This lecture discusses game theoretical lotteries. If you are interested in the strategy behind gambling lotteries, see this blog post on the game theory of Powerball.

Takeaway Points

  1. Lotteries are probability distributions over outcomes.
  2. Mixed strategies therefore create lotteries.
  3. While assigning progressively larger numbers to progressively more preferred outcomes preserves the preference ordering, the specific numbers you assign matter when considering preferences over lotteries.
  4. As a result, completeness and transitivity are insufficient to define expected utilities. Expected utilities must also handle preferences over lotteries. The next two axioms address this.

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