VHLLLau Method51.35 to 58.59 Move Average (Standard Lau)By: Ralph Laurence I. RoqueIB -1 / pArrow I-F2LZBIB -1 / pArrow I-F2L43.35 to 50.59 (Advance Lau)IB -1 / pArrow I-F2L OLL + PLL59.35 to 66.59 (CFOP to Lau ‘Beginners’)
A. Inverted Base -1 (IB -1) / pArrowEssentially, the solver needs to make a cross -1 (to stage a 2x2x3). The difference here, however, is that one hasto create in such a way that there is 0-1 rotation only, and the transition to the next stage (Inverse F2L) isflexible. The pArrow should then be misaligned to the center to its relative, polar position. Preferably, position itmisaligned already.. Then, after I-F2L, D2 to realign and fix the missing peace of the cross.Lau MethodFront Lookahead3-5 Move AvgBy: Ralph Laurence I. RoqueRegular Algs 1.F R’ F’2.f R’ f’ R3.r U R’ U’ r’1.F’ L F2.f’ L f L’3.l’ U’ L U lBack Insert 1.f’ U f 1.f U f’3-5 Move AvgHere we will just orient the last edge of the incomplete cross; onecan insert it in such a way that it also a pair when the case presentsitself. When the final cross edge is in the wrong orientation to do asimple [RL] move, align it at the right pole or your front view and doeither inserts f R’ f’ R, another is F R’ F’ (lowest move count) or r UR’ U’ r’ (ergonomically smooth). When in the back, if one does notwish to align it and just solve it in the back in a way that avoids Bmoves the algorithm is f’ U f.Front: Position your front preferably from start to finish front so you can look at the right and left poles of the IF2L stage.Lookahead: Expand your vision of the I-F2l by being able to see the right, left, and front view of the cubemaking, removing the need for B, B2, B’ moves, and being able to guess, look ahead, and predict with easeEdges needed to be solve at the other pole, and trasition well into solving the corners on the other pole (more onthat later).51.35 to 58.59 Move Average (Standard Lau)
Lookahead due to the preferred Front removes a lot of reason to cognitively rotate or relook to see the edges.And because IB-1 / pArrow was misaligned, it transitions well for I-F2L Because we solve the edges on the otherpole while solving the corners on another. This also makes it also flexible for R/L/U moves.B.1 Inverse First Two Layers (I-F2L)In this type of F2L, the edges of the “other pole” (the one that ties the red and orange together, in this case it isgreen) are solved first, and then the corners. Given that it borrows ideas from pseudoslotting, keyhole yet it doesnot necessarily fit either the concepts; its defining structure is the splitting of poles in a twisted or “invertedmanner”. Everything is conceptualized like a pseudo 2x2x3 block, pseudo-cross, inversion making this methodbe comfortably called PFOP. In omitting a corner in using D move, make sure that it is omitted so as to preparefor a 3 move insert.This makes your inspection faster and focus on trying to fix the two edges of the pole, make it, when practiced,less cognitively demanding than CFOP, Roux, ZZ, APB, and other advanced methods. Secondly afterrealigment, the last 2 pairs as well as fixing the cross becomes highly predictable making spammingalgorithms easier or intuitively fixing it because it has an easy look ahead, it limits the possible conditions ofthe edges and corners to the two slots and U frame. This method intends to make the whole solverotationless in principle every time.1st or 2nd to solve (Edges) Front 2nd or 1st to solve (Corners) Average 4-6 Moves (use u) Average 4-10 Moves Realign Using D2
Edge Disposition and Movement Patterns Case 2Case 1XY2-5 Move Avg [R, L] U movesCase 2Case 2Case 1 Case 1YY1 Move [R, L] moves [R, L] F U moves ZY/ZYX6-8 Move AvgIt is unlikely to have both of the Edges to have ZXY/ZY patterns especially when the edges areplanned on inspection, it is also plausible to avoid them entirely, further one can reduce thedifficulty by using Uw moves to bring the other pole to your vision ans change the patterns froma bad (ZY/ZYX) to a good (XY). I provided a case algorithm for these at the later partr of thisguide.I-F2L Corners The use of D moves here is highly recommended, and the principles of keyhole is important; being exposed to pseudoslotting isadvisable. I did nevertheless developed Algorithms that utilized Wide “F, U” moves here, which will be presented in the algorithmpage of this method manual. I have yet to discover their possible uses besides avoiding D moves (though, as I found, D ishighly efficient and intuitive), future PFOP method developers and investigate possible uses of it, its effect on corners, edges,possible efficiency for double slotting.The separation of the two is the cost of easily solving the Base Edge in BEO. In methods that use Cross (-1), issuesarise of not being able to predict the last edge to complete the cross, other times it requires EO-line like on ZZ, APB,which are time consuming and cognitively laborious. Others that do not do the EO-line struggle because of awkwardcases and makes it susceptible to mistakes. But in solving the first half of F2L thorugh I-F2L, it makes predicting thefinal cross edge easier as the blocks and corners that are inverted prevents the missing edge to move tounrecognizable positions. Furthermore, because of I-F2L, after alignment, transitioning to F2L rotationless is easy,removing the need to excert cognitive labor to EO.
