I have a “drop table” / “loot table” / “item table” / “whatever you want to call it” system and I need to solve two Problems. Apologies in advance for the text wall :/

The Problems:

- Calculate the probability of pulling a specific item from a table
- Calculate the probability of pulling ANY item from a table with a specific tag (such as “Epic”, “Rare”, “Weapon”, “Sword”, “Currency”, etc)

A few details about the system:

- Tables are setup with a certain number of ‘Slots’ and ‘Rolls’
**Slots**determines the total number of*unique*items that can be dropped from the table**Rolls**determines how many times we ‘pull’ an item out of the table- Each row within a table will drop one of a pre-calculated set of items
- Each row can be marked as ‘Guaranteed’, ‘Random’ or both (more on that in a bit)
- Rows have a ‘MaxRollsToConsume’ field (0 == infinite rolls), and a Weight field (used for weighted randomness, 0 Weight = never pulled)

And a bit of pseudo code for how we actually pull items out of the table

```
create a guaranteed set of rows
create a random pool of rows
create a result with a set number of slots available to fill
(note: adding an item to the result will only fill a slot if that item does not already exist in the result)
foreach row in table
if row is guaranteed, then add to guaranteed set
if row is random, then add to random pool
foreach row in guaranteed set
pull item out of row and add it to result
consume a roll
while there are rolls remaining and empty slots in the result
select a row from the random set using weighted randomness and respecting the MaxRollsToConsume field
pull item out of row and add it to result
consume a roll
if this row has reached its max rolls then remove it from the random pool
while there are rolls remaining
select an item from the current result using weighted randomness and respecting the MaxRollsToConsume field
add the item to the result
consume a roll
return the result
```

I understand how to calculate the probabilities for the ‘Guaranteed’ rows because, well, they are events that are guaranteed to happen so it’s pretty easy to calculate.

Where I’m falling short is on how to calculate the ‘Random’ rows (especially with respect to the MaxRollsToConsume field) and only pulling a certain number of times. For example, I have 5 random rows, but only 2 Rolls to consume. How do I calculate the probability of an item being pulled from one of the those 2 Rolls while also taking into account how many Rolls are allowed per row?

I’m fairly confident that if I can solve Problem 1 with some help then I’ll be able to solve Problem 2 on my own. Any help is appreciated and thanks in advance! If anything is unclear or more info is needed please let me know! ðŸ™‚