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Behavioral Mathematics for Game AI by Dave Mark

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Poisson Distributions

Another useful, if slightly more esoteric, probability curve is the Poisson distribution. Siméon-Denis Poisson originally developed it in 1838 as a way of expressing the probability of events happening over time. Accordingly, we can use it in game AI to generate events that occur at average intervals but without resorting to predictable time periods. On the other hand, we are not limited to using the Poisson distribution in connection with time-based events. We can benefit from using the unique properties of the Poisson distribution in other areas as well.

The formula for a Poisson distribution is:

The values in the equation ...

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