---
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}
