The question sounds almost philosophical, but it carries real mathematical teeth: do you actually want to maximize your probability of becoming a billionaire? In a recent Elm Wealth research note titled "Do You Really Want to Be a Billionaire?"1, Victor Haghani, James White, and Jeffrey Rosenbluth dismantle one of finance's most persistent fantasies with rigorous precision, arriving at a conclusion that should reframe how advisors and investors think about objective-setting altogether.
A Question Worth Asking
The setup is disarmingly simple. A young professional saves $2 million over a career, has 50 years to deploy it, and wants to reach $1 billion. Haghani, White, and Rosenbluth model this as 50 flips of a coin with a 60% chance of heads, where the investor bets any fraction of wealth on each flip. What is the optimal strategy? The answer, solved by UC Berkeley professor Leo Breiman in 1961, is both illuminating and sobering.
The team finds that "with the optimal strategy, Billy can achieve a 7% chance of becoming a billionaire." Against the baseline rate of roughly 0.05% for someone who has already managed to save $2 million, that 7% figure sounds compelling. It is the catch that changes everything.
The Catch Is the Point
The strategy that maximizes the probability of reaching $1 billion requires something most investors would find intolerable if they understood it fully. Haghani, White, and Rosenbluth are unsparing: "the strategy that maximizes his odds of hitting $1 billion requires him to routinely bet 100% of his wealth," which "means he'll routinely go broke." Every path that falls short of a billion ends in complete ruin. There is no middle ground, no modest consolation prize. As the team states plainly, "there's no soft landing; there's no 'I'm almost a billionaire.'"
The average bet size across all paths works out to approximately 68% of wealth, with the strategy often requiring a 100% wager on a single 60/40 coin flip. What makes this especially counterintuitive is its insensitivity to the actual odds. The team notes that "the strategy doesn't change even if the odds get much worse." Replace the 60% coin with a 51% coin, follow the identical betting pattern, and the billionaire probability collapses to 0.3%, with a 99.7% chance of total loss. The strategy is not calibrated to expected outcomes. It is calibrated entirely to hitting a single threshold, which means it ignores virtually everything else.
The Utility Argument
The deeper issue is conceptual. Maximizing the probability of hitting an arbitrary target and maximizing expected welfare are fundamentally different objectives, and the team is direct about which one deserves to win. Haghani, White, and Rosenbluth observe that "while Billy's expected wealth under the probability-optimal strategy is $70 million (the 7% chance of $1 billion plus 93% of $0), his expected utility of this billionaire-or-bust strategy is effectively negative infinity." The utility of bankruptcy, repeated 93% of the time, overwhelms even the genuine upside of a billion dollars.
The better approach is straightforward in principle. A "constant and reasonable fraction of his wealth on each flip, say 10% to 20%," produces "a certainty-equivalent wealth roughly 1.7x what he started with" for a typical degree of risk aversion. That may sound modest against the dream of a billion, but it is vastly superior on every reasonable welfare measure. The team's point is not that wealth-building is unimportant, but that the objective function chosen determines everything that follows. As they put it: "if you choose a flawed objective, you'll wind up with a flawed investment strategy."
What About Apple?
The team addresses the inevitable counterargument directly. Roughly 100 stocks out of approximately 30,000 listed in the U.S. over the past century have returned 500 times or more. But those represent just 0.3% of all listings. Haghani, White, and Rosenbluth argue that even on those terms, the coin-flip framework gives Billy a better shot at his target than stock-picking does: the optimal coin strategy yields 7%, while selecting a single 500-bagger from 30,000 companies implies far lower odds. And leverage, the obvious bridge, "would create a huge downward skew in the return distribution," not solve it.
The Objective Function Is Everything
To be clear, the team is not arguing against ambitious wealth accumulation. The argument is sharper than that: "the objective function you choose determines everything about the strategy that follows." Garbage objectives produce garbage strategies. "If you choose 'maximize my probability of becoming a billionaire,' you'll end up going broke most of the time. If you choose 'maximize my expected welfare,' you'll end up, naturally, with the highest expected welfare."
This is a discipline most investment frameworks accept in theory and abandon in practice whenever clients attach to a number.
Five Key Takeaways for Advisors
1 Arbitrary wealth targets are not investment objectives. A number like $1 billion (or $10 million, or any threshold) is not a welfare-maximizing goal. It is a threshold that, when pursued directly, distorts strategy in ways that consistently destroy value for the vast majority of paths.
2 The strategy that maximizes hitting a target is usually not the strategy that maximizes wellbeing. Probability-optimization and expected-utility optimization point to different portfolios. Advisors should be explicit with clients about which objective they are actually pursuing.
3 Risk tolerance and ruin are connected more tightly than most clients appreciate. Betting 68% of wealth on average, often rising to 100%, is not a risk tolerance; it is a recipe for bankruptcy. The coin-flip model makes the mechanics viscerally clear.
4 Return distributions are highly sensitive to leverage and concentration. Reaching a 500x target through leverage or single-stock concentration creates severe negative skew in the return distribution. Better expected-utility outcomes come from disciplined, consistent, moderate risk exposure applied over time.
5 The framework generalizes beyond billionaires. The core insight applies to any client who has attached to a round number or arbitrary milestone as the definition of success. The advisor's role is to surface the implied strategy that objective demands, and to ask whether the client actually wants to live with it.
Footnote:
1 Haghani, Victor, James White, and Jeffrey Rosenbluth. "Do You Really Want to Be a Billionaire?" Elm Wealth, 1 Sept. 2026.
