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(FMC) A guide for finding HTR's once you've found a DR

ottozing

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NOTE: This is not a guide for finding DR's. If you don't know how to find a DR in FMC/aren't a DR solver, this guide will be of no use to you. If you want to learn DR, I recommend this guide & to learn how to find DR's using EO, followed by some set up moves to 4C4E, 4C2E, or 3C2E, followed by set up moves to R, R U2 R/L F2 L', or R U/U' R.

This is the primary method of finding DR's that top solvers actually use (mostly using 4C4E). I may post a guide on this part of the solve in the future, but currently I think the resources for finding DR's are much better than the current resources we have for finishing after DR.

~

Credit to Jack Love & Rodney Kinney for being my primary source of inspiration for writing this guide. Everything within this guide is based upon their ideas & findings.

~

Intro

Generally speaking, the best way to finish a solve after you've found a DR is to do HTR, followed by solving 2 layers, leaving some E slice case such as M' U2 M U2 or M2 U2 M2 U2, followed by rewriting the HTR/Solve 2 layers steps in a way that solves the cube. Jack Love recently posted 100 example solves to the Facebook Fewest Moves group by generating human findable solutions for each scramble. Every solve uses EO followed by DR, and the vast majority continue with HTR into solving 2 layers, and then doing a rewrite. The Mo100 for these solves is less than 21 moves.

For the second step, the 2 layers you want to focus on will depend on what axis your DR is on. If your DR allows F and B quarter turns but not RLUD quarter turns, you'll want to focus on solving these layers once HTR is done to have the best chance of finding a re-write that adds 0-2 moves to your solution.

A quote from Jack Love (WR2 for FMC mo3) - "My advice if you want to get good: HTR 100% of the time. There are very few DRs for which the optimal finish after DR is findable with a non-HTR approach but not findable with a HTR approach."

Understanding corner cases

Now that we've established that HTR is worth mastering & what the last few steps are likely to look like, let's talk about something many DR solvers tend to struggle with; recognizing whether or not their DR has "good" or "bad" corners.

In short, the less quarter turns a corner solution needs, the better the DR is. DR's that need 4-5 quarter turns to solve corners (and by extension, solve HTR) are almost never worth checking unless the DR is shorter than average or very "blocky". Even then, due to the fact 4-5 quarter turn cases are guaranteed to have a fairly long HTR step, the odds of you finding the HTR that gives an optimal finish are very unlikely within the 1 hour time limit. Learning to recognize these cases before you commit to checking the DR is crucial so you don't end up wasting time.

On the flip side, DR's where the corners are solvable in 1-3 quarter turns are always something you want to check, so it would be a shame if you didn't know how to recognize every case within this range. These cases in my experience almost always have what I would consider a findable optimal finish, and it's usually 13 or less moves. I know that Jack Love's personal rule is something along the lines of "only checking DR's where the DR length + quarter turns needed for HTR = 14-13 or less", though I've personally had so little success with 4 quarter turn cases that I tend to discard them even if they're relatively short DR's. This may or may not be a skill issue on my part :p

Recently, Rodney Kinney has provided some resources on a method called "Hyper Parity" for finding and generating optimal solutions for the corners once you've found a DR. All of the resources for his method can be found here. The majority of this guide is essentially my own version of Hyper Parity, using a recognition system that I think is easier to learn for people who are used to conventional speedsolving recognition systems.

My current system for recognizing corner cases

My system, just like Hyper Parity, has three components to it. First, I recognize the corner case by looking at whether or not my U/D faces are oriented, 3/4 oriented (something like R2 U R2 U' R2), 1/2 oriented with 2 bars (something like R2 U2 B2 U B2), 1/2 oriented with one bar and one slash (R2 U R2 U R2), or 1/2 oriented with two slashes (R2 U2 F2 U R2 U2 F2). Every corner case within this PDF falls into one of these 4 categories. This is more or less the same as how Hyper Parity defines U/D orientation, except I group cases differently by not caring about AUF beforehand (For example, Hyper Parity has two different 3/4 face cases depending on the AUF, whereas I only have one)

