## Let's do math

So the new October playtest has random magic item generation in it. The tables look pretty wonky so I decided to run them through some good old mathematics.

Before you complain: First, I am running on the assumption that the DM is meant to roll on these magic item tables after EVERY encounter. The fluffy boxes of text hint that magic items should be rare but the tables also have sizable chances of not giving anything at all. Why would a DM roll on them if he didn't intend to give out an item unless it was intended to be a chance of getting an item? So I'm going to run with the idea that you're supposed to roll every time.

Second, I'm working with pure averages here by multiplying the chance of an item by the number of encounters per day to get a rough "items per day" that could be expected.

Third, I'm going to calculate averages using all three tables and the expected adventuring days from Page 11 of the DM Guidelines. So I'll give numbers for a party that fights six easy encounters, a party that fights four average encounters, and a party that fights two tough encounters. Obviously in a real game these would be mixed and matched but you should be able to get a rough estimate of what to expect.

Fourth, I'm making an assumption that the 97-99 slot of the Average Encounter table includes 1d2 rare items. It looks like a typo the way it is.

Example Math:
On the easy encounter table a result of 1-50 results in no magic items. A result of 51-100 will result in 1d2 common items (plus possibly other things but for common items I just care about that 51-100). Thus I can say that there is a 50% chance of rolling 1d2 common items. Thus: 0.5 x 0 + 0.5 x (0.5 x 1 + 0.5 x 2) = 0.75
A party will encounter an average of 0.75 common items per easy encounter.

A party fighting six easy encounters:
Common: 4.5
Uncommon: 0.45
Rare: 0.15
Very Rare: 0.03
Legendary: 0
Artifact: 0

A party fighting four average encounters:
Common: 4
Uncommon: 1
Rare: 0.3
Very Rare: 0.04
Legendary: 0.02
Artifact: 0

A party fighting two tough encounters:
Common: 2.75
Uncommon: 1.1
Rare: 0.5
Very Rare: 0.15
Legendary: 0.04
Artifact: 0.01

Interestingly the level of the adventurer has zero correlation to the power of the items he finds. Level 1 adventurers are just as likely to find a Holy Avenger at the bottom of the goblin hole as world shattering badasses are to find one at the depths of Orcus's palace.