Tuesday, March 20, 2012
One oddity in LoC and nowhere else was that the game occasionally called for a 2-16 result, but did not come with any eight siders. An early chapter of the rulebook explained how to use the dice, as is customary in many RPGs up until this day. To get a 2-16 result it instructed you to roll d10+d6.
I've long wanted to know exactly how the change of dice from 2d8 to d10+d6 affects the probabilities involved and the other day I finally sat down and did the math. Here are the results, represented visually.
Using d10+d6 instead of 2d8 flattened out the bell curve. 2d8 peaks at a roll of 9, just the way seven is the most common roll on) 2d6. With the d10+d6 combine all numbers from 7 to 11 all have an equal chance of occurring, exactly 10% chance for each.
The only other place I recall seeing this sort of set-up is Uncle Gary's new and improved wandering monster charts in the back of the Monster Manual II. He uses d12+d8 in lieu of 2d10 to create charts with many equally common monsters in the middle.
This chart shows the differences between the two methods for "roll some number or less" type situations. I don't think LoC actually uses d10+d6 for these situations, but it wouldn't be more than 3% off from a 2d8 test for any given target number.
As always, feel free to double check my numbers by doing the math yourself.