The PEG method (pairs + Erik + Gunnar) is based off of Erik Akkersdijk's and Gunnar Krig's 2x2x2 method EG, but has been moved over to 3x3x3. Here, not only the corners of the first layer are oriented as the first step, but also all the pairs are. So it will be Pairs-EG or simply PEG!
PEG differs slightly from EG. Most algorithms can be used if some of the turns are done double layer to preserve the pairs. But some algorithms destroy the pairs no matter how they are performed. In those cases, other, possibly longer algorithms need to be used.
Example: This algorithm solves EG 1 Pi D
- R U R' L' U' L R U R'
To use it for PEG, do it like this:
- R U R' l' U' L r U R'
PEG is best used together with L5E.
PEG is also useful for direct solving big cubes. The only difference is that the "pairs" have more edges and you need to do triple, quadruple, etc. layer turns to preserve them while doing EG.
This method can be divided into three groups: PEG 0, PEG 1, and PEG 2, where the number is the number of pairs correctly placed in F2L. If two adjacent pairs are swapped, it is PEG 1 (two pairs connected). If two diagonal pairs are swapped, it is PEG 0 (no pairs connected). Finally, if all pairs are correct, it is PEG 2 (4 pairs connected).
PEG 2 is a stand-alone method where you use a standard CxLL (CMLL, or rather CMSLL, because the S-slice is also free).