Aside from the 57 usual OLL cases, there are only 54 OLL cases that have OLL parity.Alright, so I have a plan to be able to solve 4x4 OLL in 1-2 steps:
1. Recognize the case (parity or non)
2 Step 1: Solve Oll, or do set-up case Step Two (if there is parity) solve parity, (then undo setup, if done.
Basically, I will need to be able to recognize 172 cases for Oll on 4x4. Here's how I worked it out:
I know some cross oll parity cases for 4x4 already. For L shapes and Line shapes, there are 3 possible edges that can flip before the L/Line case becomes a cross case; and 4 different cases for each dot oll case before it becomes a cross case. So (30*3) + (12*3) + (7*2) + (8*4) is equal to 172. Of course many cases will end up having the same case, so the number will go down. Maybe I just have to learn half of what I said if half, or a quarter, or whatever; is oll, and the rest is oll parity cases
I don't know if anyone's got an up-to-date list of algs for those, but here's one by TDM.