In Jovus' game tonight, my PC (Ilsildel) will most likely throw a mass sleep spell in a situation where failure would be Bad. Ilsildel has luck, and I've been pondering what my threshold for invoking it to make the MOS as overwhelming as possible is.
This page has some nice numbers (they match mine, so they must be good) for what the odds are, but it doesn't explicitly break out how much MOS calling for the two additional luck rolls will buy you. I worked that out, and decided to share.
The table below shows how much extra MOS, on average, invoking luck will get you, after you have made the initial roll.
Code:
Init. MOS ExRoll
Roll Imp.
3 0.0 3.0
4 0.0 4.0
5 0.0 5.0
6 0.1 5.9
7 0.3 6.7
8 0.6 7.4
9 1.1 7.9
10 1.7 8.3
11 2.4 8.6
12 3.3 8.7
13 4.2 8.8
14 5.2 8.8
15 6.2 8.8
16 7.2 8.8
17 8.2 8.8
18 9.2 8.8
Nothing in there is really surprising, but it gives a rough cut off for "Will invoking Luck significantly improve things?" as an original roll 9+, with significant fuzziness.
Um, I guess that's all. Hey, I tagged it with 'math wankery.'