The second step of my system is to look for solved/opposite/adjacent patterns which can either tell me what case I have, or at the very least, narrow it down to 2 cases. As an example, with R2 U R2 U' R2, I see that one of my 3/4 sides is a 3/4 layer, while the other 3/4 side has one opposite pair (the BU corner stickers), and one adjacent pair (the LU corner stickers). For those of you familiar with 2x2 solving, many cases have what I call an "R2 F2 R2" equivalent, and the recognition is basically the same as doing AntiCLL on 2x2. For example, if you do R2 F2 R2 before doing R2 U R2 U' R2, you 3/4 layer is now a 3/4 diag layer, the BU stickers are now solved instead of opposite, and the LU stickers are still adjacent.

This step of the recognition system, combined with the final step (which I'll talk about shortly) allows you to recognize the number of quarter turns you need without doing a BLD style trace of the corners to see whether you have even or odd parity. This in my opinion is the biggest advantage this system has over Hyper Parity. That being said, the cases which have two slashes for the U/D orientation are really hard to recognize using this system. I've personally found a system that works decently well for me, but it essentially boils down to doing 1-2 moves to turn the slashes into bars and then recognizing that case instead. I think Hyper Parity is potentially superior for these specific cases.

With these first two steps out of the way, you should now know what the optimal corner solution for your case is. The final step is simply checking whether or not you need a quarter turn AUF before and/or after the corner solution. For example, let's say you recognize that you have corners solvable with some sort of R2 U R2 U' R2 type solution. While many FMCers consider this case "good corners", there's actually a chance that the HTR will need 4 quarter turns instead of 2 or 3 (U' R2 U R2 U' R2 U). While I'm personally not a fan of 4 quarter turn HTR cases, it's technically possible that an HTR such as U' (U' R2 U R2 U) is possible for the DR, and a 6 move HTR is potentially very good depending on what case you get afterwards.

~

That's pretty much it! Some final tips for finding HTR's

1. Familiarize yourself with the corner cases in Jack's PDF that can be done in 7 moves or less & know how to solve them

2. Familiarize yourself with the corner cases that are longer than 7 moves, but can (potentially) be solved with 3 or less quarter turns

3. Learn the shortest way to go from these corner cases to a corner state that's solvable with half turns. Sometimes the shortest path will involve switching. For example, the case that gets solved with R2 U2 F2 U' R2 (the top middle case in the PDF) is a case where you'll often want to switch since on normal you need 3 half turns to get 1 quarter turn away from HTR corners

4. If your DR is one that's entirely done on normal or inverse, you want to start working on HTR on the opposite side. If you can find a promising HTR this way, when you switch back you'll have more options to finish the solve (modifying the DR to change the HTR by changing the final move, doing the entire DR differently while still getting HTR, & solving the opposing layers for the final turn of your DR instead of the normal domino layers for a 2nd option for rewriting your skeleton, albeit a less flexible option... there are 2 examples of this within the first 12 solves of Jack's example solve PDF)

5. Similarly, if your DR has a lot of variations with or without NISS (something ending in R U2 R' or R F2 U2 R), it's good to start working on HTR on the side of the scramble without variations for similar reasons to point 4

6. Sort of obvious, but the HTR triggers you'll want to be using are R (4C4E), R U2 R (4C2E), R U2 F2 R (4C4E), R U2 D2 L (4E), R U2 F2 U2 R (2E), & variations/setups to these triggers. For things like 4C6E/6CxE etc, inserting a slice to turn it into 4C2E/2CxE can potentially help you visualize possible HTR solutions as you'll have more oriented pieces. You can always remove this slice immediately after finding an HTR and rewriting it more efficiently

7. On DR's that only need 1-2 quarter turns to reach HTR, it's not uncommon to have little success by sticking to 1-2 quarter turn solutions. Expanding your search to 3-4 quarter turn solutions might be the key to finding optimal or close to optimal for a given DR

Let me know if I missed anything or if there is anything else I should add for solving HTR specifically :)
 
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