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The Miniatures War College
Advenio paratus. Egressus melior paratus.
D&D Miniatures strategy and analysis.

October 2, 2005

Curses! Numbers Again!

Another card to leak out of GenCon 2005 was Elminster of Shadowdale. Being the first of the new Epic figures there are two versions of the card. The most interesting spell IMHO is the 7th Level Spell Mystra's Curse (sight; roll twice for each of target creature's rolls and take the lower result, DC 19). This is another effect which is like Conceal where the number you need to roll determines the effectiveness of the effect. One simple notion is to think of the Curse effect as "do it, then do it again." The problem with that notion is that the probability of not rolling a 1 twice in a row is far different from rolling a 20 twice in a row. The truth is you have better odds rolling a 1 in one of two rolls as you do of rolling a 15 or better twice in a row.

To display the odds, I will use a plot showing the cumulative probability of success. Well not quite, I believe I should flip it from right to left, but then the numbers are backwards. Since I don't do this professionally then such errors are commemorate with my pay scale. The left axis shows the odds of making the rolls you need, while the bottom shows the roll you need to make or beat. It is important to note that the odds are not that of making that precise role, but that roll or better.


An image may be worth a thousand words, but a chart is worth 10x magnification. This chart summarizes the data and adds a new data point, "like rolling." It equates the odds to what you would need to roll on a d20.0 (a special d20 that rolls to the tenths place). When the odds get really ridiculous, I replace it with a 20+x notation, where it is like rolling a 20 and then needing to roll x. As you can see from the data, the curse can be well worth it's cost in points, too bad the Epic version of the card is missing this spell.

Roll Normal Cursed Like
1 100.00% 100.00% 1.0
2 95.00% 90.25% 3.0
3 90.00% 81.00% 4.8
4 85.00% 72.25% 6.6
5 80.00% 64.00% 8.2
6 75.00% 56.25% 9.8
7 70.00% 49.00% 11.2
8 65.00% 42.25% 12.6
9 60.00% 36.00% 13.8
10 55.00% 30.25% 15.0
11 50.00% 25.00% 16.0
12 45.00% 20.25% 17.0
13 40.00% 16.00% 17.8
14 35.00% 12.25% 18.6
15 30.00% 9.00% 19.2
16 25.00% 6.25% 19.8
17 20.00% 4.00% 20 + 5
18 15.00% 2.25% 20 + 11
19 10.00% 1.00% 20 + 17
20 5.00% 0.25% 20 + 20

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