Donjon dice odds

[Sonja]

I consulted some mathematicians and found the following useful statistics related to dice rolls in Donjon:

When creating a character's attributes and rolling 3d6 and keeping only the median die, the odds are:

6	7.4%	****
5	18.5%	*********
4	24.1%	************
3	24.1%	************
2	18.5%	*********
1	7.4%	****

Now if you roll a pool of d20 and only look at the highest die, what is the average result you will get?

1d20	10.5
2d20	13.8
3d20	15.5
4d20	16.5
5d20	17.1
6d20	17.6
7d20	18.0
8d20	18.2
9d20	18.5
10d20	18.6
11d20	18.8
12d20	18.9
13d20	19.0
14d20	19.1
15d20	19.2
16d20	19.3

Peace,

Sonja