APB
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APB (Athefre's pair and block) is a 3x3 speedsolving method invented by James Straughan. It is based on 2x2x3 blockbuilding and algorithms resulting in a high TPS.
Contents
Steps
 223: Build a 2x2x3 block on the left. The current recommended way to do this is to solve a Roux First Block in dL and add the DF and DB edges. Another way is to build a 2x2x2 then extend to a 2x2x3.
 dBR pair: Create an F2L pair that belongs at back (the DBR corner + the BR edge) and keep it on the U layer.
 EOPair: Orient all edges while inserting the pair. There are 63 total cases averaging 5.76 moves.
 LXS: Solve the final three pieces (FR + DR edge + DFR corner) of the F2L. This step contains 116 algorithms averaging around 8.59 moves.
 LL: Solve the last layer using any LL method. Since the edges are already oriented, the solver can use ZBLL which has 493 algorithms. Another approach is OCLL + PLL which has 28 algorithms and COLL + EPLL which has 46 algorithms.
Variants
1. APBCDRLL is a variant of APB that uses CDRLL and L5EP
 223: Build 2x2x3 block on the left. Itâ€™s usually good to do a Roux FB and finish the 2x2x3 by solving the DF and DB edges.
 dBR pair: Create an F2L pair that belong at back (DBR+BR) and keep it on the U layer.
 EOPair: Orient all edges while inserting the pair. There are 63 total cases averaging 5.76 moves.
 dFR pair: Create an F2L pair on the front (DFR+FR).
 CDRLL: Solve the last layer corners while ignoring the DR edge. CDRLL contains 42 algorithms averaging around 11 moves.
 L5EP: Solve the 5 remaining edges. L5EP contains 16 algorithms.
2. APBLEORCP is a combination between APB and LEOR which allows for much lower algorithm count and mid solve CP
 1X2X3 block: build 1x2x3 Block at the left or the right (it better being at the opposite side of your dominant hand) this step is the same as Roux and LEOR
 EOStripe: Orient all edges while simultaneously solving DF and DB. this step is the same as LEOR
 CPPair: solve the back pair (usually the RB edge along with the DRB corner) while permuting all of the corners. The beginner way to do it uses 10 algorithms to solve a paired pair and doing CP. the advanced way uses 210 algorithms and solve the CPPair from any case possible.
 LXS: Solve the final three pieces (usually the FR + DR edge + DFR corner) of the F2L. This step contains 116 algorithms averaging around 8.59 moves. This step is completely RU(S) gen.
 2GLL: solve the last layer using 84 algorithms that uses only RU(S) gen.
3. APBCP is a variant of APB that uses CP to do 2GLL. The method has about 830 algorithms.
 223: Build a 2x2x3 block on the left. The current recommended way to do this is to solve a Roux First Block in dL and add the DF and DB edges. Another way is to build a 2x2x2 then extend to a 2x2x3.
 dBR pair: Create an F2L pair that belongs at back (the DBR corner + the BR edge) and keep it on the U layer.
 EOCPair: Orient all edges while permuting all of the corners while inserting the pair. There are 630 total cases.
 LXS: Solve the final three pieces (FR + DR edge + DFR corner) of the F2L. This step contains 116 algorithms averaging around 8.59 moves.
 2GLL: solve the last layer with 84 algorithms consisting of R U S moves.
Pros
 Mostly algorithms, which is 7075% of the solve
 Good ergonomics, allowing for higher TPS
 No rotation required
 Low movecount
Cons
 High algorithm count
 Mid solve EO, although a solver can easily get good at EO recognition by tracking the FR edge while creating the pair that belongs in the back, hence making EO recognition very easy.
 Since it's a very new method the algorithms are not very developed and because of that tutorials are lacking.