ADVANCEMEnts

• Upon arriving at the EO step, the DR edge can be solved along with the EO.

  • View APB EODR algs 

• When creating a pair after the 2x2x3, this pair can be set up to where it is one move away from being paired instead of fully connecting the two pieces. The EOPair step would then pair and insert the pair while orienting all edges. Or go even further with the corner and edge in positions that take more than a single move to pair up. There are likely situations where using an algorithm to build this pair + insert + complete EO will be better than having pair and EOPair being separate steps.

• The corner that is in the pair can be twisted or be the corner that goes with the other edge. Then this situation can be corrected during one of the algorithm steps. LXS, Twisted and or Swapped CDRLL, or while placing the other pair when using the L5EP variant. Correcting during EO is a possibility but the algorithms would need to be good.

• Instead of creating pairs that involve the D layer corner and an E layer edge, one of the pairs that occupy the D layer can be created. Then the LXS step will solve the remaining corner and two edges.

• Pseudo pairs may slightly improve efficiency. A corner can be paired with an incorrect edge or orientation. Then corrected during the EOPair step or LXS can solve the three remaining pieces while correcting the pair.

• If a pair is already solved in place, the user can set up another pair and do EOPair + place the final edge.

• Create or set up pair, EO + place pair + solve the other edge that goes with the pair. This forms a 1x2x2 and creates the LSLL state. This will be useful for any future LSLL advancements that are competitive with ZBLL. ZBLL users may also find it useful to use this algorithm set in certain situations.

• After EOPair place the two remaining F2L edges and continue with any of the sub-variants from the EOFE variant of Nautilus. It may also be possible to combine the two F2L edges step with the proceeding step of EOFE.

Will the future of APB be advanced combining of EO and the pair formation? Techniques such as EO and setting up the corner when the edge is in certain positions or EOPair when the pair is a move or two away from being formed. We will see. It will likely be worth analyzing when it is best to do EO and the pair in different orders. Pair then EOPair, Pair then EO, EO then pair, Pair then EO+DR edge. In some cases it may be easier and or more efficient to do an option other than always creating a pair then using an EOPair algorithm.

After the 2x2x3, there are 135 cases to orient the edges and solve just the BR edge. To include the DBR corner, consider that it can be in the U layer in one of three possible orientations or in the R layer in one of three possible orientations, resulting in a large number of one step EOPair cases.

If we orient the BR edge while solving the 2x2x3, there are 70 to 80 EO plus BR edge cases, significantly reducing the total number of one step EOPair cases.

But by using the symmetry and intersection of the U and R layers, the number of corner cases can be reduced. The corner can be within the UL, UR, or DR line. At UL or DR, an AUF and/or ARF can be used before the algorithm to change the orientation of the corner relative to U or relative to R. If the corner is within the UR line, either AUF or ARF are possible and would allow for a choice of orientation change for specific sets.

For a single orientation of DBR on the U layer, there are 448 cases to pair and solve DBR and the BR edge while orienting all other edges. The average number of moves using the <U, R, F, f, S> move set is 7.00 when generated and sorted by MCC in Batch Solver. Adding in .75 for pre-AUF for a 7.75 average one step EOPair would bring the overall method down to 44-45 moves. However, this doesn't include the ~2 move average for setting up the corner if case reduction is desired. It may be possible to influence while solving the 2x2x3. Possibly by forcing DBR into a desired position, orienting the BR edge to reduce the number of one step EOPair cases as stated above, or generally orienting any edges to remove the possibility of six misoriented edges. There is also possibly a good iterative solving strategy to make one step EOPair intuitive.

Another idea is to solve the last pair after EOPair then finish with CDRLL and L5EP. This isn't recommended since it's not as suitable for speedsolving. But it is an option. After EOPair solve the opposite side pair. Then finish with CDRLL and L5EP. Versus BR edge > EOLE > DCAL, APB's EOPair > Pair is more ergonomic, the same number of moves, and fewer algorithms. Another great benefit is that CDRLL + L5EP works for both 2x2x3 on the left and 2x2x3 on the back. If 2x2x3 on the back is used with BR edge > EOLE > DCAL, the algorithms for DCAL aren't good due to the restriction of having the E slice edges solved, combined with the fact that the two D layer corners are on the front. But in APB the ergonomics are much better and the movecount is even lower than having the 2x2x3 on the left. So you can choose to use block on left for slightly better ergonomics or block on back for slightly lower movecount.

Block on left steps:

Step 1: 2x2x3 on the left.

Step 2: Create the pair that belongs in the back (dBR).

Step 3: Use the EOPair algorithms to insert the pair while orienting all remaining edges.

Step 4: Solve the pair that belongs in the front (dFR).

Step 5: CDRLL.

Step 6: L5EP.

Block on back steps:

Step 1: 2x2x3 on the back.

Step 2: Create the pair that belongs on the left (dFL).

Step 3: Use the EOPair algorithms to insert the pair while orienting all remaining edges.

Step 4: Solve the pair that belongs on the right (dFR).

Step 5: CDFLL.

Step 6: L5EP.

APB can also be applied to other methods such as ZZ, LEOR, and some of the CP first methods. In ZZ EOLine users can use a similar strategy for the right side block. In the first step you create a pair and keep it on the U layer. Then use a single algorithm to insert the pair while solving the remaining three pieces. Below are the algorithms for when the front pair (dFR) has been created:

View algs