Thinking in Probabilities

Steve
Mar 31, 2023
3 min read

Updated: Jun 7

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. -Samuel S. Wilks

In investing, as in life, we don’t deal in certainties. We navigate a fog of incomplete information, where outcomes are unknowable and decisions must be made under uncertainty.

Thinking in probabilities, then, isn't option—it’s a survival strategy. It's the foundation of sound investing and economic reasoning.

The goal isn’t to predict a single outcome, but to build robust processes that perform across a range of potential futures—shaped by the existence of tail risks, black swans, and non-linear payoffs.

Process Over Outcome

There’s a common misconception that good decisions are defined by good outcomes. But we know better.

A poor decision can still yield a good outcome due to luck; a good decision can yield a bad one due to variance.

The correct lens, at least in large part, is expected value (EV): the probability-weighted average of all potential outcomes. Over enough trials, outcomes converge toward the EV. This framework is used by many; from traders to poker players, but even then, the path matters.

Consider this example:

Flip a coin. Heads, you double your net worth. Tails, you lose everything.

EV is zero - but the downside is fatal. You’ve taken on ruin risk—a violation of the first principle of compounding: don’t get knocked out of the game.

Ergodicity and Why the Casino Isn’t Gambling

Many ask: “Isn’t investing a gamble?”It’s a fair question, but it misunderstands the distinction between uncertainty and edge.

Yes, outcomes are uncertain. But when the process is sound, when you have an edge, when your downside is capped and upside is scalable, you’re not gambling—you’re operating a strategy.

The casino doesn’t win every spin of the roulette wheel. It wins over time. That’s ergodicity in action:

Time averages diverge from ensemble averages if ruin is possible.

A gambler might win in the short term, but ruin looms if they repeat the same high-risk bet. The casino, in contrast, operates a system where outcomes average out favorably over time.

Survival > Brilliance (It's a Loser's Game)

Nassim Taleb coined the phrase “alternative histories” in Fooled by Randomness: each observed outcome is just one path among many. Howard Marks reiterates this: we can only observe one reality, but many others could have unfolded.

So what matters is not just expected value, but distribution shape and survivability.

"Don’t be the six-foot man who drowned in the river that was five feet deep on average."

This is where the Kelly criterion becomes relevant:

Bet the fraction of capital that maximizes long-term growth, while avoiding the risk of ruin.

Kelly implicitly balances risk and reward, optimizing for compound growth, not just win rate. But crucially, it assumes ergodic conditions—that outcomes average out over time, and capital isn't wiped out along the way.

In real-world investing, especially in VC and high-risk assets, ergodicity often fails. The left tail isn’t just unpleasant—it’s terminal.

Asymmetry Is the Game

This leads us to one of the most powerful mental models in investing:

Heads I win, tails I don’t lose much. — Mohnish Pabrai

We seek asymmetric bets—where the upside is multiples of the downside. This is true in public markets, but especially so in venture capital.

Most startups fail. The EV of the portfolio hinges on a handful of outliers. A 10x winner can offset many zeros—but only if the fund survives long enough to capture it.

That’s why capital allocation, position sizing, and timing of follow-ons are not tactical choices—they are strategic imperatives.

Reflexivity (Briefly)

In certain domains, expectations shape outcomes. This is the realm of reflexivity, as described by George Soros.

Markets don’t merely reflect reality—they help construct it. Investor beliefs affect funding, which affects runway, which affects product, which loops back into valuation.

Recognizing this feedback loop doesn’t negate probability—it sharpens your understanding of it.