# 5x5x5 last two tredges: AvG vs bigcubes.com



## blah (Jun 16, 2009)

So I finally got my V5 3 days ago  Turned out to be better than I expected 

Anyway, I came across a couple of sources (including cutex.info, bigcubes.com, Erik's video, etc.) claiming different numbers of cases for the last two tredges: one said 2, another said 7, another said 12, another said 15... Point is, I was completely confused.

So this was what I did: Defining the last two midges as solved, we have 4! = 24 cases. And after many many many hours of work, I've categorized them into 8 groups.

*A*



























*B*






*



*





*C*



*









*

*D*








*E*








*F*








*G*





*H*





All cases within the same group can be transformed into the asterisked case either by doing a U2, or by flipping one of the tredges. You never have to do both, i.e. U2 _and_ flip one of the tredges. And to flip one of the tredges, you need an average of exactly 2 moves, you can see how I arrived at this number later on.

So in other words, excluding the solved case, there are only 7 algorithms needed for the last two tredges, and there isn't even a need to mirror any of them. I suck at mirroring on the fly (be it L/R or F/B), so this is definitely good for me.

To flip one of the tredges:
0 moves: 1 case
1 move: 3 cases
2 moves: 13 cases
3 moves: 5 cases
That gives us an average of (0+3+26+15)/22 = 2 moves.

Now, AvG versus bigcubes.com. With the bigcubes.com tredge-pairing method, the probability of ending up with each case is obvious, you just have to count the number of cases in each group:
A: 1/3 (easiest, intuitive case )
B: 1/6
C: 1/6
D: 1/12
E: 1/12
F: 1/12
G: 1/24
H: 1/24

With AvG, it's a little different: Cases C, D, E, F and G can only occur if they were already like that right from the start, i.e. once the centers were done. So the _combined probability_ of cases C, D, E, F and G occurring is 1/(24*23) + (1+4+2+2)/(24*23*22*21) = 0.00185, that's 0.2%. *(Someone double check this for me please!)*

So actually, the only cases that ever appear are A and B (and of course H). Solving A is intuitive. So you only need to learn one alg to solve B if you're doing AvG tredges.

If you get cases C, D, E, F or G, consider yourself unlucky and do the alg for either A or B to reduce the case to A or B. There really isn't any point in learning algs for these cases because they occur so rarely that you don't really get to practice them at all and you'll probably take longer to recall them than to do 2 algs.

Besides, for cases like D and G, you probably would've recognized them while pairing tredges and fixed them while it was still easy.

P/S: Keep in mind that this entire post is made by someone who just got his V5 3 days ago, and hasn't even decided which tredge-pairing method to use. *It might be full of errors so don't just take what I said for granted, double check the cases and probabilities and whatever on your own and please feel free to point out my mistakes.* I don't claim to know much about each tredge-pairing method, but whatever I've just presented represents my independent study on the last 2 tredges.


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## AvGalen (Jun 16, 2009)

I haven't checked the numbers, but I only have 1 thing to say about your conclusion for AVG: *Exactly*

I actually don't know how to do the bigcubes method (I am sure I could figure it out though). When I tell people that use bigcubes-method that I only know 1 alg for edge-pairing (the parity-fix B3) and that that occurs roughly 50% of the time they think I am kidding.

It seems that there are currently 3 common ways for edge-pairing (not counting exotic methods like K4 or corners-first or direct solving)
1) Bigcubes for first 8 tredges, Bigcubes algs for last 4 tredges
2) Bigcubes for first 8 tredges, AVG for last 8 semi-pairs
3) AVG for all 24 semi-pairs

All of these methods seem to be equally fast and speed is more based on the cuber and the amount of experience/practice than on the method.
(I prefer AVG because it is just as fast and only requires learning that 1 alg)


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## blah (Jun 16, 2009)

AvGalen said:


> 2) Bigcubes for first 8 tredges, AVG for last 8 semi-pairs



I've been thinking about this for a day or two now but I haven't really tried this yet, mainly because of the fear of hybrid methods being inferior (because most of the time, they _are_). Who uses this (and is fast)?


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## mazei (Jun 16, 2009)

I used to when I tried out Bigcubes method. With practice it is the same speed as my normal 2-edge pairing.


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## blah (Jun 16, 2009)

blah said:


> All cases within the same group can be transformed into the asterisked case either by doing a U2, or by flipping one of the tredges. You never have to do both, i.e. U2 _and_ flip one of the tredges.



Let me try to make this clearer.

*A*
Intuitive.

*B*
You have to learn an alg for either B2 or B3. B1 and B4 can be transformed into B2 or B3 by flipping the appropriate tredge. B2 and B3 can be transformed into each other by doing a U2.

*C*
You have to learn an alg for either C1 or C4. C2 and C3 can be transformed into C1 or C4 by flipping the appropriate tredge. C1 and C4 can be transformed into each other by doing a U2.

*D*
D1 and D2 can be transformed into each other by doing a U2. Avoidable while pairing other tredges.

*E*
E1 and E2 can be transformed into each other by flipping any tredge.

*F*
F1 and F2 can be transformed into each other by doing a U2.

*G*
Duh. Avoidable while pairing the other tredges.

*H*
Duh.

Which means, if you use bigcubes.com tredge-pairing, there are 6 algs you have to learn:
1. B2 or B3
2. C1 or C4
3. D1 or D2
4. E1 or E2
5. F1 or F2
6. G


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## Mike Hughey (Jun 16, 2009)

blah said:


> AvGalen said:
> 
> 
> > 2) Bigcubes for first 8 tredges, AVG for last 8 semi-pairs
> ...