B.2 First Two Layer (F2L Proper)At this stage, you remove cognitive overload and generate a state of precision predictability, this last twopairs increase TPS due to good look-ahead and remove A LOT of possibilities. From 124,416 possibleF2L states, reduced to 1681 F2L states, (41 x 41) having only 41 F2L cases, most of which, to anintermediate CFOP solver already know. All of these cases can be inserted rotationless. Additionally youcan even learn double slotting or easily develop a mental image to do so. In reality if we do consider thewhole state of both it has 10,368 states (whether they are paired or not paired at the moment), but on apractical note we can exclude those cases where there are just U from AUFs (it is 2,592) and R AUFs(1,296) considerably, if we took the higher end (the purely mathematical, without pragmatics) it is still114,068 states lower. It is recommended however, to solve the back then the front for VHSL.Sample algorithm1.L U2 L’ U2 (L U’ L) / R’ U2 R U2 (R’U R)2.Sledge/Reverse Sledge [R/L]3.Sexy Move4.Reverse Sexy Move5.R U R’ / L’ U’ L6.Rw U R’ U’ Rw’ / Lw’ U’ L U Lw7.R U2 R’ (U R U’ R’) / L’ U2 L (U’ L’ U L)8.R U R’ (R U R’ U’) R U R’ / L U L’ (L U L’ U’) L U L’9. M’ U2 R’ U R U M / M U2 L’ U L U M’10.U' R' F R F' R U' R' / U L F' L' F L' U L11.U' R U' R' U2 R U' R' / U L' U2 L U' L' U' L12.U' R U R' U F' U' F / U2 F U F' U' L' U L13.R2 U R U’ R2 / L2 U L U’ L214.Rw’ U R U’ M’ / Lw’ U L U’ M15.Fw R’ Fw’ / Fw’ L FwAverage 9-14 Moves(Not considering VHLS 6-9)B.3 - C.2 Two Look COLL / VHLS + VHLLThe philosophy of the Lau (PFOP) method is to efficiently use cognition without overusing it. Thisimplies prediction, lookahead, better inspection, and rotationless solve with relatively competitive movecount. While one can use ZBLL, ZBLS, VLS, it takes longer recognition time. Therefore, the standardmodel for PFOP would have been for me COLL if one intended to do the front slat insert first (asback VHLS is inefficient to do), and Intuitive VHLS + COLL when the final slot to be solved is in thefront view, as this is more efficient. Only use VHLS if it is already set up, if not, do Two Lokl COLL.VHLS / S-VLS / W-VLS COLL EPLL VHLL Average Moves 24-30
This is not to say that the use of the ZB method is not acknowledged; one may use that and master it as itwould benefit you more if you do so. The intentional recommendation for using Intuitive VHLS + COLL is ittransitions well and it can be readily mastered. I also recommend an alternative like just do OLL because it’salso fine. VHLS is approximately 32 algorithms, plus ust learning just 30-42 COLL. The advantage is itreduces it to 4 possible outcomes: PLL Skip, H/U/Z perms all of which are easy to recognized andpredict. Only really an unexpected OLL skip would have you do 1/17 of the orher non edge PLL.Advantages of Lau Method (PFOP)1.Easier inspection and early planning - The method allows efficient planning ofthe pArrow and the first two F2L edges during inspection. Unlike EO-basedsystems such as Petrus or ZZ, it does not require tracking edge orientation,reducing cognitive load and inspection pressure.2.Maintains rotationless solving - The structure naturally supports rotationlessF2L, improving fluidity