Here is how the beginner's PLL works:
The worst case for a beginner, using 4 algs, is that there will be 4 PLL steps. Most of the time it's only two steps. Break it down like this:
1. Align *one* corner piece in the U face with the matching edge in the second layer. It does not matter which corner, as long as it *matches* the edge below it in the second layer. There are four cases here:
A. Only one corner is lined up. The other three corners do not match. Run a 3 corner cycle and all corners will be solved. You have to look to determine whether a clockwise or anti-clockwise corner cycle is required and run the right one.
B. Two corners now match and they are right next to one another. Rotate the U face until one of the other corners matches, then run the appropriate 3 corner cycle as in (A) above.
C. Two corners line up and they are diagonal from each other. This is the worse case, and requires two 3 corner cycles. Run either of the 3 corner cycles. Then twist the U face until *only* one corner matches, as in (A) above. Then run the appropriate 3 corner cycle and all corners will be in place.
D. All corners already match. No need to do any corner cycles.
2. Now that the corners are in place, the edges need to be moved to the right places. Look at the U face and see how many edges are out of place. Cases:
A. 3 edges out of place. Look at the edges to be moved, and either run a clockwise 3 edge cycle, or an anti-clockwise 3 edge cycle, as appropriate.
B. 4 edges out of place. This is the worst case scenario and requires two 3 edge cycles to be run. Choose either of the 3 edge cycles and run it immediately. No need to choose any particular side, just run it. Now one edge will be aligned and the other 3 are not. Just run the appropriate 3 edge cycle as in case (A) above.
C. All four edges in place. You're done; cube is solved.
So what you are doing now is a 4 look PLL. You can reduce this to a 2 look PLL by learning a *total* of 7 PLL algs:
1. Clockwise corner cycle
2. Anti-clockwise corner cycle
3. Clockwise edge cycle
4. Anti-clockwise edge cycle
You should already know the four above.
5. H permutation which swaps 4 edges.
6. Z permutation which swaps 4 edges.
7. Y permutation for swapping diagonal corners.
Look here for pictures and algs of H, Z, and Y under the "2 look PLL" part of the page:
http://cubefreak.net/twolook.html
With those additional 3 algs, your worst case scenario will always be a 2 look PLL.
I hope this makes sense.
Brian.
