Adjust raw expected value for risk aversion on large stakes
A 50% chance of losing everything is not equivalent to a certain 50% loss — adjust for your actual risk tolerance.
Why it works
Raw expected monetary value ignores diminishing marginal utility: the pain of losing $10,000 is not just ten times the pain of losing $1,000; it can be much larger if the loss would meaningfully damage your situation. Utility theory formalizes this: for large stakes, convert monetary values to utility before computing EV. Practically, this means being willing to pay a premium to reduce variance when the downside would be catastrophic.
How to do it
- For each scenario, ask: "If this outcome happened, how would it actually affect my life relative to my current position?"
- Downscale the subjective value of outcomes that would be genuinely catastrophic beyond what the dollar amount suggests.
- Be willing to accept lower raw EV in exchange for a variance reduction that protects against ruin.
- Use the Kelly criterion or similar tools for decisions where ruin is a real scenario (gambling, highly concentrated investments).
Evidence
Expected utility theory (von Neumann & Morgenstern) and its successors (prospect theory, Kahneman & Tversky) establish that people’s subjective response to outcomes is non-linear, justifying risk adjustment beyond raw EV in high-stakes decisions. (observational)
Prospect theory describes how people do behave, not necessarily how they should; normative risk adjustment requires honest assessment of personal utility, which is hard.
Sources
- Kahneman & Tversky (1979), prospect theory: an analysis of decision under risk, Econometrica
Common mistake
Applying risk adjustment to small-stakes decisions (avoiding a coin-flip for $20) where expected value alone should dominate, while under-applying it to genuinely catastrophic scenarios.
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More practices for Expected Value Thinking: Deciding Under Uncertainty
- Enumerate scenarios and their probabilities before deciding
Write down each meaningful outcome, assign a probability, and compute the weighted total.
- Judge decisions by the process, not the result
A good decision that produces a bad outcome is still a good decision.
- Calculate the expected value of gathering more information
Before researching further, ask whether the additional information is actually worth the cost to obtain.
- Accept positive-EV decisions even when they feel uncomfortable
If the expected value is clearly positive, take the decision — even if most individual outcomes are losses.
- Look for decisions with asymmetric upside — large potential gain, small defined loss
Seek situations where the worst case is bounded and small while the best case is large and open-ended.
- Keep a decision journal to score your EV estimates
Log your probability estimates and payoff predictions, then compare them to what happened.
Related concepts
- Bayesian Thinking: How to Update Beliefs Rationally
Holding beliefs as probabilities and updating them when evidence arrives
- Thinking, Fast and Slow, Made Usable
Two systems, the biases they create, and when to slow down
- Mental Models: Charlie Munger’s Latticework Approach
Building the multi-disciplinary toolkit that lets you see what single-discipline thinkers miss
- Opportunity Cost Thinking: What You Give Up When You Choose
The hidden price of every choice — and the practices that make it visible