Expected Value: Decision-Making Under Uncertainty
Probability theory and economics, formalized by Blaise Pascal and Pierre de Fermat · Various, including von Neumann and Morgenstern's Theory of Games (1944)
Expected value is the sum of all possible outcomes of a decision, each weighted by its probability. It provides a rational framework for choosing between uncertain prospects, guiding decisions toward the option with the highest long-term payoff.
Core Concepts
The Problem
How can one make consistent, optimal decisions when outcomes are uncertain and intuition is unreliable?
The Claim
By calculating the expected value of each alternative, you can objectively compare options and systematically improve decision quality over time, even though any single outcome may be bad or good.
Key Evidence
- •Mathematical proof from probability theory
- •Pervasive application in finance, insurance, and game theory
- •Empirical studies show that decision makers trained in EV improve long-term results
Practical Implication
A process based on expected value reduces the emotional sting of individual losses and prevents overreaction to short-term results. It encourages a focus on the quality of the decision process rather than outcome, fostering a growth mindset and better risk management.
Nuance & Limits
Expected value requires accurate probability estimates, which may be difficult in novel or complex situations. Additionally, diminishing marginal utility of money and risk aversion mean that raw dollar EV may not capture true subjective preferences (see expected utility theory).
Source Material
Videos
Duke explains how poker players use expected value to make decisions.
Citation Density
Extremely high – foundational concept in economics, statistics, and decision science
Related Ideas
Sunk costs should not influence future decisions because they are not part of expected value calculations.
Practical application of probability to exploit mispriced odds.
Gaps
- ⚠ Psychological barriers to using EV: overconfidence in probability estimates
- ⚠ Ethical considerations when using EV in life-or-death or highly personal decisions
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