The Fallacy of Averages

Consider the flipping of a fair coin. Over an infinite number of flips, you can expect a 50/50 split between heads and tails. However, in a limited number of flips, such as ten, the results can deviate significantly from this average. The fewer the flips, the more variability you may witness. This phenomenon is known as the Law of Large Numbers.

While we often assume this law applies broadly, it doesn’t hold true for individual outcomes. A large number of trials is needed for it to be relevant, and many real-life situations don't offer this luxury.

When an activity is not repeatable indefinitely, we must be cautious in expecting to achieve its average result.

Understanding Outcomes

Playing Russian Roulette multiple times yields vastly different results compared to the average outcome of multiple players each taking a single turn. For example, if six individuals play once, statistically, one will die while the remaining five win $6 million each. This yields a total payout of $30 million, or an average of $5 million per player.

However, if you choose to play six times consecutively, your expected outcome shifts. While the odds remain 1 in 6 for death, if you continue to play, your chances of survival plummet. The more you play, the more likely you are to face dire consequences.

The expected financial gains illustrated through repeated plays highlight the distinction between individual and group averages. The concept of ergodicity becomes relevant here; if the population outcome aligns with the time average outcome, the system is deemed ergodic. Otherwise, it is non-ergodic.

The Game Over Scenario

In the context of Russian Roulette, if you die, your ability to play ceases, rendering your future earnings zero. You can only continue to accumulate wealth if you remain alive. Situations that result in a "game over" nullify future gains and skew averages.

These scenarios are pervasive, manifesting in bankruptcies, injuries, mental health crises, and relationship breakdowns.

While you may think, “I’m cautious; why would I engage with Russian Roulette?” the reality is that many aspects of life mirror the mechanics of this game, where losses can overshadow future gains.

The Balance of Performance and Survival

In theory, success hinges on performance; however, in practice, survival trumps performance. The most successful employees are often those who manage to avoid burnout. This principle applies across various domains, including investment, business, and personal relationships.

Short-term consequences may seem negligible, but they can accumulate into significant long-term effects. For instance, while the immediate impact of smoking might be minor, its long-term consequences can be severe.

In repeated activities, the risk of irreversible events can absorb future gains. Therefore, it’s crucial to approach activities with caution. When exercising, for instance, prioritize safe practices over maxing out your weights, as one serious injury could sideline you for an extended period.

Instead of chasing maximum growth at all costs, focus on achieving sustainable growth while ensuring your well-being.

Making Informed Decisions

Acknowledging that irreversibility does not equate to avoiding risks is essential. Rather, it means recognizing the non-ergodic context and choosing risks that won't jeopardize your life if they backfire.

Understanding how ergodicity applies to decision-making can help you avoid irreversible blunders.

This video explores the concept of Russian Roulette in a gaming context, illustrating the risks and potential rewards of high-stakes decision-making.

Here, the focus shifts to a game where the stakes are so high that one loss means never playing again, emphasizing the importance of risk assessment in life choices.

Thank you, Foster CoWriting, for your collaboration in refining this piece.