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On algs the major reason why people say learning them isn't worth it is they're too lazy to learn algs.

I personally find the hard part of learning algs is retaining them. I can learn it quickly but remembering it for more than a few days or about a week is harder. I get sick of drilling the algs.

On algs the major reason why people say learning them isn't worth it is they're too lazy to learn algs.

I personally find the hard part of learning algs is retaining them. I can learn it quickly but remembering it for more than a few days or about a week is harder. I get sick of drilling the algs.

It gets easier the more you learn. But beyond oll pll learning more algs has got a lot more of diminishing returns for 3x3. Working on F2L is usually a faster way to improve until a point.

@ColorfulPockets I was definitely not asking you to shame Kit lol. It's just that you guys were discussing that you used to keep track of everything in your head and said it wasn't working as well anymore. I also used to keep track of everything in my head too, and it worked fine. These methods of organization (the ones I sent to you) were pretty interesting to me and seemed relevant so I thought I'd share them. Although the methods do focus a lot on email, they're really about the four follow-up categories: calendar, tasks manager, resources, and read-later - any inbox, email being just one example, can flow into those four categories.
The main point being that if you actually funnel all your tasks and events into a task manager and a calendar, you'll actually be motivated to look at them - as opposed to keeping some events in your head, some in your email, etc, and only some in your calendar. Centralization.
Again, not trying to shame Kit, just offer advice. Unless you're offering a recurring segment on shaming Kit - that I might be interested in.

Ben already mentioned the generating functions thing for calculating positions on the subreddit. A different Ben (benpuzzles, the one who's really into FTO) also recently did a video about how the number of paths is related to Fibonacci numbers, using that to get a lower bound for god's number for FTO.

I also wrote two short Python functions to calculate the number of scramble sequences and the number of "canonical" move sequences in the Probability Thread a few months ago. (For canonical move sequences, you declare ahead of time that, say, if you have L and R moves next to each other, then they must be in the L-R order and not the R-L order. This means that the number of canonical move sequences is less than the number of non-cancelling move sequences, although the number of paths/cases will still be the same Fibonacci numbers either way.)

Spoiler: learning algs

I think Kit has this completely right: whether learning algs is good or not is dependent on the cuber. Blanket statements like "ZBLL is good and you should learn it" or "full OLL is useless and 2-look is good enough" are completely nonsensical, and yet it's all too common to see people suggesting not-quite-as-exaggerated versions of those two statements.

I really dislike the process of learning algs, but I like being able to use them in solves, so there's some tension there…

Regarding confusing algs with each other, that's definitely a problem I have too. I use like three ZBLL algs that start with D R' U' R D' (one of which is Gb perm) and I sometimes just confuse them with each other. There are some 2GLL cases where the "standard" algs most people use are Sune combos, but for some of them I use a completely different RU alg (e.g. R U R' U' R' U2 R U R' U R2 U2 R') just so my muscle memory for that alg is a separate thing and there's less risk of messing things up.

There's one very nice property of OBTM that STM/BTM doesn't have: there's a unique decomposition of moves on a single axis into outer block moves. Not so for block moves. Let's say we're looking at an n×n×n cube (n ≥ 2).

Assuming the cube's layers are only misaligned along the U-D axis, you can represent the rotation angle of each of the slices, relative to some independent reference, as some number from 0° to 360°. This gives a free module of rank n, (ℝ/(360°))^n. Since rotating the whole cube shouldn't affect the penalty, we can take the quotient by the rank-1 submodule corresponding to all whole-cube rotations along the U-D axis, leaving us with a rank-(n−1) module.

(N.b. if you don't know what a "free module" is, just think of it as a vector space, except that the coordinates are angles (and hence wrap around at 360°) rather than numbers you can freely multiply and do whatever with.)

With OBTM, we have the moves 1Uw, 2Uw, 3Uw, 4Uw, …, nUw, 1Dw, 2Dw, …, nDw. This is a set of 2n generators within (ℝ/(360°))^n, but if you quotient out by the submodule of whole-cube rotations, we get [nUw] = [nDw] = 0 and [kUw] = [(n−k)Dw] for all 1 ≤ k ≤ n−1, effectively leaving us with only n−1 generators. A set of (n−1) generators for rank-(n−1) ⇒ all of these are independent, and there is an essentially unique way of writing any misalignment in terms of (possibly-fractional) outer block turns. The only source of non-uniqueness comes from replacing, say, 2Uw with (n−2)Dw, but these are really the same move written in different ways anyway.

