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Behavioral Mathematics for Game AI by Dave Mark

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Sigmoid Functions

One of the more useful, and therefore oft-used, functions is the sigmoid function. Specifically, the name sigmoid refers to a function with an “s-curve.” Therefore, sigmoid functions are actually an entire family of curves. We will examine some of the more common ones below.

The Logistic Function

The most common of these is the logistic function. It pops up in a variety of applications ranging from biology, economics, probability, statistics, and (strikingly relevant to us) the mathematics of behavioral psychology.

The formula ...

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