YMove Method

The LBLY Method is a 3x3x3 beginner method. It is a layerbylayer method with workspace similar to the 8355 Method and SAM. The basic design goal is to rely only on a single algorithm, the elementary commutator F R' F' R. The LBLY method shares the singlealgorithm property with Less is More, which also uses F R' F' R, and SAM, which like the 8355 Method uses the elementary commutator of type F R F' R'. Both LBLY and Less is More can be viewed as simplifications of the 2algorithm method by Philip Marshall.
The LBLY method is an example for beginner level intuitive solving, since in all but one step the focus is on moving a single piece with the elementary commutator.
The Ymove
The method is built around the use of a single algorithm, which this method calls the Ymove. We define
 Y = F R' F' R.
In what follows "do a Ymove" means doing a Ymove or its inverse defined for any two faces that share an edge, not just F and R. What really matters is that a Ymove performs some really simple operations on the cube with little side effects. The Ymove
 only affects the cubies along three cube edges meeting at a corner (a Yshaped region, therefore the name),
 cycles three edges around that corner, one edge is flipped,
 swaps two corners, including a certain rotation.
The Ymove, together with some elementary quarterturn moves to prepare and restore the cube, can solve the cube in a simple manner.
Procedure
Step 1: Solve 4 Bottom Edges
 Use elementary moves.
 Since the only restriction is to preserve solved bottom edges, elementary moves for prepare, work, and restore are sufficient.
Step 2: Solve 3 Bottom Corners
 Use Ymove to move corner cubies between top and bottom layer.
 The Ymove also rotates the cubies. Worst case is bottom facelet on top, which you can do with Y and a sideway Y, or with three standard Ymoves.
 Or use elementary prepare/work/restore.
 Not much harder than Step 1 because only the bottom layer has to be preserved.
 Leave one corner unsolved as part of the free workspace.
Step 3: Solve 3 Middle Edges
 Use Ymove to move edge cubies between top and middle layer.
 Pick Ymove to do the move with or without flip.
 Prepare bottom with D to put free corner cubie at the foot of the Ymove that you want to do. Restore afterwards.
 Straightforward because we can focus on moving and flipping a single cubie, and because we can do Umoves freely and have a free corner cubie in the bottom.
 Leave the edge above the free corner unsolved as part of the free column.
Step 4: Adjust Swap Count of Remaining 5 Edges
 We would like to solve the remaining edges with Ymoves in a standard prepare, Y, restore conjugate. Such moves do an even number of edge swaps. Therefore, first count the number of edge swaps that we need to perform.
 If even, proceed to Step 5.
 If odd, perform a quarter Uturn, then proceed to Step 5.
 If confusing, count again after the single Umove. Or solve one or two of the edgies, and then count. Correct with single U as needed.
 This works because a single U amounts to an odd number of swaps.
Step 5: Solve Remaining 5 Edges
 Use Ymoves and symmetric conjugates like U Y U' to move and flip edge cubies in the top layer and the workspace edge in the middle.
 Make sure to only do an even number of U quarterturns to preserve the even swap count created in Step 4.
 Straightforward because we can focus on a single edge cubie and how to move and flip it with Y.
 There are minor restrictions on the order in which we solve the edge cubies. Start with solving two adjacent edgies in the top layer, say the two in the back away from the workspace. Adjacent and not opposite to each other because Y works on adjacent cubies. In the top layer because we need the workspace edgie until the end.
 Straightforward also because after solving 3 edges the remaining 2 fall into place automatically. We cannot get stuck with a single swap missing because in Step 4 we made sure that there is only an even number of swaps. If there is a mistake, simply redo Step 4.
 With 3 of the 5 edges solved and the last 2 edges in their correct position, either we are done or we need to flip those 2 edges in place. This is a standard application of two Ymoves.
Step 6: Position Remaining 5 Corners
 Use two Ymoves. Use Y to move a corner cubie out of the top layer into the bottom workspace corner, then use Y' to bring it back into the top layer in a different position.
 For example, y U y' U', where y is the 'upsidedown' Ymove that affects the workspace edge and two edges in the bottom (as opposed to in the top).
 Straightforward because we can focus on moving a single cubie. But we have to do it twice, back and forth between top and bottom with Y and Y', in order to preserve the edge cubies.
 Straightforward also because after positioning 3 corners the remaining 2 fall into place automatically. We cannot get stuck with a single swap missing, since after solving the edge cubies there can only be an even number of corner swaps. Count them.
 Optional for efficiency, but natural: First check the corner cubie in the bottom workspace. If it is from the top layer, focus on moving it to the top with the right orientation (works if top facelet is on the side). Then undo that Ymove by its inverse bringing an other corner cubie down.
Step 7: Solve Remaining 5 Corners
 Use four Ymoves. Use YY to rotate a corner cubie in place without moving it, then swap in another corner cubie and use Y'Y' to rotate it into the opposite direction while restoring the cube.
 For example, yy U y'y' U', where y is the upsidedown Ymove.
 Straightforward because we can focus first on rotating a single cubie, then on rotating a second cubie in the opposite direction.
 To rotate the bottom workspace cubie, apply additional preparation moves, perhaps simply turning the entire cube, so that it is moved to the top together with the second cubie. Or apply the ymove sideways.
 The yyy'y' move applies one clockwise and one counterclockwise rotation. Do this twice to handle the case of three clockwise (or counterclockwise) rotations. Or use yyyyyy with appropriate U setups to do three rotations in the same direction.
 Finishing the last rotations with pairs of clockwise/counterclockwise rotations works because the cube can only have inplace cubie rotations that add up to multiples of 360 degrees.
Comments
Remarkably, it is sufficient to focus on a single cubie at a time and use a single sequence (in several different ways). Focus on one cubie and move it with Y while flipping/rotating it along the way. Clearly, if we really could move and orient single cubies, then we could solve the cube. The catch is that there always are side effects. There is no move changing only a single cubie. Therefore, it is a nontrivial statement that we can do Ymoves in the way described focusing mostly on a single cubie, although two or more cubies move. The laws of the cube ensure that in the end the last cubies fall into place and/or are oriented automatically.
With only minor changes LBLY (and 8355, SAM) becomes a beginner's edgesfirst method: Postpone step 2 until all edges are solved. In this way LBLY becomes an edgesfirst method similar to the Philip Marshall Method, but using only one of the two algorithms of Marshall's method.