Post originally by Trevor Barrie at 2004-10-19 13:59:52
Converted from Phorums BB System

NPC Brown Cow wrote:
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That 50-50 chance is if you only look at the cumulative frequency of the distribution, it ignores standard deviation and assumes that one roll influences the next, which is not the case.
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What are you talking about? The only assumption required is that a d6 roll has six equally likely results. (Obviously, real physical dice aren't going to be mathematically perfect, but whatever biases exist are unlikely to be both major and systemic.)

Yes, I'm ignoring standard deviation. I'm also ignoring the quadratic formula, the pigeonhole principle, the predicate calculus, and any number of other mathematical terms that have absolutely nothing to do with the question at hand. Calculating probabilities for dice is a simple counting problem. It's true that the results for large numbers of dice approximate a normal distribution, meaning that you can use standard deviations to approximate the probabilities, but doing this for only three dice is just silly. With that few dice, not only is the approximation going to be fairly crude, approximating isn't even particularly easier than calculating the exact probabilities.

Finally, not that a normal distribution is symmetric about the mean. If you're using a normal distribution to simulate 3D6, you've already implicitly conceded that the probability of rolling 10 or less is 50%.