# Ergodic Hypothesis The average outcome across many people isn't the same as the average outcome for one person over time. In non-ergodic systems - which includes most things that compound - the typical individual experience is far worse than the average suggests. --- ## The distinction A system is ergodic if the time average (what happens to one entity over time) equals the ensemble average (the average across many entities at one moment). Flipping a fair coin is ergodic. Compound returns are not. **The casino example.** Imagine a game: 50% chance to win 50% of your wealth, 50% chance to lose 40%. The expected value is positive (+5% per round). Across 100 players at once, the average wealth grows. But follow one player through 100 rounds. Each round multiplies wealth by either 1.5 or 0.6. Over time, the typical player's wealth approaches zero, even though the "average" across hypothetical parallel universes is rising. **Time average vs expected value.** Expected value calculations assume you can somehow experience all possible outcomes simultaneously. In reality, you experience one path through time. For multiplicative dynamics, the geometric mean (time average) is the relevant measure, not the arithmetic mean. --- The distinction cuts through several related essays. [[Paying for growth]] asks when growth creates value versus consumes capital. The ergodic lens sharpens this: a growth strategy with positive expected returns can still destroy a specific business if the path involves periods of negative cash flow severe enough to threaten survival. The ensemble of all companies trying this strategy may "win on average" while most individual companies fail. [[Cash and profit]] is fundamentally about this gap. Accounting profit is an ensemble concept - it tells you what the average period looks like. Cash is a time-series reality - it tells you whether you survive the path. A business can be profitable on average and still run out of cash, because you can't spend ensemble averages. The serial acquirer studies reinforce the point. [[Constellation]] and [[Lifco]] compound precisely because they never bet the company on a single acquisition. Each deal is sized so that failure is survivable. [[Danaher]] runs the same logic at the operating level. They size bets to ensure the path through time doesn't include ruin, regardless of expected returns.