PLL parity isn't a true parity fix, just some silly 2-2-cycle you need for the reduction method. But as far as the real parity (OLL parity for reduction users), which is two edge pieces swapped, you cannot avoid getting it 50% of the time, although if you are willing to mess up centers a bit you can fix it with just an r or u turn and a commutator.
And TsColin, please learn some notation that doesn't suck. For 4x4 most people will use U for top layer only, u for 2nd to top layer only, Uw for top two layers, and don't use commas, and the 2 (for a double layer turn) usually goes after the turn.
So, your "2r, 2U, 2r, 2U*, 2r, 2u" is written "r2 U2 r2 Uw2 r2 u2".
(Incidentally, a better alg is: Uw2 Rw2 U2 r2 U2 Rw2 Uw2.)
If you want to cheat, count the number of slice turns you make in a normal 4x4 scramble. If that number is:
- Solve centers with an even number of slice turns. (even+even=even)
- Solve centers with an odd number of slice turns. (odd+odd=even)
Double turns count as 2. Ultimately you want an even number of slice turns before you get to the 3x3 stage. And like qqwref said, PLL parity technically isn't even a parity... :P
Cage: First two centers/ First center/ Edges
step 2: solve like a 3x3
Step 3: fix parity errors
Step 4: Solve the remaining 4 centers/ 5 centers/ 6 centers
parity is possible, chinese food and chocolate milk dont mix, which one.
The only way to solve without parity is Cage method.
For the OLL parity use the speedcubing method
(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2
Nope.. cage has parity.
based on what i've heard, cage has a form of parity that is easy to solve.. i'm probably wrong but that's what i've heard.. the OLL fix for the parity case for reduction is just a pain to learn but it has a type of pattern and rhythm to it.. it's not too bad to get used to
Check out the last post on that page.
Cage doesn't have parity. If you get the OLL parity or the PLL parity case on the last two edges, then you just do the parity algorithm, but it is counted as a last two edges algorithm. If you didn't get those cases, you would have just done another algorithm.