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Math · Intermediate

Decisions Under Uncertainty

How should you choose when outcomes are uncertain? Start with expected value, see how the St. Petersburg paradox exposed its limits, discover utility and why insurance can be rational, find the betting fraction that grows wealth fastest, learn the famous 37% rule for knowing when to stop searching, work out what a forecast is worth, and balance exploring against exploiting.

7 lessons~35 min0/7 complete
Start courseHelpful background: Probability
1

Expected Value and Its Limits

Averages, paradoxes and utility.

  1. Expected ValueThe long-run average
  2. The St. Petersburg ParadoxAn infinitely valuable game?
  3. Utility & RiskWhy insurance makes sense
2

Strategies

Betting and stopping.

  1. The Kelly CriterionHow much to bet
  2. When to Stop LookingThe 37% rule
3

Information and Learning

What knowledge is worth, and how to gather it.

  1. The Value of InformationHow much is a forecast worth?
  2. Explore or Exploit?Learning while you choose