# New type of 2x2 scrambler



## qqwref (Oct 11, 2009)

http://mzrg.com/miniSites/scramblers/222 11moves.html

I'd like to propose for this to become WCA-official but this type of thing isn't under consideration right now so there is no point in posting it in the WCA forum yet. Anyway this is a modification of the current WCA-official scrambler. Here are the changes:
- The official scrambler does 500 moves to find the random position, but this one is better because it simply picks a random position directly.
- This scrambler will discard scrambles that are 7 or fewer moves from solved (this happens <20% of the time). This means that with this scrambler there are no incredibly easy solves! I think this could restore some legitimacy to the 2x2 single solve event.
- The scrambles here are always 11 moves (the maximum number of moves a 2x2 scramble could require) so there is no way to tell how easy a scramble is by looking at the moves.
- I removed the "minimum scramble length" thing because that was not necessary.
- I cleaned up the code a LOT, removing any unused functions and rewriting some things to make them smaller without changing what they did. (For comparison's sake, this is 10kb and the official one is 16kb.)


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## esquimalt1 (Oct 11, 2009)

I'm liking it a lot


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## Tim Major (Oct 11, 2009)

qqwref said:


> This means that with this scrambler there are no incredibly easy solves! I think this could restore some legitimacy to the 2x2 single solve event.



But, but, but... I like easy scrambles...

Edit: 1st scramble I tried: F U F' R F U' F2 R U R' U'

A bar properly already made, do maybe the scrambles aren't such a bad idea.


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## hr.mohr (Oct 11, 2009)

qqwref said:


> - The scrambles here are always 11 moves (the maximum number of moves a 2x2 scramble could require) so there is no way to tell how easy a scramble is by looking at the moves.



Very nice, great work!


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## qqwref (Oct 11, 2009)

ZB_FTW!!! said:


> qqwref said:
> 
> 
> > This means that with this scrambler there are no incredibly easy solves! I think this could restore some legitimacy to the 2x2 single solve event.
> ...



Careful. I said there no *incredibly* easy solves. This does not mean there are no easy solves ever. There is still a component of luck and there will always be some scrambles that are easier than others. It is even possible to get a scramble with one layer solved on this scrambler, but the CLL will be at least 8 moves including AUF ;-) I just want to prevent scrambles that are so easy that slower competitors get sub-2 second times because they see it all from inspection. Look at this: sub-1.5 single, 7 second average - is that fair, and is the single solve representative of that person's skill? No, it is not.


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## esquimalt1 (Oct 11, 2009)

I agree with the example of slower competitors getting sub 2 singles. Hopefully if the WCA accepts this scrambler, 2x2 single will involve more skill.


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## fundash (Oct 11, 2009)

I like it!

Now all i need is an east sheen 2x2...


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## Jake Gouldon (Oct 11, 2009)

Aren't some states impossible to reach because the scramble is always exactly 11 moves?


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## qqwref (Oct 11, 2009)

Jake Gouldon said:


> Aren't some states impossible to reach because the scramble is always exactly 11 moves?



There's no proof that every position can be solved in 11 moves, but it seems to be possible most of the time.


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## DavidWoner (Oct 11, 2009)

qqwref said:


> This scrambler will discard scrambles that are 7 or fewer moves from solved (this happens <20% of the time). This means that with this scrambler there are no incredibly easy solves! I think this could restore some legitimacy to the 2x2 single solve event.



....................

Wrong.

R U R' U R U2 R' U
F R' F' R U R U' R'
F U R U' R' F' R U
etc

All incredibly easy, all >7 moves.

F R2 U' F' R'
R U' F2 R F
U F2 R U'
etc

All short, none of them are obviously easy, except to experienced solvers.

And what happens to the old records? As with the change in multiBLD, this would make the old records a lot harder to beat. I like the idea of outputting all 11 move scrambles, I suggested something similar to Arnaud for when an easy scramble came up in the weekly comp. However, dropping all <8 move positions is stupid.


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## qqwref (Oct 11, 2009)

DavidWoner said:


> R U R' U R U2 R' U
> All incredibly easy, all >7 moves.
> [...]
> However, dropping all <8 move positions is stupid.


I think you are completely misinterpreting what I mean by "incredibly easy". I mean stuff where the solution is very few moves, not stuff where you happen to know how to solve it. The cases you gave are easy but not "incredibly easy". I'm not talking about the kind of scrambles where you get really nice times, I'm talking about the kind of scrambles that are not just "really nice", but completely unfair to anyone who was not at the competition.

The reason I chose <8 was because it is not arbitrary. Obviously we NEED to have something that prohibits stupid **** like F R U2 R' from showing up in competition, but there's no way the scrambler can decide how easy a scramble will be for a human solver and still be method-independent. A scrambler doesn't know the difference between a sune and R U' R U2 R U' R'. Discarding everything 7 moves or fewer will prevent most stupidly easy scrambles from showing up while discarding less than 20% of the legit ones. If you have such a problem with easy 8+ move scrambles existing, why don't you suggest a better way to get rid of the incredibly easy ones?



