The bell-curve for Luck

[Bruno]

I don't have a clue how to mathematically figure out what the bell-curve looks like for a Luck'd reroll - in this case looking at "roll three times, take the lowest". So I wrote a little perl script and had it roll 10 million times and crunch the results while I was working on other, less interesting XML things. I hope someone else finds this interesting, or possibly even useful.

And hey, five minutes later, here are the results (expressed as decimals rather than %ages - 1 = 100%, 0.5 = 50%, etc):

3: 0.013832
4: 0.040677
5: 0.078090
6: 0.120218
7: 0.158806
8: 0.182009
9: 0.162288
10: 0.119093
11: 0.072197
12: 0.035351
13: 0.013187
14: 0.003452
15: 0.000706
16: 0.000089
17: 0.000006
18: 0.000000

Note: I'm fairly sure there were 18s in there, they're just falling below the precision in my output.

EDIT: Here it is again expressed as %ages for folks that prefer that:
3: 1.3832%
4: 4.0677%
5: 7.8090%
6: 12.0218%
7: 15.8806%
8: 18.2009%
9: 16.2288%
10: 11.9093%
11: 7.2197%
12: 3.5351%
13: 1.3187%
14: 0.3452%
15: 0.0706%
16: 0.0089%
17: 0.0006%
18: 0.0000%