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.
- Lotteries are probability distributions over outcomes.
- Mixed strategies therefore create lotteries.
- 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.
- 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.