Expected Value
Expected value is the weighted average of all possible outcomes, where each outcome is multiplied by its probability. It's the core tool of Probabilistic Thinking for comparing decisions under uncertainty.
How It Works
If a bet has a 50% chance of winning $100 and a 50% chance of losing $40, the expected value is (0.5 × $100) + (0.5 × −$40) = $30. Even though you might lose on any single try, repeatedly taking bets with positive expected value is how you win over time.
Why It Matters
Expected value forces you to weigh both the probability and the magnitude of outcomes — not just whether something "could" happen. A low-probability event with catastrophic consequences can have a large negative expected value, which is exactly why Margin of Safety matters: you're protecting against the tail of the distribution.
Connections
Warren Buffett and Charlie Munger think in expected value constantly. Buffett looks for investments where the expected value is overwhelmingly positive — situations where the downside is limited and the upside is large. This is Probabilistic Thinking applied to capital allocation.
Base Rates provide the starting probabilities you need before you can calculate expected value. Without a realistic sense of how often outcomes occur, your expected value calculations are built on sand.