I think I may have discovered a new fact. If I'm doing it right, d2s always yield a higher average result than d3s if both allow exploding dice (if you roll max, roll again and add the result). I don't remember much math about infinite series, though, which I believe I would require in order to prove it. I only have empirical indications of this. Still, it means that the minimum die size in this game will have to be a d3, lest there be a case where reducing an ability score improves your effectiveness.
Limit of 1/2+3/4+...+2n/(2^n-1)+(2n+1)/(2^n) as n approaches infinity from 0
vs
Limit of... 1+1+...+3(2n)/(3^n-1)+3(2n+1)/(3^n) as n approaches infinity from 0?
I don't even know if I've set those up properly, much less if they hold to my hypothesis.
Well, I'm not big into infinite series, but the chances of having a d3 explode just four times is 1 in 81. This would result in a roll of 13 - 14.
The chances of having a d2 explode four times is 1 in 16. This would result in a roll of 9. If you wanted a d2 explosion to reach the same likelihood of that d3, you'd need to have it explode about six times for 1/64, meaning a d2 would do 13 'damage' a bit more often than a d3 would do 13 - 14. So your reasoning is sound - The lower the dice, the more powerful its potential for mind boggling explosions
Something you may consider is having a cap of re-rolls equal to the maximum roll on the dice. So, a d2 can only explode twice for a total of three rolls (5 - 6 damage). A d3, however, could explode three times for a total of four rolls, a d4 a total of four times for a total of five, etc. Or you could make the maximum number of rolls equal to the max dice roll to make things less confusing. This would mean a d2 could only explode once, for a total of two rolls.
With the max roll system, larger dice are suddenly powerful tools that can one-hit anything on a lucky streak, while smaller ones become reliable founts of bonus damage without being overpowered. Feats and such could also expand an explosion's range (Certain weapons can explode an additional time, for example), and perhaps even improve the threat range for the initial strike. Suddenly, daggers aren't quite as laughable as they used to be, and great axes can decapitate things without rolling a critical success.
And, since you're playing with dice theory,
this is pretty dang useful for determining the chances of something happening. It doesn't do exploding dice, but it's great for anything else a home brewer might need.
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