Average of exploding dice?

[Rvdvelden]

My pet peeve with exploding dice is the holes in the distribution.

My pet peeve with exploding dice is the holes in the gaming table.

 

[interwyrm]

Holes go away? How do you end up with a value of 5?

All you're doing is pushing the holes around. There are still dips in the PDF, they're just not all zero any more.

Cheers, -- N

I think the suggestion was...

1
2
3
4
5
6+0
6+1
6+2
6+3
6+4
6+5+0
etc.

 

[Gez]

I think the suggestion was...

1
2
3
4
5
6+0
6+1
6+2
6+3
6+4
6+5+0
etc.

Which accounts to about exactly the same thing.

If they roll 6 then 1,
Nifft has (6-1) + (1)
Brehobit has (6) + (1-1)

Whether you substract one from the exploding die or the reroll die doesn't change anything to the total sum...

(Now, it would be different for a system like Ars Magica's where it's a multiplication rather than an addition.)

 

[brehobit]

Holes go away? How do you end up with a value of 5?

All you're doing is pushing the holes around. There are still dips in the PDF, they're just not all zero any more.

Cheers, -- N

You win. 5 is missing, so is 10, 15, etc.

Ah well, thinking isn't my strong suit.

Mark

 

[Aeric]

In my day, exploding dice were called "open-ended rolls." And that's the way we liked 'em!

 

[Nifft]

You win. 5 is missing, so is 10, 15, etc.

Don't feel bad. I didn't notice about 6 (and 12, 18, etc.) being missing until someone else pointed it out.

Seeing the bumps & valleys in the distribution is really helpful.

Cheers, -- N

 

[Christian]

Holes go away? How do you end up with a value of 5?

By ... rolling a 5?

 

[Nifft]

By ... rolling a 5?

You ... read his post?
The ... context makes it clear.

C ... heers, -- N

 

[Gez]

First I inferred the same thing as interwyrm.

But what brehobit meant was that if you roll 1, 2, 3, 4 or 6 it's what you got; while if you roll 5 you reroll a die and add it to 5. So you can get:
1
2
3
4
6
5+1, 5+2, 5+3, 5+4, 5+6
5+5+1, 5+5+2, 5+5+3, 5+5+4, 5+5+6
5+5+5+1, etc.

 

[Grakarg]

Holy Thread Resurrection Batman!

Ok fellow math-masters, I need your help on this, and I can't seem to find a clear concise answer anywhere...

What is the average result for exploding dice when you're rolling multiple dice?
Example, whats the average result when rolling 2d6 vs 4d6 when open ended dice are involved?
What about when different die types are included, like 2d6+1d8+1d12?

Thanks for your input!

If you care, here is why I want to know:
I'm running a Super Hero game using Savage Worlds. I'm having trouble gauging the hero's power level vs opponent's toughness and damage dealing potential. Mainly because you start to stack multiple dice and dice types that can all explode. If I can ballpark a character's average, I can set targets that will provide a more interesting encounter, instead of the opponents getting blasted apart like wet tissue paper by the heroes; or destroying the heroes with a sideways glance by my villain.