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Expected Value

Decide based on probability-weighted outcomes, not possibilities.

Explanation

Expected value is a way to evaluate decisions by considering both the potential outcomes and how likely they are to happen. You calculate it by multiplying the probability of each outcome by its value, then adding them all up. This helps you avoid being swayed by either extremely unlikely positive outcomes (like winning the lottery) or extremely unlikely negative ones.

Real-World Example

Startup offer: 10% chance of $10M exit = EV of $1M. Steady job: 90% chance of $200k/year × 5 years = EV of $900k. Lottery ticket: 0.00001% chance of $100M = EV of $10 (but costs $20 = negative EV). Insurance: Small certain loss to avoid large unlikely loss = negative EV but worth it if loss would ruin you.

How to Apply

List all outcomes. Assign probabilities (must sum to 100%). Multiply probability × value. Sum everything. If positive, and you can repeat = do it. If negative = avoid unless protecting against ruin. Remember: EV only works with many repetitions or if you can survive the worst case.

Related Topics

probabilityriskmath

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