I really don't think there is anyone really fast who uses this as their standard method. But I'm fairly sure Erik can do it well, and I suspect his times with this method are fast.


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## Leviticus (Jun 16, 2009)

I just use Frank's method. I experimented with AvG but it wasn't working for me. I probably didn't give it a fair go but Arnaud helped me with my 5x5 times when I was trying to get faster from ~3.00 minutes  Now I average 1.40.


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## Am1n- (Jun 21, 2009)

For the edge pairing, I use Bigcubes method for the first 8, the last 4 I put a wingedge next to the centeredge, flip the edge and restore the center, I don't know if that's any good, but I can get sub4 with it, and only need 1 alg (D2).
(including 1 --> 1.5 min for 3x3x3: F2L; 4-look LL)

mvg


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## masterofthebass (Jun 21, 2009)

For the last 4 edges, i really just freestyle solving 2 of them. The thing about bigcubes method, is that you don't really notice parity. Almost every solve requires a last 2 edges alg, and they are mostly similar speeds. Learning them is actually quite easy, and they are pretty quick. With AvG, you end up getting either parity, or no parity, so it makes you notice when you have it . 

@Arnaud, I personally don't think AvG is as fast. I think Erik is just too good at it. No one else near the top of 5x5ing uses AvG. A lot of people are using your method, and that's great, but I don't the method is truly that fast.


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## Kian (Jun 21, 2009)

masterofthebass said:


> For the last 4 edges, i really just freestyle solving 2 of them. The thing about bigcubes method, is that you don't really notice parity. Almost every solve requires a last 2 edges alg, and they are mostly similar speeds. Learning them is actually quite easy, and they are pretty quick. With AvG, you end up getting either parity, or no parity, so it makes you notice when you have it .
> 
> @Arnaud, I personally don't think AvG is as fast. I think Erik is just too good at it. No one else near the top of 5x5ing uses AvG. A lot of people are using your method, and that's great, but I don't the method is truly that fast.



what about for use on the last 4 edges? I just started learning freeslice once I got 6 and 7 last week because AVG is just too inefficient for them and I've thought about doing freeslice for the first 8 and avg for the last 4 for 5x5. it seems like that might be nearly as fast as the algs for bigcubes. I will need to practice and see, though. And I'm still not nearly as fast with freeslice as I am with AVG, but I'll get there.


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## jcuber (Jun 21, 2009)

blah said:


> AvGalen said:
> 
> 
> > 2) Bigcubes for first 8 tredges, AVG for last 8 semi-pairs
> ...



I use this sometimes, but only if after bigcubes first 8 there is a semi-pair already formed (I like to force a solved semi-pair, though). If there are no semi-pairs, I just use 2 at at time once and continue with AVG.


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## Dene (Jun 21, 2009)

AvGalen said:


> It seems that there are currently 3 common ways for edge-pairing (not counting exotic methods like K4 or corners-first or direct solving)
> 1) Bigcubes for first 8 tredges, Bigcubes algs for last 4 tredges
> 2) Bigcubes for first 8 tredges, AVG for last 8 semi-pairs
> 3) AVG for all 24 semi-pairs



As Dan said, the way I do it is freeslice the first 8 edges, then freestyle the next two, then solve the last two with one of the algorithms. The other option is to solve 1 of the last 4 edges, then to solve the last 3 in one intuitive step. It just depends on how they get left after freeslice.


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## AvGalen (Jun 22, 2009)

masterofthebass said:


> For the last 4 edges, i really just freestyle solving 2 of them. The thing about bigcubes method, is that you don't really notice parity. Almost every solve requires a last 2 edges alg, and they are mostly similar speeds. Learning them is actually quite easy, and they are pretty quick. With AvG, you end up getting either parity, or no parity, so it makes you notice when you have it .
> 
> @Arnaud, I personally don't think AvG is as fast. I think Erik is just too good at it. No one else near the top of 5x5ing uses AvG. A lot of people are using your method, and that's great, but I don't the method is truly that fast.


That makes no sense to me. That's like saying Bigcubes-pairing isn't as fast, but you are just to good at it :confused:. If you want to break the WR you have to pick a method, practice with it like crazy and develop your own extra tricks. Bigcubes was there before AVG and many people that are very fast now never seriously tried AVG. Erik learned AVG from me way before I published it and he never seriously tried Bigcubes. I guess we will never know how fast you would have been with AVG and how fast Erik would have been with Bigcubes. We will see in the next couple of years if others will practice AVG as their main method and can break the WR.

And you are wrong about Erik being the only one. What about Mátyás (he uses a freestyle variation of AVG where he rotates the cube more often to switch buffers)

This sounds to me like a "Fridrich is better than Petrus/Roux/xxx" debate and we both know those don't go anywhere


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## mazei (Jun 22, 2009)

Well I average 1:45 now with something like AvG, except I rotate and my pairing slice is anything that is comfortable.


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## mazei (Jun 22, 2009)

Okay, did very few splits and this is the conclusion. My current method averages around 55+- seconds but when I used the BigCubes method I have the same average. So I'm back to which should I use?

Edit
Now after a few more splits I can see a 6 second difference between the 2. My current method is more comfortable for me since I need the freedom of re-gripping to look ahead.


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