I'm trying create a new single-item selection system that has either identical or close to the identical probability of an existing multi-item selection system.
The current system has multiple "tables", each containing multiple items. Both a table and each item inside of that table have a selection probability. That is to say we determine if a table is used based off of its probability, and then we go through each item in that table and determine if that item is selected based on the specific items probability.
Using the new system, I want there to be only one table containing one item. The one table should have the combined probability of ALL the old systems table probabilities and the one item should have the combined probability of ALL the old systems item probabilities.
Would this mean that I would simply find the average of all the tables and the average of all the items and that is the new probability for the table and item?
I'm also curious if there is way to shift the old systems table probability on to the item? That is to say, the table would ALWAYS be selected, and the probability of the item in that table would adjust based on the tables previous probability. Is this possible?