and reducing unnecessary cube turns. With mastery, thismay allow higher TPS due to ergonomic efficiency.3.Moderate move count - The method maintains a competitive move count whilebalancing structure and flexibility, avoiding excessive inefficiency.4.Strong ergonomic potential - Emphasis on D-layer usage, wide U moves, andpole-based solving can create ergonomic turning patterns once adapted to.5.Improved lookahead and prediction - The structured transition into F2L propermakes lookahead easier and allows clearer prediction of upcoming pairs and thelast layer.6.Develops advanced slot awareness - It trains recognition of keyhole andpseudoslotting opportunities, encouraging deeper slot control.7.Efficient last layer pathway - The recommended VHLS/VLS + COLL pathwayprovides an efficient and structured last layer, often guaranteeing a cross stateafter COLL.8.Lower cognitive demand than EO-based systems - Does not require strictedge orientation tracking like Petrus or ZZ, making it mentally lighter duringsolves.
Disadvantages of Lau Method (PFOP)1.Initial unfamiliarity of I-F2L - The Inverted F2L phase is not intuitive for most cuberstransitioning from CFOP, Petrus, and other methods which may temporarily reduceTPS.2.D-move adaptation required - Frequent D-layer usage at the corner part of I-F2L canfeel awkward or regrip-heavy for cubers not accustomed to it.3.Possible reliance on left-handed algorithms - Depending on pole orientation, someleft-handed algorithms may be necessary.4.Requires mastery of rotationless solving - To maximize efficiency, cubers mustlearn and practice approximately 41 rotationless F2L cases (potentially fewer withdouble slotting).5.Higher algorithm count than other CFOP Alternative - Although structured, themethod still involves a large number of algorithms, similar to criticisms aimed at CFOP,ZB.6.More complex last layer pathway - VHLS/VLS + COLL is less simplistic than thestandard OLL to PLL approach.7.Preference toward full cross methods - Some cubers may prefer solving a full crossimmediately rather than using a 2×2×3 or delayed-cross structure.8.Not as low move count - While efficient, it does not outperform blockbuildingmethods like Roux, Petrus, or ZZ in raw move count.
u L u’ u L’ u’u2 L’ u’ L u’L u L u’ L’‘u L2 uu R2 u’L R’ U2 L’ RR’ u R u’ R’L u’ L’ u L’u2 L u L’ 6RealignRealignCase 0 Case 1 Case 2 Case 3 Case 4 Case 5I-F2L algorithmsPart 1 (without Edge Pair)There is no need for realignment here at the moment because it depends upon howone approaches getting the second pair. The objective of this algorithm set is to solveit in the most optimal way. Kindly just focus on the blue edge that is misaligninstead of the other pair.Case 0 Realign
u’ D2 R D2 u R U R’F’ L D’ L’ D L F LL’ U’ L u L’ u’R U R’ u’ R uF’ L F L’u L’ u’u’ R’ uR U R’ u L u’L u L u’ L’R’ u’ R’ u RF’ L’ FU’/U R’ U/U’U/U’ L U’/U ‘u L2 uu R2 u’L R’ U2 L’ RR’ u R u’ R’ReaL u’ L’ u L’lignCase 0 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6I-F2L algorithmsPart 2 (with Edge Pair)I decided to give the Edge algorithms with Edge Pairs for the person reading this tounderstand how it influences the edges. All other combinations are just differentversions of these 5 cases.
