EG is a fairly advanced 2x2 method originally developed by Erik Akkersdijk and Gunnar Krig, and completed by me i also think that since i completed 1/3 of the method, its only fair i should be in the name. i'm thinking either EGD, or EDGE(Erik David Gunnar Expert method) if its ok with Erik and Gunnar
basically you solve one side of the cube, not necessarily permuted (like Ortega first layer.) i believe this step averages 3 moves. then you orient the last layer and permute both layers in one step. there are 143 algorithms for this, and they are divided into 3 sub-cases
Case 1: first layer is correctly permuted. this is just COLL optimized for 2x2. there are 47 algs for this case, averaging 8.79 moves.
Case 2: there is a "bar" in the first layer, where only two pieces need to be switched. you place the "bar" in the BD position and the solve the cube. there are 48 algs for this, averaging 8.43 moves.
Case 3: this is the one i designed. it is where the first layer is entirely mispermuted, where a diagonal swap is needed. the FL does not need to be in any specific position to solve the cube, maybe an AUF at the end. there are 48 algs for this case, averaging 8.58 moves.
this gives step two a total average of about 8.6 moves.
so 3 move FL+ 8.6 move solve+ .75 move AUF(needed only 3/4 of the time)= 12.35 move solution.
not only does it have a low move count, it is only 2-look, potentially 1-look with an easy first layer. this method is perfect for anyone who can easily recognize COLL cases on a 2x2 without referencing the first layer.
i think the only reason it has not gained popularity is because it was incomplete until last saturday! Erik and Gunnar have already started learning it, and i plan to start sometime soon as well.
any feedback is highly appreciated, and if anyone wants to start learning the first two cases, they can be found on Erik's 2x2 page. the third case should be up there soon.