One of the strange things seen in the original documentation is the existence of (R). Normally, parentheses are used around groups of moves to denote finger tricks. But why just one move? And why do we occasionally see (R)'? It doesn’t seem to make sense.
The original documentation was brief but clear on the subject:
In many cases in the course of a process a different hole is moved to the RU position by a move of the R face. As the relative position of the holes in the R face is irrelevant to the structure of the process, the required move may be R, R', or R2. It is therefore noted as (R). Sometimes also (R)' occurs, which means that the move executed at (R) earlier in the process should be inverted.
So what does this look like in practice? Say we have this case here:
If we look in the list of algs, we can see that the algorithm for this case is U2 (R) U' M' U (R)' U2. Fair enough, but surely this algorithm only works for one particular order of the R edges? For instance, what if we have this case?
The basic setup is the same, but the place where the second edge goes is different. Do we need to learn three algorithms for every single case? The recognition would be a nightmare!
Or so you think. See, the algorithms are set up in a clever matter. In the second case, the two edges we are placing in are opposite to each other. Imagine, rather than doing an R turn, we do an R2 instead:
Now the second hole is lined up correctly, and we can carry on with the rest of the algorithm, making sure to do an R2' rather than an R' at the end. The algorithms always solve whatever is in the RU slot, so we can simply move the other unsolved slot up to the RU position whenever we need to make some sort of R turn!
In summary: whenever you see an (R) in an algorithm, look for the other unsolved slot in the R layer. When you find it, turn the R face in whatever way it needs to be turned to ensure it is in the RU position, and continue on as normal. Then, when an (R)' move is seen, simply do the inverse of the move you originally did.