I-F2L algorithmsPart 1 (Single Corners and Corner Pairing) R U f’ U’ f S R2 S’f F’ R2 f’ FR U’ R’ S R2 S’R U’ R’ f F’ R2 f’ FU’ R U’ f’ U’ f R’ U’ F R F’R U R2 U’ RS’ U f R2 F’ RU (R U’ R’) U (R’ U’ R)U’ (R’ U R) U’ (R U R’)R U2 R’ U R U R’ U R U R’Corner Pairing (Advance)L2 U2 L2 S U2 S’M2 U2 M2 S2 U2 S2M F2 M’ U’ S R2 S’Single Insert (For Beginners Lau, Not Accounting Corner Pairing)All white corners that are at the side can be inserted in 3moves with realignment (R U R’ / R U2 R’/ R’ U’ R/ etc)Those that are on the top however, can be inserted 4moves (with R2 F moves) or 6 moves, making it the whitenot on top then 3 move insert.Those at the bottom may or may not require D move, when *if itis on the Edge pole it does, otherwise it does not. You can alwaysaboid making a with top when you put the corners on the top bychanging the way you do U moves that way it is just in total 6-7moves rather than 9-10 moves.R’ U’ R U’ S R2 S’R’ U’ R U’ f F’ R2 f’ F#1 #3 #4 #5#6 #7 #8 #9#10 #12 #13To be Continued...
F2L (Proper) algorithmsBest Page to Learn ishttps://speedcubedb.com/a/3x3/F2L/F2L_1#google_vignetteLearn Backslot and Mirror cases.I will handpick the what I consider the best algorithm per cases in thefuture
U2 (R U2 R’)U (R U' R') R' F R F'U’ F’ U Fd' (L' U L)F R’ F’ Rr U R' U' r RR U R’U F' L' U' L F U (F' U F) (R U' R') U2 F R' F' R2 U2 R'Vandenbergh-Harris Last Slot (VHLS) algorithmsCase 2 Case 2 Case 3 Case 4 U (F' U2 F) (R U' R') M U R U' R' U' M' U2 (R U' R') U' (R' F R F') U2 (R' F R F') U2 (R' F R F') Case 5 Case 6 Case 7 Case 8 U (R U R') U2 (R' F R F') U' (R U' R') (F' U F) Case 9 Case 10 Case 11 Case 12 U' (R U2 R') (F' U F) y L U F' U' L2 U L F R' F2 U' F U R U2 (F R' F' R) U2 (F R' F' R) Case 13 Case 14 Case 15 Case 16 F U R' U' F2 U F R (R U' R') U2 (R' F R F') (R U' R' U') (R U R' U2) R U R’ U F (R U R’ U’) F’(R' F R F')Case 17 Case 18 Case 19 Case 20 U2 r U' r' U' r U r' S' R U R' S U' F' L' U L F U2 F' U L' U L F y L F' L2 U' L U F
y U2 F U R U' R' U' F'R U' R2' F R F' R U2 R'y ‘ R’ U’ RF’ U’ F F' U' L' U' L U FU' F' U2 F R' F R F' R U2 R' F' U F R U' R' R U' R2' F R F' U2 R' F R F' Case 21 Case 22 Case 23 Case 24 S R U R' U' S' y' U2 r' U r U r' U' r U R U2 R' F R' F' R U R U2 R' U' y' R' U R Case 25 Case 26 Case 27 Case 28 F’ U’ F U’ f (R U R’ U’) f’ F' U2 L' U L F R U' R' U F' L' U' L U' F Case 29 Case 30 Case 31 Case 32 U2 F' U' L' U L U F y' R D r' U' r D' R2 U' R (R U R’ U’) f (R U R’ U’) f’ R U R’ F (R U R’ U’) F’To better use the VHLS Algorithms that I put forth, those in bold text are consideredthe recommended ones, as they are more ergonomic, have fewer moves, arerotationless, or are both. Those text in red however, are those that have rotations,although in this guide some are in bold text, to consider the audience preference butstrictly speaking the guiding principle is rotationless. Those texts in green arerecommended algorithms that modify or change entirely to be rotationless, moreergonomic, less move count or both, some are cancellation and repairing algs as not allVHLS algs especially in the guide i dominantly used are better to follow.
