I have a question. I've "created" (not sure if the idea has been thought of before) a "new" (not sure if you could call it that) method (extension) for 2x2 called Twisty Ortega, or TO. It basically enhances the first step of Ortega to make it extremely quick and easy at the small expense of a few extra algorithms for the second step. Also, it suggests learning more PBL algorithms to reduce cube rotations and AUFs. Here's the basic idea:
Solve a side with one corner permitted to be disoriented. This step rarely takes more than 3 moves, making lookahead to the second step very quick and easy.
In one of 23 algorithms, orient all corners on the cube (7 OLLs + 14 algs for OLLs with a twisted first side corner). This step is called TOLL, or Twisty OLL. All of these are <R,U> 2-gen
In one of 14 algorithms, solve the rest of the puzzle. This step is called PBL/P2L, or I sometimes call it EPBL for "Enhanced Permutation of Both Layers."
I have learned all of the algorithms and have this method in complete, active use. I use this method for all solves and even used it at the Peach State 2015 competition and got a sub-5 Round 1 average (
https://www.youtube.com/watch?v=L-yluXWOL30) and ended up in the top 10 (I think) for that first round. I globally average around 4.6-4.7 with this method. I also like this method because it provides a much wider array of options on how to solve the first side. I'll often work out multiple ways to solve a side to try to find a nice, fingertrickeable (that's a new word, I guess) 1st step with an easy 2nd step. I was wondering, since this method is fully developed and in use, if I should create a separate thread for this. Here are some example solves on alg.cubing.net
Example solve #1
Example solve #2
If you want more example solves, please tell me.