Carry on... (although I think we should look at L7E in general)I really like the idea of mixing in L5C with Roux. The method I use for L7E in the latest LMCF still isn't optimal, and so I was thinking about L7E skips and I think there is an option to force L7E skips without 3,000 algorithms.
It isn't a modification to Z-CELL, it's a modification to Roux with L5C, but anyway.Consider this modification to Z-cell:
With current movecounts that gives 7+7+10.75 (ish)+4+12(ish)=40.75 which is very very good. If you go the other route and get a movecount of 15 or less for L7E then you have 7+7+10.75 (ish)+15=39.75 which is revelutionary tbh.1. When generating the 614 L5C algorithms, choose variants where the FR edge is dislocated/disrupted; this should not add any moves to the average since in almost every case the FR edge will be disrupted
2. For each of the 614 L5C algorithms, memorize the effect that it has on the FR edge; more specifically, memorize the starting location of the edge which ends up in the FR slot after the L5C algorithm (location + orientation)
3. Now solve first block, and back right corner.
4. We are now at the L5C step. Having looked ahead during solving of the back right 2x2 block, you know where the FR-destined edge is (in one of 7 possible locations); now use M/U moves to place that edge in the correct location such that it gets automatically solved by the L5C algorithm. According to my calculations the average number of moves this will take is about 4, with no case taking more than 5; however there is a 1 in 7 chance the FR edge is already in the FR slot which is a case we cannot easily resolve without learning another 614 algorithms
5. Do the L5C algorithm; now in 6 of 7 cases, you skip the FR edge
6. Finish with Roux L6E-EOLR
Using this method, 6/7 (85%) of the time we skip the FR edge and go directly to L6E. 1 in 6 (14%) we need to solve the FR edge after L5C. It is of course possible to learn 3 sets of L5C algorithms to deal with that 1 in 6 chance, but probably not worth it for most people.
So using this method, almost every solve you skip the last roux slot (7.5 moves average according to PapaSmurf), and that step is 'replaced' with pre-location the FR edge into the correct location such that it is automatically solved by the L5C algorithm, and that step takes around 4 moves average, so we dropped the move count by 3.5.
For the extremist who is willing to learn 1800 algorithms, you learn 3 variants of each L5C algorithm, the two additional variants deal with the case where the FR edge is already in the FR slot and oriented, the other case is where the FR edge is already in the FR slot and disoriented. While few people would learn all 1800 algorithms, those cases are crazy awesome, because if you knew the 1800 algorithms, then if the FR edge is in the FR slot (oriented or disoriented), you now get a full last-slot skip, since you do not need to pre-locate the FR edge and it is solved by the L5C algorithm variant. So in that case, you save a full 7.5 moves over Roux (plus, possibly an extra move and a half based on L5C taking slightly less than CMLL).