R U R' U R U' R' U R U2 R' R U R' U r' F R F' r U2 R' L U2 L' U' L U' L' R U R' U' R' F R2 U R' U'R U R' U' F'Corners of Last Layer (COLL)Vandenbergh-Harris Last LayerF (R U R’ U’)*3 F’ Case 1 Case 2 Case 3 Case 4 R U R' U R U L' U R' U' L F R U' R' U R U2 R' U'R U R' U' F'R U' L' U R' U L U L' U L R' U' F' R U R' U' R' F R2U2 R' U2 RCase 5 Case 6 Case 7 Case 8 R U2 R2 U' R2 U' R2 U2 R R2 D' R U R' D R U RU' R' U R U R' U RR' F2 R U2 R U2 R'F2 U' R U' R'Case 9 Case 10 Case 11 Case 12 R U R' U R U2 R' F R' U2 R F' R' F U2 F' R R U' L' U R' U' L Case 13 Case 14 Case 15 Case 16 R' U' F U F' R U F U2 F' R' U2 R U2 L U' R' U r’ R F' L U2 L' F L F' U2 F L' Case 17 Case 18 Case 19 Case 20 R' U' R U' L U' R' U L' U2 R R' U L U' R U L' Case 21 Case 22 Case 23 Case 24 F U R' U' R F' U' R' U2 R F U2 F' U' R' F U' F' U R R' F R U' R' U' R U R' F' R UR' U' R' F R F' RR2 D' R U R' D R U R U' R'U' R
F R' F' r U R U' r' R' U R2 D r' U2 r D' R2 U' RCorners of Last Layer (COLL)R' U' R U' R' U2 R2 U R' U RU2 R'Case 25 Case 26 Case 27 Case 28 R2 D R' U2 R D' R' U2 R' F R U' R' U R U2 R' U'R U R' U' F'R U2 R' U' R U' R2 U2 R UR' U RR' U R U2 R' L' U R U' L Case 29 Case 30 Case 31 Case 32 R' U R2 D r' U2 r D' R2 U' R F R U R' U' R U' R' U'R U R' F'Case 33 Case 34 Case 35 Case 36 R U2 R D R' U2 R D' R2 R' U2 R' D' R U2 R' D R2 F' r U R' U' r' F R Case 37 Case 14 Case 15 Case 16 R' U2 R U R' U' R U R' U'R U R' U Rl' U' L U l F' L' F r U R' U' r' F R F' R' U' R U R' F' R U R' U'R' F R2The way I organized this is, the easiest to recognized first, with the exception of Sune and Antisune as they are moderately hard to recognize and awkward to executive, other even prefer not toinclude that nevertheless I believe they are just as importan to learn. I handpicked everyalgorithms considering their move count level of familiarit.Vandenbergh-Harris Last Layer
Edge Permutations of The Last Layer (EPLL)I provided both the R U moves algorithms and the M U moves, as it really depends how one endsthe cube preferably. Most of the algorithms are highlighted in bold because they are equally asreasonable enders. M moves in the edge perms are generally known to be the most ergonomic bya lot of cubers, R U are traditional as well and could maintain consistenc. the H per R U algorithmhowever may not withstand or level with its M U move alternative, still I added that to reason thateven EPLLs can be done through R movesM2 U M2 U2 M2 U M2M2 U' M2 U2' M2 U' M2'M2 U M2 U M2 U M2 U M2 U M2 U (AUF)R2 U2 R' U2 R2 U2 R2 U2 R' U2 R2H Perm Z Perm M2' U M2' U M' U2 M2' U2 M'(U) M' U M2' U M2' U M' U2 M2'R' U' R U' R U R U' R' U R U R2 U' R'Ua Perm R U R' U R' U' R2 U' R' U R' U R(U2) M2' U M U2 M' U M2'(U2) R U' R U R U R U' R' U' R2Ub Perm R' U R' U' R3 U' R' U R U R2(U2) M2 U' M U2 M' U' M2(U2) R2' U R U R' U' R3 U' R' U R'Vandenbergh-Harris Last Layer