So I have had a wondering of how various algorithms are made and why people use them. Some are generated. Some are discovered and popularized. For example, the lefty Nb perm is said to have less overwork then the righty Nb algorithm. Why is this and how does it affect speedcubing? How are these algorithms discovered/popularized?
Algs are often generated by programs like Cube Explorer, and sometimes by experimentation. Algs are generally popularized via Youtube, Discord, or forums like SS.
Inverse: Think of this as "undoing" the alg. If I have R U F' D B' L2 as the original alg, then to undo it I'll have to start with undoing the last move with an L2, then the second-last with a B, then the third last with a D', etc., eventually leading to L2 B D' F U' R'. If you do the original then the inverse, the net change will be nothing, and likewise if you do the inverse first then the original.
Mirror: Literally what it says. Pick an axis to mirror on, e.g. the front-back axis. Using the same example as above, R U F' D B' L2 becomes R' U' B D' F L2. If you hold a cube up to a mirror and do the original alg, what you see in the mirror will be the mirrored version, and vice versa.
A lot of PLL cases are self-inverse (if an alg solves it, so does its inverse) and/or have reflection symmetry (same concept but with mirroring), so you can often try inverting or reflecting an alg to see if the fingertricks are better. This trick is less applicable to other common alg sets (e.g. OLL, CLL) because less of the cases are self-inverse or have reflection symmetry.
In fact, "self-inverse" almost never applies to OLL—the only two OLL cases that are self-inverse are OLL skip and OLL 20.
This doesn't by itself mean that inverting an alg is useless. For instance, M' U M U2 M' U M and its inverse (M' U' M U2 M' U' M) both solve the same OLL case; one may be faster than the other depending on which hand you do M moves with. What it really means that you cannot tell from the OLL case alone (i.e. without considering the specific alg) which case the inverse alg will solve.
Algs are not cases. Algs are move sequences. Cases are patterns on cubes. You can always invert algs (more technically, you can do this because the algs live in a mathematical structure called a "group"), but you can't always invert cases.
If this seems too complicated: don't worry about it.
Inverse: Think of this as "undoing" the alg. If I have R U F' D B' L2 as the original alg, then to undo it I'll have to start with undoing the last move with an L2, then the second-last with a B, then the third last with a D', etc., eventually leading to L2 B D' F U' R'. If you do the original then the inverse, the net change will be nothing, and likewise if you do the inverse first then the original.
Mirror: Literally what it says. Pick an axis to mirror on, e.g. the front-back axis. Using the same example as above, R U F' D B' L2 becomes R' U' B D' F L2. If you hold a cube up to a mirror and do the original alg, what you see in the mirror will be the mirrored version, and vice versa.
A lot of PLL cases are self-inverse (if an alg solves it, so does its inverse) and/or have reflection symmetry (same concept but with mirroring), so you can often try inverting or reflecting an alg to see if the fingertricks are better. This trick is less applicable to other common alg sets (e.g. OLL, CLL) because less of the cases are self-inverse or have reflection symmetry.
In fact, "self-inverse" almost never applies to OLL—the only two OLL cases that are self-inverse are OLL skip and OLL 20.
This doesn't by itself mean that inverting an alg is useless. For instance, M' U M U2 M' U M and its inverse (M' U' M U2 M' U' M) both solve the same OLL case; one may be faster than the other depending on which hand you do M moves with. What it really means that you cannot tell from the OLL case alone (i.e. without considering the specific alg) which case the inverse alg will solve.
Algs are not cases. Algs are move sequences. Cases are patterns on cubes. You can always invert algs (more technically, you can do this because the algs live in a mathematical structure called a "group"), but you can't always invert cases.
If this seems too complicated: don't worry about it.
