Exploding Dice Maths

its but more than the averages if you take a second look, its most significant for smaller dice

the average of 3d4 non exploding is 7.5, and the average of exploding 3d4 is 10

the average number is off by at least .5 in every die type

D4 = 3 & 1/3 VS 2.5
D6 = 4 & 1/5 VS 3.5
D8 = 5 & 1/7 VS 4.5
D10 = 6 & 1/9 Vs 5.5
D12 = 7 & 1/11 Vs 6.5

but if your going to use the numbers in the first one then you should be fine

My current spreadsheet uses straight averages. I’ll build in the ‘exploding averages’ for the ability score dice rolls in my sheet. I’ll use the calculated values above rounded to 1 significant digit after the decimal point.

Thanks for finding the site for those.

John

oh i cant open his sheet from home, it sounded like he didnt see the difference between avg and explode on higher dice

Nope I do. I was just saying that for a ‘ball park’ I’ve always considered the average of an exploding die to be the “regular Average + .5”. Which is pretty close for d6 and above.

john

Because I had to enumerate the dice rolls on Action Dice, there’s no good way to build in the calculated values above for Action Rolls. However, I might be able to fudge it.

For instance, it’s impossible to roll a ‘4’ on a d4 Attribute, since rolling a 4 requires you to re-roll and the minimum you get is 5. Therefore, if I change the expected value of the maximum roll for each die type to the Maximum Value + Average Value (With Exploding), that might give a more accurate result. It’s way too much enumeration to include the exploding die results as well since it’s limitless.

Will see how it goes.

John

Not sure what you’re saying. I was indicating that to compute the probability of beating a specific TN with an Action Roll (2d10 + dX), I enumerated all the possibilities. Otherwise, the calculation gets too messy and used summations, etc. Exploding dice throws a wrench in the works

John

Not sure what you’re saying. I was indicating that to compute the probability of beating a specific TN with an Action Roll (2d10 + dX), I enumerated all the possibilities. Otherwise, the calculation gets too messy and used summations, etc. Exploding dice throws a wrench in the works

JohnJohn,

Found these links…
This (http://topps.diku.dk/torbenm/troll.msp) is a tool that can run dice simulations and compute statistical probabilities for complex dice rolls. Try using this as the die roll formula

sum (accumulate y:=d6 while y=6) + sum (2d10)

This will roll 2d10 plus an exploding d6. If you click on the calculate probabilities button you’ll get a histogram of results.

This was written by Torben Mogensen, a CS professor at DIKU. He also wrote a 29-page paper, “Dice Rolling Mechanisms in RPGs,” (http://www.diku.dk/hjemmesider/ansatte/torbenm/Troll/RPGdice.pdf)in which he discusses many of the dice rolling mechanisms implemented by Troll and some of the mathematics behind them. If you read section 3.4, “Open ended rolls” you’ll see a formula to calculate the average of an exploding die.

Hope you find it useful!

Scott