"Unexpected results" Topic

I know when the results of rolling two D6 is a bell curve. Was looking for a 2 through 18 result and thought about using a D6 and a D12. At first I thought the results would favor the lower scores, brought down by the D6. However when charting the result it turned out to be a bell curve with a flat top, a plateau.

2D6 produces a triangular distribution, not a bell curve. It may be considered as a very crude approximation to a bell curve but is a fair way from it.

No matter what the number of possibilities on each die the result will always have the same shape for 2 dice together – a distribution that rises linearly to a maximum, stays at that value for some results and then falls back in the same way that it rose. The 'plateau', as you so aptly call it, is that maximum and is a single value if the two dice have the same number of sides.

To get something approaching a Normal distribution (Maths speak for a Bell curve) you need to throw more dice – you will never reach a true Normal distribution but after about 6 dice the result is not that far off.

Go with 2D10 instead.

It is also triangular, but modifiers only change the percentages by 1% per level of change, and you get more granularity out of them in the 2 – 20 results.

anydice.com is your friend.

Anyway, adding 2 distributions together is known in mathematics as a convolution operator. When adding a infinite amount of independent distributions, the result is a Gaussian distribution (aka normal disribution, bell curve , …).

2D6 is definitely NOT a bell curve. It is a non-uniform distribution, but that doesn't make it bell curve.

>2D6 is definitely NOT a bell curve

By accumulation of single events it is just one step ahead towards the approximation to the bell curve from 1D6 :-)