Flipping Coins & Breaking Hearts

It started with a 60% edge and a promise of infinite wealth. It ended with a margin call and a broken spirit. Investing isn’t just about finding positive expectancy; it’s about surviving the volatility that comes with it. Here is how to stop flipping coins and breaking hearts, and start compounding wealth without the emotional trauma.

The Paradox of Positive Expectancy

Having a mathematical edge does not guarantee survival. In a game where a coin is biased to land on heads 60% of the time, a player possesses a distinct positive expected value (+EV). Intuitively, one should bet aggressively to maximize profits. However, betting the entire bankroll on each flip ensures that ruin is inevitable; while the expected value of a single "all-in" bet is positive, the probability of eventually hitting a losing streak and losing everything approaches 100% over time.

This counterintuitive reality highlights a critical gap in financial intuition: maximizing expected value is not the same as maximizing wealth growth. Many investment professionals [see: gwern [1]] fail to distinguish between arithmetic mean returns (which favor maximum leverage) and geometric mean returns (which account for the compounding effect of volatility and the risk of ruin). In real-world markets, unlike the controlled experiment, the edge is often unknown, and the "coin" may not even be biased in your favor, making bet sizing even more critical than asset selection.