With BTM, we have the moves 1U, 2U, 3U, …, nU, 1-2u, 2-3u, 3-4u, …, (n−1)-nu, …, which is a much larger set of generators, with n(n+1)/2 elements; even if you quotient out by the whole-cube rotations, this leaves n(n−1)/2 generators. We get unique decomposition when this is equal to n−1, and the only way that can happen is if n = 2 (which makes sense, since that's where OBTM and BTM are truly equivalent). If n > 2, then n/2 > 1 and hence n(n−1)/2 > n−1, so there's definitely no way our generating set can be linearly independent, which also means the decomposition will fail to be unique.

For a concrete example, let's look at a 3×3×3 and do an E move to a solved cube. Now, instead of using the "obvious" decomposition as 2U^−1, there are other possible decompositions, such as U^0.5 2U^−0.5 D^−0.5. With this choice of decomposition, we never need to do a move of more than 45° to fix the cube. In other words, no misalignment penalty!

With BTM, how should you choose which decomposition to use to judge for misalignments? It's already non-obvious for n=3, and it only gets worse as you increase n, where the system of equations gets increasingly underdetermined.

Spoiler: some history on misalignment penalties

Also worth looking at the really old regulations here. Back in 2007, the allowed misalignment was essentially "line to line", which is a bit harsher than the 45° standard we now use, but you could misalign any number of layers and still have only a +2 penalty, not DNF! In other words, a U D2 or U2 D2 would have counted as +2 by those rules.

That changed in 2008 to something that resembles our current regulations a lot more. 45° turn limit, maximum of one pair of adjacent layers misaligned beyond that to still be considered solved.

If you clicked on those two links, do you notice something? The regulations used to have pictures in them!

On the topic of twitch I think that cubing works well because with a good streamer doing sighted events it is essentially The just chatting stream category with a visual element, I also think it is better than YouTube as at the moment it Is not oversaturated and the community is older and more mature so the chat is generally still like a normal conversation in most streams and not just little kids trying to get attention (see: any YouTube comment section). Also I think things like channel points, bits and subs help make things interesting with options for challenges and community interaction (for example I have Various options for channel points to get me to do any WCA event and even 6bld).

Also @ColorfulPockets thanks for the raid on my 6bld attempt stream it helped get me to affiliate and was really cool as I am a massive fan of both this podcast (I think it might have been the stream of the podcast but I’m not 100% sure) and your videos.

I also want to mention I am learning ZBLL (very slowly) and I think most people overestimate how hard it Is to learn algs and also the importance of learning them.

The 222/skewb/pyra scramblers in TNoodle all use random search, and are always forced to be exactly 11 moves long (iirc). (For pyraminx, this applies to the non-tip part of the scramble. This is not related to the 6-move scramble filtering, which does count tips.) God's number happens to be exactly 11 moves for all three of these puzzles, but most states can be solved in 10 or less. If you always use the same move order when searching, the first solution found will almost always start with the first move you search, then a 10-move optimal solution, or the first two moves + 9-move optimal solution, or something along those lines.

Spoiler: mega scrambles

That's… interesting. The distance distribution of the individual edges is closer than I'd expected.

I still suspect that the joint distribution is slightly (but noticeably) biased, though. Now that Kit's done some work on demonstrating that the individual edges have the right distribution, I should get off my lazy bum and do the same calculation for multiple pieces.

I primarily start my solves with blockbuilding rather than star (iirc @GenTheThief does as well) and having free corner-edge pairs helps this a lot. I did a small-scale experiment back in May, by visually inspecting scrambles with csTimer's "draw scramble". 50 moves definitely had too many free pairs (p value ~ 0.0004), while 60 moves, 70 moves, or 80 moves didn't have a statistically significant bias due to my small sample size.

Also, I don't remember if I came up with the term or if I read it somewhere else, but I like to think of "QTM" as standing for "quantised turn metric", rather than "quarter turn metric". Calling fifth-turns on a megaminx a "quarter turn" bothers me so much. (And what about "HTM" / "half turn metric"? I've always preferred "FTM" / "face turn metric" anyway.)

Spoiler: mirrored moves

Back when the Giiker was first released, Ben Whitmore did a thing where he simultaneously solved the physical cube and the virtual cube with different scrambles, where the virtual cube's moves were the inverse of the physical cube's moves (so U became U', L became L', etc., but the moves were still on the same faces). If you haven't seen it yet, go check it out.

edit:

Spoiler: budget relay

Maybe there should be an additional rule that says you can't use the same model more than once. Like, you can't just use three Little Magics.

My attempt:
Cubes: Tengyun M ($26), Guhong v3 M ($12), Cubing Classroom 45 mm ($4)
47.938, 49.736, 47.481, (52.097), (47.416) = 48.385 average

Didn't have any other cube under $12 that's worth using to fill in the third spot.