When a trade blows up disastrously, we tend to start with a question: What did the trader get wrong about the investment itself? Shouldn’t it have been obvious that demand for a com­pany’s product was falling? Or, wasn’t it apparent that the recent trend in interest rates couldn’t hold forever? The same holds true when things go spectacularly right—everyone looks for evidence of savvy and perception. We’re inundated with articles about how the investor saw the potential in a business Wall Street had written off or spotted a danger everyone else had minimized.

Rarely does anyone write a profile about the brilliant money manager who consistently gets the size of their investments right. Yet the decision of how much to wager is at least as critical as deciding what to invest in. If you have a knack for picking strong investments but tend to bet too much on them, a few unlucky breaks can wipe out your assets and knock you out of the game. We both have learned this lesson through a tough experience. One of us—Victor—was a founding partner in Long-Term Capital Management, the large hedge fund that suddenly lost more than 90% of its money in 1998. Fearing a disorderly unwind and contagion, the New York Federal Reserve convinced banks that LTCM traded with to put in $3.6 billion and take over the fund. The LTCM experience prompted multiple books and numerous articles about how the fund’s investment ideas went badly wrong. But less has been written about the sizing of those trades—or an approach to sizing that would have led to a happier outcome.

Ironically, the sizing decision should be easier to get right than the investment selection decision. You’re not competing against others in making sizing choices. Your good decision doesn’t require someone else to make a bad one. In contrast, active investment selection is zero-sum. For every buyer who was right, there’s a seller who was wrong, and vice versa, making uncovering ­superior investments the most competitive sport on the planet.

But thoughtful decision-making about sizing doesn’t usually come naturally. And it doesn’t help that most people receive little, if any, formal training on the topic in the classroom or on the job. Many young, highly paid financial professionals struggle to grasp intuitively the importance of sizing. When we’re starting our careers, our human capital is high—there are many more paychecks and gainful employment opportunities ahead—and our financial capital is relatively low. As a result, we don’t often face consequential investment-­sizing decisions in our personal lives until middle age, when we have more wealth at risk and less time to make up losses.

Simple trading games can reveal how much people struggle with investment sizing. You may want to test your skills by playing two such games: the Coin Flip and Crystal Ball Trading challenges, which you can find at elmwealth.com/sizing-games. We bankrolled about 200 financially sophisticated subjects with $25 to $50 to play these. Each game gave players an ­advantage—for example, a coin to bet on that they knew had a higher probability of coming up heads—and allowed them to decide how much to wager on a series of bets. Even with a built-in edge, about 25% of the players went bust in both games. It’s an understatement to say their performance was underwhelming.

And then there’s the real-world artifact of the “missing billionaires,” the jumping-off point of our recent book and shorthand for affluent families’ inability to maintain their relative wealth in the incredibly rewarding investment environment of the past 125 years, which delivered returns far in excess of growth in real per-capita income.

Sizing decisions help explain why wealth is hard to maintain. Assume you can bet on a coin that you know has a 60% chance of landing heads, a commonly used thought experiment for discussing decision-­making under uncertainty. Let’s say you’re retired with savings of $5 million, and you’re given the opportunity to place 25 consecutive bets on this biased coin. What would you do?

One path might be to find the betting strategy that maximizes the expected value of your wealth. Mathematically the strategy is simple–just bet 100% of your wealth on each flip. By the end of 25 flips you have a 99.9997% chance of losing all your wealth, but you’d also have a 0.0003% chance of expanding your wealth about 33 million-fold. Expected value is the average of possible payouts weighted by the probability of each one occurring, and the absurdly rare but absurdly large positive payout is enough to bring that average to $500 million. Few would choose this strategy: You’d be all but guaranteed to lose all your wealth. (FTX co-founder Sam Bankman-Fried has favored this approach, and we all know how that turned out.)

Bell Labs mathematician John Kelly popularized another strategy, which maximizes the expected growth rate of your wealth over the long run. Apply the Kelly criterion to our coin bet—all you need to know is the probability of heads and the payout ratio of a winning bet, which in this case is $1-to