Dominions 3: The Awakening/Magic/Abbreviations

Magic Path Abbreviation Conventions
Throughout the Wiki, you may see arcane abbreviations such as "1E1N1?". Worse, you might see something like "1E1N1?(100 AEFW, 50 AEFW)". These are not attempts to shut you out of the game, but rather cunningly-wrought abbreviations intended to prevent someone from writing "one level in Earth, one level in Nature, plus an additional level of either Air, Earth, Fire or Water, plus a 50% chance of yet another level in either Air, Earth, Fire or Water."

See the advantage? Here's how you read it:


 * A = Air
 * S = Astral
 * B = Blood
 * D = Death
 * E = Earth
 * F = Fire
 * N = Nature
 * W = Water

A number in front of one of these indicates a magic level in that Path, so "2A3N" would indicate a mage with two levels in Air and three levels in Nature.

It's pretty easy, except that Astral uses an "S" because "A" was already taken by Air.

Less used, are the following:


 * H = Holy
 * U = Unholy
 * ? = Random

Levels of holiness (or unholiness) are occasionally listed alongside the magic paths if the mage also happens to be a priest. These are often omitted, however.

Finally, many magic-using leaders in Dominions 3 have a certain random factor thrown in, which is represented by a question mark. So when you see "2E1N1?", it means two levels in Earth, one level in Nature, and one level in some random path.

The random magic path information can get a bit deeper, however. Each "?" tends to have more info behind it than can be easily conveyed, so you'll sometimes see an abbreviated explanation parenthesized after the "?", something like "(100 AEFW, 50 AEFW)".

The number is the percentile chance that an additional magic path will be granted, and the letters are the possible paths. Thus for this example, the mage will get an additional path or either Air, Earth, Fire or Water, and there is a 50/50 chance that they will get yet another level in one of those paths.

Examples

 * 2D3S: Two levels of Death magic, three levels of Astral magic.


 * 1E1N1H: One level in Earth, one level in Nature, one level in Holy.


 * 2D1?: Two levels in Death, one level of a random path.


 * 2E1? (100 EFDN, 50 EFDN): Two levels in Earth and one random choice which will provide one level in Earth, Fire, Death, or Nature, along with an additional 50% of yet another level in Earth, Fire, Death, or Nature.


 * 2E1? (10 EFDN): Two levels in Earth and one random choice which has a small chance (10%) of providing one level in Earth, Fire, Death, or Nature.

Statistics
Just a little note on how to figure out the odds in a random path choice. Let's grab an example from above:


 * 2E1? (100 EFDN, 50 EFDN)

So this mage has two levels in Earth and one random choice which will provide one level in Earth, Fire, Death, or Nature, along with an additional 50% of yet another level in Earth, Fire, Death, or Nature. What are the odds that we'll end up with a mage with 4 levels of Earth?

Well, they are not good. You start off with two levels in Earth. Then you have a 100% chance of getting EFDN, so you are going to get one of those four, guaranteed. So you have a 25% chance of getting another level in Earth... meaning that one in every four of this type of mage you buy will be a 3E mage.

Then, you've got a 50% chance of yet another level in EFDN. Meaning a 50% chance of another 25% chance of getting Earth.

Multiplying out all your odds gives us:

1/4 * 1/2 * 1/4 = 1/32, or about a 3% chance of getting a 4E mage. Not odds you'd want to plan a strategy around.