I've attempted a post in statistics/probability, but the people there don't seem to comprehend calculus and thus aren't able to formulate a solution. So this is a re-post, sleightly altered to fit the topic category.
I want to take a problem with discrete steps in it and refine those steps to a continuous set of points.
The set of discrete points is the outcomes of rolling 2d6, [2..12]. For any range in the set I can determine the probability of the result being within that range of outcomes. The reverse is also true: Given a probability I can determine the range of outcomes spanned.
But two dice is a very rough approximation of a bell curve; as the number of dice approaches infinity, the distribution of outcomes approaches the shape of a bell curve.
I'd like to express this transition from 2d6 to infinite-d6
I want to take a problem with discrete steps in it and refine those steps to a continuous set of points.
The set of discrete points is the outcomes of rolling 2d6, [2..12]. For any range in the set I can determine the probability of the result being within that range of outcomes. The reverse is also true: Given a probability I can determine the range of outcomes spanned.
But two dice is a very rough approximation of a bell curve; as the number of dice approaches infinity, the distribution of outcomes approaches the shape of a bell curve.
I'd like to express this transition from 2d6 to infinite-d6
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