Average of exploding dice?

[InVinoVeritas]

Okay, smarty pantses, what are the odds your die will explode when you roll it?

For those that don't know, I mean blow up good.

My dice explode every time I roll them. I don't know what's wrong with yours.

 

[Nifft]

My pet peeve with exploding dice is the holes in the distribution. For example, you can't roll exactly 6 on an exploding d6 -- or any multiple of 6.

I came up with something which I've been calling "d5+1" -- on a natural 6, you get 5 + a re-roll. The expected value of any roll is exactly 4, and all results are possible.

Cheers, -- N

 

[Christian]

My pet peeve with exploding dice is the holes in the distribution. For example, you can't roll exactly 6 on an exploding d6 -- or any multiple of 6.

I came up with something which I've been calling "d5+1" -- on a natural 6, you get 5 + a re-roll. The expected value of any roll is exactly 4, and all results are possible.

Although it's less intuitive to think about, the math is actually easier, cause you're always adding a number from one through five to a multiple of five, which is simple in our base ten counting system ...

 

[brehobit]

Huh, how does that second term work? I must think in too straightfoward a manner.

Think of it this way:
The expected value is equal to the expected value of a single (non-exploding) roll plus 1/6th of the expected value (you're just doing it again one sixth of the time).


Mark

 

[brehobit]

It's freyar's result, without the geometric series.

Yep, and the same as mine other than you separated the non-exploding and exploding "first" roll and I put them together. (Plus you _solved_ the equation unlike lazy me

It's always fun to see how people think about things like this...

Mark

 

[Lanefan]

My pet peeve with exploding dice is the holes in the distribution. For example, you can't roll exactly 6 on an exploding d6 -- or any multiple of 6.

Agreed.

I came up with something which I've been calling "d5+1" -- on a natural 6, you get 5 + a re-roll. The expected value of any roll is exactly 4, and all results are possible.

That's exactly how we do it; our term for it is "open-ended roll". We worked out that on any size die the average goes up by 0.5. We used this a lot in one game where critical hits were scaled back to near nothing and instead all damage rolls of any kind were open-ended.

Lanefan

 

[brehobit]

My pet peeve with exploding dice is the holes in the distribution. For example, you can't roll exactly 6 on an exploding d6 -- or any multiple of 6.

I came up with something which I've been calling "d5+1" -- on a natural 6, you get 5 + a re-roll. The expected value of any roll is exactly 4, and all results are possible.

Cheers, -- N

Another trick is to have the reroll number be one less than the max.

The average stays the same, but the distribution tightens a little and the holes go away.

Not sure if it's easier, but it works.

Mark

 

[Nifft]

Another trick is to have the reroll number be one less than the max.

The average stays the same, but the distribution tightens a little and the holes go away.

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

 

[Rabelais]

So Stat-monkeys, what's the average number of posts in a thread where there is a math question?

 

[Blackrat]

Okay, smarty pantses, what are the odds your die will explode when you roll it?

For those that don't know, I mean blow up good.

Well this page answers that quite good in peasant terms http://plato.stanford.edu/entries/qt-quantlog/ . Ofcourse I'm so incredibly smart that I couldn't explain it in terms anyone here would understand so I had to post a link to this page .

To give a numerical answer: The probability that your dice blows up is 50%. It either does or does not.