

  • Target $1000 (a 10x return): P(A) = 1 - (1000 - 100) / 1000 = 10%

  • Target infinite: P(A) = 1 - (infinite - 100) / infinite = virtually impossible

As you can see, the higher your target, the lower your chances. Li Yongle correctly points out that aiming for massive returns significantly diminishes your probability of success.

However, his crucial mistake is applying this gambling formula to investing. He concludes that the chances of winning in the stock market are also incredibly low. This reveals a fundamental misunderstanding of investing. It suggests he either hasn't studied investing seriously or has had some unfortunate experiences. While his math skills might be sharp, applying them to investing without understanding the nuances is a major flaw. Investing is more art than pure science.

He shouldn't simply extrapolate gambling principles to the stock market. Even with $1 million, I wouldn't assume a 5/6 probability of making $200,000 without a deep understanding of the companies, the market, and market psychology.

The gambling formula fails to capture the dynamic nature of companies. A company isn't just a static number; it's a collective of intelligent individuals working on products and services, creating compounding effects and navigating inflation. It's a constantly evolving organism, not a fixed target in a game of chance. Li Yongle's error lies in treating the stock market like a casino.

Formulas Aren't Magic: Why Context Matters

So, here's the key takeaway: you can't just blindly apply any formula without understanding its limitations. Context is king. A formula designed for one situation might be completely inappropriate for another. Using the wrong tool for the job leads to, well, the wrong conclusions. And in this case, the dangerously wrong conclusion is that the stock market is just a casino. It's a seductive idea, especially when you're looking at short-term volatility, but it's fundamentally flawed. Treating investing like gambling ignores the crucial differences between the two, and that's a mistake that can cost you dearly.


Youtube link: https://www.youtube.com/watch?v=AadaEc6pJpw&feature=youtu.be

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