# [zbmethod] Re: Idea time again...

```--- In zbmethod@yahoogroups.com, "Mike Bennett" <[EMAIL PROTECTED]>
wrote:
> What if you finished the F2L minus one pair?  As long as the corner is
> in the top layer, you have one of 3 possible cases.  Corner with white
> facing up, left, or right.  If you place this corner, there are 6
> possible cases for each of the 3 orientations above for fixing LL
> corner perm.  Most of these are simple and intuitive (just different
> ways to place the corner: RUR', U'F'UF, etc.).  18 cases total, not
> bad.  You could learn the 14 cases for when the corner is in the
> correct spot, if you wanted, but you pretty much always avoid those
> with some careful solving of the first three pairs.  COLL and CLL
> would come in handy, too.```
```
I take it back.  There are really only 8 cases for when the corner is
already in the right spot, and these come up 1/5 of the time, so it's
probably a good idea.  One of those is even just FRUR'U'F' or its
inverse. 18 + 8 = 26.  Still not bad to get all the LL cases down to
no corner perm.  All in all, this step should average between 5 and 6
moves by my calculations, but probably closer to 5.  If I can find
nice enough algs, perhaps even under.

> Next, if you solve the final middle layer edge, you can orient the LL
> edges at the same time.  20 more cases for fixing the LL edge
> orientation (edge in place but flipped: 4, edge at UR flipped: 8,
> mirrors of the last 8: 8).  38 cases (most of them are just 3 cycles
> of edges), and you're left with a no corners perm ZBLL.  Add in those
> cases, and you've got 72 more (76 with the edge PLL's).  114 total
> algs (just about half of which are reflections), but I'm not sure of
> the length yet.  I'll keep working on that and post again.

I was wrong again.  There are 3 cases for when the edge is in place, 3
for when it's in place but flipped,  and then the other 8 and 8.  That
makes 22 instead of 20.  The average length for these should be
between 7 and 9, but I'm not certain yet.  The upside to this is that
they're all performable with only MU and RU moves.  The hardest cases
are when 4 edges are flipped, but I'm working on ways to solve those
quickly. (read: Cubesolver, here I come...)

Anyway, that's about 124 algs total, a good chunk of which we all
already know.  The average length is about 12 or 13, so it's
comparable to learning ZBLL, but there are a whole lot less of them.

> 1/27 cases would be a simple edge PLL to finish.  If you could learn a
> few extra cases to place the final middle layer edge while also
> playing with corner orientation, you could increase that number
> substantially.  I know this may be a potentially longer method in
> terms of number of moves, but having an edge PLL for possibly 1/13.5
> solves or more has some definite potential. 1/162 solves, you get a LL
> skip!

Around 27.5% of the time, you're left with a Sune or Antisune ZBLL
case.  1/12 of those cases are just the normal algs.  Between those
and the edge PLL cases (not including the long Z perm), you have
greater than a 1/12 chance for a 7 move or less solve.  I wouldn't
mind getting a Sune only solve once an average.

As for the final move count, that's still a bit up in the air.
Assuming a 23 move F2L minus the last pair, 6 moves to place the final
corner and permute the U corners, 9 moves to place the final middle
edge and orient the U edges, and 14 to finish with ZBLL, that's still
a 52 move average.  However, I'm fairly certain you can get the F2L
step down closer to 20 using Xcross and opposite color solving, and
the other numbers are highballing it (just in case).  I think the
final average will be closer to 46-48 moves.  On top of only using 1/7
of the algs required for ZB (and only having 1/7 of the decision
choices to make on the fly, not to mention learning), it's got a great
potential for spike times with skips and short cases.  A great
possible case that includes all of the steps could be as short as 17
moves after the F2L step.  With a decent F2L, that's a non lucky
sub-40 moves.  Good enough for an advanced rank on the FMC.  Of
course, full ZB will inevitably average fewer moves, and have the
potential for bigger spikes and fewer moves, but I think this is a
nice compromise for number of algs and potential.

> -Mike

P.S.  This groups is too quiet.  Someone else post already.

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