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Answer by valadil for Understanding "randomness"

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Here's a simple answer. Consider Monopoly. You roll two six sided dice (or 2d6 for those of you who prefer gaming notation) and take their sum. The most common result is 7 because there are 6 possible ways you can roll a 7 (1,6 2,5 3,4 4,3 5,2 and 6,1). Whereas a 2 can only be rolled on 1,1. It's easy to see that rolling 2d6 is different than rolling 1d12, even if the range is the same (ignoring that you can get a 1 on a 1d12, the point remains the same). Multiplying your results instead of adding them is going to skew them in a similar fashion, with most of your results coming up in the middle of the range. If you're trying to reduce outliers, this is a good method, but it won't help making an even distribution.

(And oddly enough it will increase low rolls as well. Assuming your randomness starts at 0, you'll see a spike at 0 because it will turn whatever the other roll is into a 0. Consider two random numbers between 0 and 1 (inclusive) and multiplying. If either result is a 0, the whole thing becomes a 0 no matter the other result. The only way to get a 1 out of it is for both rolls to be a 1. In practice this probably wouldn't matter but it makes for a weird graph.)


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