Dice Probability Generator

[LibraryOgre]

Oh, my, this is useful

http://anydice.com/

It lets you plug in different dice combinations and compute the probability. It doesn't help with exploding or penetrating dice systems, but it makes a wonderful tool for the more simple progressions, with easy to use displays.

[Slipperychicken]

It actually does do exploding dice*. Check the function library on the site.


* (albeit with some limitations: it can only go out to a finite number of explosions, a number which the user can set, and I believe the probability rounds down to zero after about 0.001%)

EDIT: And if you're willing to put some work into it, you can do some pretty complex stuff. I once helped to write an Anydice script which allows a user to compute damage distributions in Shadowrun 5e, which considers factors like the attacker's attack pool, the defense pool, the weapon's armor-penetration value, the weapon's damage value, the defender's soak dice. I don't believe we got around to it, but it would have been simple to include things like damage-reduction and whether the attacker was using a luck point for the roll. If you wanted to, you could probably do the same thing for D&D 3.5 attack rolls.

[oxybe]

output dX named "dX, not exploded"

loop DEPTH over {Y} {
set "explode depth" to DEPTH
output [explode dX] named "dX, exploded at most [DEPTH] times"
}

View: Roller / Data: Normal

X is the number of faces on the die(4, 6, 8, 10, 12, 20, 100)
Y is the number of possible explosions you want to allow.

You'll see a dropdown for "dX, not exploded" or "dX, exploded at most [DEPTH] times", allowing you to either throw the dice unexploded or exploded.

press Calculate to set everything in stone and Roll to give you one output. If you plan on reusing the same exploding dice formulat (like, say, you'll always be checking if a fistful of d6's explode), you can just keep hitting "Roll" next to the output dropdown to generate new values

So let's say we're playing with the old Pathfinder gun rules and someone is using a gun where the damage is upped to 3d6.

you make it so:

output d6 named "d6, not exploded"

loop DEPTH over {12} {
set "explode depth" to DEPTH
output [explode d6] named "d6, exploded at most [DEPTH] times"
}

View: Roller / Data: Normal
d6, exploded at most 12 times - 3 - ROLL

and it will give you
4, 3, 21

This means you rolled a 4, 3, 21 (6+6+6+3)

EDITS:
Here is a link to the formula, ready to use.

Also: cleaned up the formula a very tiny bit. you can go up stupid lengths in the depth, like 1000, but anything past 4 explosions is a less the 0.01% chance of being rolled