Risk and Uncertainty

Evaluating probabilities, expected value, and making decisions under uncertainty.

Risk vs. Uncertainty

Risk: Outcomes are unknown, but probabilities are known or estimable.

• Example: Roulette. You know the odds.

Uncertainty: Outcomes and probabilities are unknown.

• Example: Will this startup succeed? Unknown and hard to estimate.

Most important decisions involve uncertainty, not pure risk.

Expected Value

The probability-weighted average of all possible outcomes.

EV = Σ (probability × outcome)

Example - Job offer:

• 60% chance the company thrives: +$50,000/year value
• 30% chance it stagnates: +$0 value
• 10% chance it fails and you're job hunting: -$30,000 value

EV = (0.60 × $50,000) + (0.30 × $0) + (0.10 × -$30,000)
   = $30,000 + $0 - $3,000
   = $27,000 positive expected value

When EV Thinking Breaks Down

1. You can't survive the downside

• A bet with +EV but 10% chance of bankruptcy might not be worth it
• You need to survive to play again

2. One-time decisions

• EV assumes many trials averaging out
• For single decisions, variance matters

3. Non-financial values

• Some outcomes can't be quantified
• Relationships, health, meaning

The Kelly Criterion

How much to bet when you have an edge.

Kelly % = (bp - q) / b

Where:
b = odds received on the bet (payout/stake)
p = probability of winning
q = probability of losing (1 - p)

Key insight: Even with a positive expected value, you shouldn't bet everything. Optimal bet size balances growth and survival.

Practical application: For major decisions, don't go all-in even when odds favor you. Maintain reserves.

Fat Tails and Black Swans

Normal Distribution (Thin Tails)

Most outcomes cluster around the average. Extreme events are extremely rare.

• Height
• Test scores

Fat Tail Distribution

Extreme events are more likely than normal distribution predicts.

• Stock market crashes
• Pandemics
• Startup success

Implications

In fat-tail domains:

• Don't underestimate extreme events
• Single events can dominate long-term outcomes
• Historical averages may be misleading
• Prepare for scenarios outside "normal"

The turkey problem: Every day confirms the turkey's belief that life is safe, until Thanksgiving.

Asymmetric Risk/Reward

Not all risks are created equal. Look for asymmetry.

Asymmetric Upside (Good)

Limited downside, unlimited upside.

Examples:

• Learning a new skill (time invested, potential lifetime returns)
• Starting a side business (limited capital at risk, potentially large gains)
• Asking someone out (momentary awkwardness vs. potential relationship)

Strategy: Take more of these.

Asymmetric Downside (Bad)

Limited upside, large or unlimited downside.

Examples:

• Driving drunk (minor convenience, potential death/prison)
• Ignoring chest pain (avoid hospital visit, potential heart attack)
• Insider trading (moderate gain, prison)

Strategy: Avoid these regardless of probability.

The Barbell Strategy

Combine extreme safety with extreme risk. Avoid the middle.

Example portfolio:

• 90% in ultra-safe assets (treasury bonds)
• 10% in high-risk/high-reward speculations

Why: You're protected from ruin while maintaining exposure to extreme upside.

Life application:

• Stable income + risky side projects
• Secure job + aggressive investments
• Safety in most areas, calculated risks in few

Dealing with Uncertainty

Scenario Planning

When you can't predict the future, plan for multiple scenarios.

1. Define 3-5 plausible scenarios
2. Determine what you'd do in each
3. Look for actions that work across scenarios
4. Create tripwires for when to shift strategies

Example - Career planning:

• Scenario A: Industry grows (invest in skills)
• Scenario B: Industry stagnates (diversify skills)
• Scenario C: Industry declines (prepare exit path)

Pre-Commitment

Decide in advance what you'll do under certain conditions.

Examples:

• "If the investment drops 20%, I sell."
• "If I don't have product-market fit in 18 months, I shut down."
• "If my net worth reaches X, I retire."

Why: Removes emotion from future decisions.

The Margin of Safety

Build buffers for things going wrong.

• Project takes 50% longer than estimated? Plan for it.
• Emergency costs 6 months of expenses? Have it saved.
• Key supplier fails? Have backup options.

Engineering principle: Design for loads greater than expected.

Probability Calibration

Most people are poorly calibrated. They say "90% confident" when they're right 70% of the time.

Improve Calibration

1. Track predictions - Write them down with probabilities
2. Review outcomes - Were you accurate?
3. Adjust - If you're overconfident, widen your ranges

Probability Vocabulary

Be precise about uncertainty:

The Outside View vs. Inside View

Inside View

Looking at the specific details of your situation.

• "This project is different because..."
• "Our team is especially capable..."
• "We've thought this through carefully..."

Outside View (Reference Class Forecasting)

Looking at what happened to similar situations.

• "What's the base rate for projects like this?"
• "What happened to others who tried this?"
• "How long do projects like this typically take?"

The outside view is usually more accurate. Use it to sanity-check your inside view.

Example:

• Inside view: "Our startup will succeed because we have a great team and product."
• Outside view: "90% of startups fail. What makes us different from the 90%?"

Decision Matrix for Risk

Practical Risk Checklist

Before a risky decision:

□ What's the worst realistic outcome?
□ Can I survive that outcome?
□ What's the probability of the worst outcome?
□ What's the expected value?
□ Is there asymmetric upside or downside?
□ What's the base rate for situations like this?
□ What margin of safety do I have?
□ What's my exit strategy if things go wrong?
□ Have I stress-tested my assumptions?
□ Am I being appropriately uncertain?

Key Takeaways

1. Expected value matters, but so does survival - Don't bet what you can't afford to lose
2. Seek asymmetric upside - Limited downside, unlimited upside
3. Respect fat tails - Extreme events are more common than we expect
4. Use the outside view - Base rates beat intuition
5. Build margins of safety - Things will go wrong
6. Calibrate your confidence - You're probably overconfident
7. Distinguish risk from uncertainty - They require different approaches