## January 10th, 2010

### Exploding Dice

So here's a nifty thing I learned today.

In some RPGs, you roll exploding dice: if a die rolls its maximum value, you add that value and re-roll, repeating as necessary. So what's the expectation value for such a die?

The expectation value for a normal N-sided die is = (1+2+...+N)/N = (N+1)/2.

For an exploding die, you just multiply that by N/(N-1).

So a normal d6 rolls on average 7/2 = 3.5, and an exploding d6 rolls on average 7*6/5*2 = 4.2.

Keen!

(This comes from this "a mathematical analysis of exploding dice". I tried to do the general case analytically, but couldn't get the algebra to work out. I was never any good at that kind of math...)

### Stan

I don't think I've mentioned lately how glad I am that we have free trans-Pacific videophone, which lets you have your partner attend the annual winter holiday party remotely.

(Well, once you remember to run back home and grab the laptop, anyway.)

I didn't cook anything this year; instead I took the boring support role and brought plates & napkins & cups. This involved me standing in the paper products aisle at the grocery store for far too long dithering over how many and what kind of plates to get. I have no idea why ti took me a full five minutes to decide. Tyranny of choice, I suppose.

Had a lovely time catching up with friends I don't get to see often enough. I was a bit low-key, probably because we stayed up really late last night watching Iron Man on DVD.

In less than a week, I will be in Japan. WOW!