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@jemoka / Jemoka Knowledge Base / raw/concept/kbhlottery.md
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--- title: "lottery" source: https://www.jemoka.com/posts/kbhlottery/ --- A lottery is a choice problem, where each outcome has a certain probability: \begin{equation} [S_1:p_1, \dots, S_{n}:p_{n}] \end{equation} where, \(S_{j}\) has \(p_{j}\) chance of occurring. utility of a lottery For a lottery, the utility thereof is the probability of a state happening times the utility of the state: that is, \begin{equation} U([S_1:p_1, \dots, S_{n}:p_{n}]) = \sum_{i=1}^{N} p_{i}U(S_{i})} \end{equation}