First, my apologies to math haters...

Hum…

I've done some nerdy computations this week-end about exploding (?) dice. One of the interesting conclusions is that +2 to an AD is *always*, in mean, better than being able to explode on the maximum -1. So one well-known feat is actually underpowered.

This is true if the maximum value on the die is the only other exploding value. If the 1s also explode, either from the Bold Heroes campaign quality or the Tales of the Rascal feat, it does not hold true for the d4.

I derived the formula a while back for determining the mean value of a die with x sides that explodes on y results as f(x, y) = (x + 1) / (2 * ( 1 - (y / x)))

f(4, 1) = 3

^{1}/

_{3}f(4, 2) = 5

f(4, 3) = 10

As you can see, going from 1 exploding face to 2 exploding faces adds 1

^{2}/

_{3} while going from 2 exploding faces to 3 exploding faces increases the mean from 5 to 10.

However, this is only the case with the d4. For the larger die types, the mean value is higher after adding +2 than adding a 3rd exploding face to the dice.

But there are other factors to consider. I suspect, though I have not done the math for it, that the standard deviation will be higher on dice that explode on more sides. This would mean that you would have a better chance for achieving both higher and lower rolls. For example, if you need to generate a score of 12 on an exploding d4, your odds may be better if you explode on a 2nd side rather than just add +2 to the final result. Again, I haven't done the math for the standard deviation calculations, just pointing out it is another factor that needs to be considered.

Would anyone be interested in a translation ?

Unfortunately, I don't know French. (cursed monolingual US Americans) So, yes please.

Also, the link didn't work for me directly. There were some extraneous characters in the link that I had to clean up.