A lottery as a random variable

Before deciding it is worth modelling: a lottery is nothing but a random variable to which winnings are attached.

Remark — A lottery is a random variable with winnings

A single-player random game (or lottery) is a situation in which the player chooses an action and the outcome depends on chance. Formally: a random variable $X$ with outcomes $e_1,\ldots,e_n$ of probability $p_i=P(e_i)$ and winnings (positive or negative) $v_i$. The expected value $\bar V = \sum p_i v_i$ is the main decision parameter: “on average how much do I win”.

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Topics: Probability
Concepts: Lottery · Expected value · Random variable
Methods: Expected value
Skills: Probability calculation · Modelling