Post originally by NPC Brown Cow at 2004-10-13 06:44:11
Converted from Phorums BB System

Trevor Barrie wrote:
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I don't understand your comment about dice in the "Success Rolls" section. The expected result of a 3D6 roll is 10.5. A roll where you succeed on a 10 or less represents a 50-50 chance. This is basic arithmetic; how much room for debate could there be?
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Apparently, quite a bit.

There is nothing "basic" about it.

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.

Standard deviation for 3d6 is 2.96, I'm going to round it to 3 to make things easier for the example.

For any one roll, as one roll doesn't effect the roll that came before or after it, there is a ~68%* of the dice coming up in the first standard deviation, a range from 7.5 to 13.5.

There is a ~95%* chance that our single roll will fall some where in the second deviation, 4.5 to 16.5

The third standard deviation encompasses ~99%* of the rolls.

So all we can say about any roll is that it has a 68% chance to roll between 8 and 14 or a 95% chance to roll between 5 and 17.


*These are approximate numbers, I don't have access to my statistics books right now or I'd look up the actual numbers. Sorry if that's a problem.