Re: [HOE] Math question

["Johnny Burlin" <Johnny.Burlin@home.se>]

Perhaps I'm missing something important here but I get the impression that
you guys want to calculate the average of a damage roll xDy.

The average of a die with reroll is:

x is the average
n is the number of sides

x =  n(n+1)/(2n) + x/n

Or, in words, the average is the sum of all sides divided by the number of
sides, plus the average of a single roll divided by the number of sides
(when you get an ace you reroll and the average of that roll is the average,
but the chance of getting it is just 1/n).

Time to simplify:

xn = n(n+1)/2 + x

xn-x = n(n+1)/2

x(n-1) = n(n+1)/2

x = n(n+1)/(2n-2)

For a d4 you get:
4*5/(8-2) = 20 / 6 = 3.3333

For a d6 you get:

6*7/(12-2) = 42 / 10 = 4.2

For a d10 you get:

10*11/(20-2) = 110 / 18 = 6.1111

(Earthdawn players might recognize these as step 3, 4 and 6 respectively.)

So the damage xDy can be expressed as:

avg. = x*y(y+1)/(2y-2).

/Johnny