Ok. I've done some more experimenting, and I've come up with a few new ideas. Because Gilles' method uses opposite color solving for the F2B, and because we've heard so much from Chris Hardwick lately about opposite color (and it works), I decided to try to apply this to my new Step 4 idea. For the last step, you can start by either inserting the DB pair, or use the DB pair for the opposite color, and finish your solve with an M2.
I tried this a lot tonight, and it went much better than I was afraid of. The only thing I really had problems with was recognizing which pieces to permute with certain ELL cases, but since I only know a few ELL cases anyway, I think I'll chalk it up to that. :) My best time using this was a 16.42. Not lucky, in that I inserted one edge easier using my opposite color, inserted the second, and finished with an ELL case. All three substeps totalled about 14 moves, which is a little better than average for that scenario. There are really 4 separate scenarios for solves this way. The first is when all the edges are oriented after inserting DB. Ideally, I would like to learn the 16 or so cases to finish off the edges. They're all relatively short and easy to accomplish using only MU moves. They average under 7 moves per alg. All but 4 or so are very easy to recognize, and the final 4 I have some ideas for. This should come up nearly 15% of cases, if you can start with any of the 4 M edges for DB. This is by far the nicest option, because of how short and quick the algs are, but also the least frequent. Placing the DB edge intelligently, though, we can get this more often. The second special scenario is when the DF edge places itself, or is very simple to place after the DB edge. This leaves you with an ELL case to finish. I believe the ELL's average around 12 moves to finish. Again, also this step uses only MU moves, and is incredibly quick. Using the few ELL's I know, I managed a 15.02 and a 15.92, neither of which were lucky at all. Both were 3 short substeps. Considering my best non lucky is a 14.33 with a ZB case I know, I'd say a 15.02 on my second day isn't too bad. :) That's actually .65 seconds faster than my fastest normal Roux time ever. The third special case group is much less frequent than the first two, and comprises all of the miscellaneous cases I've found that are easier and faster than the other ways. Good examples are (M'U)*4 and various others built from that. Speaking of which, Jason, what do you think of U' (L U' l') U (M'U)*3 (L U L') U? Others that fall into this category are M2U2M2U2, ME2M'E2, etc. This group will hopefully be much more full once I figure out some nicer optimizations. Gilles, I'd really like to know how you found your special cases for step 4. I think I may be able to adapt some of them to this. There are certainly some unpleasant cases that come up, and I'd like to see if I can shorten them at all. The last group is the normal group of solves. In these, you place DB, then place DF and orient the remaining 5 edges, then finish the LL edges. This is where the most difficult cases are, and also some of the nicest. The first substep is placing the DB edge, and averages 3.5 moves, but if you start with any of the 4 possible DB edges, this drops to under 3. Sometimes it works well to perform a d2 after this step, if you actually have to place the edge to DF. Next, inserting the DF edge while orienting edges averages 6.5 moves, but I have some ideas about how to shorten that. When placing the DB edge, it's often possible to either influence the orientation to your liking, either by preserving a good one, or swapping a bad one. 50% of the time, this only requires adjusting the U face to insert from the opposite side. The cases I'm having trouble finding good ways to fix are when the DB edge is properly oriented prior to insertion. The only good ways to insert it also preserve orientation of the other 5 edges. This is something I need to work on. Finally, you need only permute the LL edges, averaging ~6.75 moves. A possible route to take involves always achieving an easy orientation with the DB edge, so that you can orient the remaining 5 and permute them all at once. There are really only 6 possible orientations after the DB edge is placed. 1 is correctly oriented, another is 3 edges on top (the 'magical' orientation from Gilles' method). The first takes zero moves, obviously, and the second takes 3 (or 4, if you need to AUF). Incorrect adjacent edges takes at least 7 moves to orient, incorrect opposite edges takes a minimum of 9. All 4 U edges incorrect is an unfriendly case requiring at least 12, but for all of these groups, the ELL's are about as good as it gets. The cases that are tricky are the ones with DF and UF incorrect. These cases can be changed to correct orientation in 7 moves, or inserted with correct orientation in 8. This leaves you a L5E option with an average of 7, but worse recognition, or an EPLL for 1 extra move and easier recognition. Things to think about. I spent most of work tonight figuring out average move counts for the steps, and working out the odds of nice cases. With practice, you can place any of the DB edges in under 3, finish the L5E if they're oriented in under 7, finish with ELL if the F2L comes up solved in 12, or finish the normal way in 13, but the latter two can be lessened considerably if you wisely insert the DB edge, and choose the nicest edge to start with. Starting with any of the 4 possible DB edges gives you an almost 16% chance for an O5E skip, a 34% chance for an easy F2L finish, and leaves you with under half of the cases giving you a 'normal' solve, because that option needs the most optimizing still. Going with these odds, one can average around 15 moves quite easily with this method. Going slowly (because I'm still learning most of the algs ;P) I took some average move counts earlier. 13 17 16 12 17 13 20 17 20 7* = 15.2 10 12 18 11 16 18 17 15 15 13 = 14.5 12 12 16 13 17 16 17 11 18 18 = 15.0 = 14.9 overall * was an OLL skip after placing DB. With more ELL's and better P5E, I think this will drop nicely. If nothing else, the 15.02 was exciting enough to convince me to press on with this, even if it turns out to be less efficient or slower than what's already out there. Still, I'm convinced this step can be sub-4 pretty well. At least....in theory. ;P Anyone with ideas, criticism, suggestions, etc, please post. Gilles and Jason especially. Don't be so quiet, guys. -Mike P.S. Ron's Cube solver sticker applet is a life saver. ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. 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