Ergodicity: Why One Bad Decision Can Outweigh a Thousand Good Ones

Ergodicity: Why One Bad Decision Can Outweigh a Thousand Good Ones

The Core Idea

In 1738, mathematician Daniel Bernoulli solved a puzzle that would take nearly 300 years to fully understand: why do humans consistently reject gambles with positive expected value? The answer lies in a concept called ergodicity - and understanding it transforms how you think about career decisions, risk-taking, and building a meaningful life.

Ergodicity describes whether ensemble averages (across many people or outcomes) equal time averages (for a single individual over time). When outcomes are non-ergodic, what works for the group doesn’t necessarily work for you. One catastrophic loss can eliminate you from the game entirely, making all future opportunities irrelevant.

For technical leaders navigating career choices, startup opportunities, and life decisions, ergodicity offers profound wisdom: survival is the most important strategy. You must remain in the game to benefit from positive expected value over time.

The St. Petersburg Paradox

Consider a coin-flip game:

The expected value is infinite - on average, you win unlimited money. Mathematically, you should pay any finite amount to play this game. Yet no rational person would pay even $1,000 to play once.

Why? Because while the ensemble average (across infinite players) is infinite, your time average (your single attempt) is almost certainly a small amount. And if you bet your life savings, one bad outcome ends the game for you permanently.

This is non-ergodicity: you can’t experience all possible outcomes over time because ruin eliminates future opportunities.

Ergodicity in Career and Life

Career Example: The Startup Gamble

Imagine two paths:

  1. Path A: Join stable tech company, $200K salary, steady growth
  2. Path B: Join early startup, $120K + equity potentially worth millions or zero

Expected value calculation might favor the startup (1% chance of $10M = $100K expected value plus salary). Across 100 engineers taking such bets, the ensemble does well - a few strike it rich.

But you’re not 100 engineers. You’re one person with one career, one family, one set of financial obligations.

Ergodic considerations:

If failure means bankruptcy, career damage, or family crisis, the positive expected value is misleading. You’ve left the game before you can benefit from the ensemble average.

Non-ergodic thinking: Optimize for staying in the game, not maximizing single-bet expected value.

Technical Debt: The Irreversibility Trap

Consider architectural decisions:

Expected value analysis treats both equally based on probability-weighted outcomes. But ergodicity reveals asymmetry: reversible mistakes are learning opportunities; irreversible mistakes compound over years.

Jeff Bezos calls these “one-way doors” vs. “two-way doors.” One-way doors (non-ergodic) deserve extreme scrutiny because they eliminate future option value. Two-way doors (ergodic) reward experimentation because you can always return.

The Ruin Problem in Personal Finance

Why do financial advisors recommend diversification even when concentrated bets have higher expected returns?

Consider two strategies over 30 years:

  1. Diversified: 8% annual return, low volatility
  2. Concentrated: 20% average return, but 30% chance of -50% year

Mathematically, strategy 2 has higher expected terminal wealth. But it’s non-ergodic: one catastrophic year early on creates a hole so deep that even great future returns can’t recover your original position.

Time amplifies this: with strategy 1, each year compounds on your prior wealth. With strategy 2, you’re rolling dice where ruin becomes increasingly likely over time. You experience your time series, not the ensemble average across parallel universes.

The Mathematics of Staying Alive

Ole Peters, the physicist who revitalized ergodicity economics, offers a simple formula:

Time-average growth rate = Ensemble-average growth rate - (Variance / 2)

Key insight: variance kills time-average returns. High volatility strategies with great ensemble averages deliver terrible time-average outcomes because occasional losses compound negatively.

Practical implication: For decisions you’ll experience sequentially (career, investments, relationships), minimize irreversible downside even at the cost of upside. For decisions you can parallelize or retry cheaply, maximize expected value.

Applying Ergodic Thinking

Principle 1: Identify Irreversible Decisions

Irreversible (non-ergodic):

Reversible (ergodic):

Rule: Maximize optionality on irreversible decisions. Move fast on reversible ones.

Principle 2: Optimize for Survival, Not Expected Value

Ask not “What’s the expected outcome?” but “What happens if I’m wrong?”

Career decision framework:

  1. What’s the worst plausible outcome?
  2. Does worst outcome eliminate future opportunities?
  3. Can I make multiple attempts?
  4. If yes to #3: Optimize for expected value
  5. If no to #3: Optimize for survival + upside optionality

Example: Joining a promising startup vs. established company

Principle 3: Create Parallel Opportunities

Transform non-ergodic situations into ergodic ones through parallelization:

Non-ergodic: Quit job, bet everything on single startup idea Ergodic: Keep job, prototype on weekends, validate before committing

Non-ergodic: Rewrite entire system in new architecture Ergodic: Strangler fig pattern, gradually migrate, maintain rollback capability

Non-ergodic: Invest savings in single stock Ergodic: Dollar-cost average into diversified portfolio over time

Parallelization lets you experience ensemble averages across your own attempts rather than as one sample in someone else’s ensemble.

Principle 4: Build Absorbing Buffers

Increase your ability to survive negative outcomes:

These buffers convert potentially terminal outcomes into setbacks you can recover from, keeping you in the game long enough to benefit from positive expected value.

Principle 5: Distinguish Ensemble from Time Series

When reading success stories, ask: “Am I seeing ensemble averages or time averages?”

“The average startup founder is a millionaire” - This is an ensemble average across all founders. Your time series might be: failed startup → financial stress → career setback.

“Aggressive investing outperforms” - Ensemble average across many portfolios. Your time series with poor timing: -40% crash → forced selling → locked in losses → missed recovery.

“Technical risk-taking leads to innovation” - Ensemble across companies. Your time series: bet on wrong technology → system rewrite → delayed features → customer churn.

View success stories as ensemble outcomes. Plan your decisions as time series you must survive.

Reflection Questions

  1. What irreversible decisions am I facing? How can I increase optionality before committing?

  2. Where am I optimizing for expected value when I should optimize for survival? What’s my personal “ruin threshold”?

  3. Which risky situations can I make ergodic through parallelization or small repeated bets?

  4. What buffers do I need to survive negative outcomes in my key life domains? (Financial, career, relationships, health)

  5. Am I mistaking ensemble averages (other people’s outcomes) for my expected time series?

  6. What one-way doors am I approaching that deserve extreme scrutiny? What two-way doors am I over-thinking?

Living with Ergodicity

Understanding ergodicity doesn’t mean avoiding risk - it means understanding which risks are survivable and which are terminal.

Take enormous reversible risks: try new technologies, experiment with processes, test bold ideas, have difficult conversations. These build antifragility.

Take extreme care with irreversible risks: choosing co-founders, major career pivots, architectural commitments, financial leverage. These determine whether you stay in the game.

The paradox: True long-term risk-taking requires short-term risk management. You can only benefit from positive expected value if you survive long enough to experience it.

Your life is not an ensemble average across parallel universes. It’s a single path through time. One catastrophic outcome you can’t recover from ends the game. Optimize for staying alive, building buffers, maintaining optionality, and making enough survivable bets that time-average outcomes favor you.

The goal isn’t to avoid all risk - it’s to take only risks where you can afford to be wrong, learn, and play again tomorrow.

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