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clickbait: 'Trying to assign value to an uncertain state? The weighted average of outcomes is probably the tool you need.',
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text: 'The expected value of an action is the [-mean] numerical outcome of the possible results weighted by their [-1rf]. It may actually be impossible to get the expected value, for example, if a coin toss decides between you getting \\$0 and \\$10, then we say you get "\\$5 in expectation" even though there is no way for you to get \\$5.\n\nThe expectation of V (often shortened to "the expected V") is how much V you expect to get on average. For example, the expectation of a payoff, or an expected payoff, is how much money you will get on average; the expectation of the duration of a speech, or an expected duration, is how long the speech will last "on average."\n\nSuppose V has discrete possible values, say $V = x_{1},$ or $V = x_{2}, ..., $ or $V = x_{k}$. Let $P(x_{i})$ refer to the probability that $V = x_{i}$. Then the expectation of V is given by:\n\n$$\\sum_{i=1}^{k}x_{i}P(x_{i})$$\n\nSuppose V has continuous possible values, x. For instance, let $x \\in \\mathbb{R}$. Let $P(x)$ be the continuous probability distribution, or $\\lim_{dx \\to 0}$ of the probability that $x<V<(x+dx)$ divided by $dx$. Then the expectation of V is given by:\n\n$$\\int_{-∞}^{∞}xP(x)dx$$\n\n## Importance ##\n\nA common principle of reasoning under uncertainty is that if you are trying to achieve a good G, you should choose the act that maximizes the expectation of G.',
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