DavidWoner said:


> F R2 U' F' R'
> R U' F2 R F
> U F2 R U'
> All short, none of them are obviously easy, except to experienced solvers.


It's not entirely about whether you can see the solution. Take R U' F2 R F for instance: this can be solved by doing z' y L' U' L R U R'. Even if someone can't SEE the solution from inspection, the scramble is objectively easy and thus they have a higher chance of getting a really lucky skip (in this case, LL skip in 6 moves qtm!) and then achieving a time that I don't want to have to compete with. Similarly the first one could plausibly be done with guimond as y2 R U R' R2 F2 U'. The fact is even though these scrambles might be hard to see from inspection they are still objectively easy and provide an extra-high chance of an extra-low time to an inexperienced solver.



DavidWoner said:


> And what happens to the old records? As with the change in multiBLD, this would make the old records a lot harder to beat.


I was thinking we could just discard all solves below a certain threshhold - 2.00 seconds, say, or the best time in the WC09 final, which was 2.46 seconds. I don't know what the best 8+ move solve in competition was but it's probably around there.


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## DavidWoner (Oct 12, 2009)

qqwref said:


> Obviously we NEED to have something that prohibits stupid **** like F R U2 R' from showing up in competition



Obviously? No. I can't think of a single reason that doesn't amount to whining about fairness.



> The reason I chose <8 was because it is not arbitrary ... Discarding everything 7 moves or fewer will prevent most stupidly easy scrambles from showing up while discarding less than 20% of the legit ones.



Uhh... <8 IS arbitrary, you never go about explaining where that particular number comes from. As I recall, Javier's 1.63, Patrick's NAR, Eric's current NAR, and this most recent scramble from WC were all FOUR moves. Not five or six or seven, but FOUR. So wouldn't discarding all positions <5 moves from solved make a _lot_ more sense?



> why don't you suggest a better way to get rid of the incredibly easy ones?



Because I honestly don't give a **** if some random noob has a better 2x2 single time than me. I don't understand why you seem to.



> DavidWoner said:
> 
> 
> > And what happens to the old records? As with the change in multiBLD, this would make the old records a lot harder to beat.
> ...



14	Erik Johnson	1.72	USA	US Nationals 2009
20	Phil Thomas 1.86	USA	Wisconsin Open 2008

maybe more.

If you want to kill all the sub 2.46 times, there are a ton more.


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## blade740 (Oct 12, 2009)

I think the scrambler is a good idea, but I don't think there's a fair way to remove old records.


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## Edmund (Oct 12, 2009)

Yeah, if a solution has to be x amount of moves how the hell are we supposed to beat .96?


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## esquimalt1 (Oct 12, 2009)

Edmund said:


> Yeah, if a solution has to be x amount of moves how the hell are we supposed to beat .96?



I believe Erik's 0.96 solve was 8 moves.


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## DavidWoner (Oct 12, 2009)

esquimalt1 said:


> Edmund said:
> 
> 
> > Yeah, if a solution has to be x amount of moves how the hell are we supposed to beat .96?
> ...





Erik said:


> Scramble #2 of finals: F' U' F' R2 F2 R U2 R' U F U R2 U F' U2 F2 R' U R F' R U2 R2 U' F
> Solution: x2 U R' U' R U R' U'
> hint: got to know your sexy moves to see what will happen in inspection...


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## esquimalt1 (Oct 12, 2009)

Alright, so then it was 7 moves.


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## Erik (Oct 12, 2009)

Ya 7 moves is not that uncommon at all. We can start the discussion again about easy scrambles if you want... but move count is no indicator for easy-ness. If you have a J perm as scramble it's also like 8 or 9 moves, but ridiculously easy... at the same time Derrick and me often race 5 moves scrambles for fun... I can tell you they can be VERY hard...


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## TomZ (Oct 12, 2009)

Nice work! The credits list is growing nicely...

I strongly disagree with setting a minimum move count. Maybe it is a good idea to block some scrambles, but setting the limit at 7 moves is ridiculous. That represents nearly 8% of all scrambles. This means that in over 33% of averages of five there would be at least one seven move (or less) position. Scrambles of six moves or less occur in 8% of averages of five, still quite a lot to discard. Setting the limit at 5 might make sense, but 7 is just wrong.
Getting lucky is part of the game, after all.

"The scrambles here are always 11 moves (the maximum number of moves a 2x2 scramble could require) so there is no way to tell how easy a scramble is by looking at the moves."
How is that a new feature?
Secondly, setting a 11 move minimum is just a waste. Move count is a terrible indicator of difficulty. It would seem like a good idea to mask 4-move solves (if they remain) but there is no need to hide a solve is 8 moves. And (in theory at least) the solvers should not even be able to find this out in the first place.

Good work on the cleaning up. I didn't really bother to do that as it doesn't make much of a difference and consumes heaps of time, but it's nice.


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## qqwref (Oct 12, 2009)

TomZ said:


> "The scrambles here are always 11 moves (the maximum number of moves a 2x2 scramble could require) so there is no way to tell how easy a scramble is by looking at the moves."
> How is that a new feature?


It's not new in the sense that it has never been done before, it's new in the sense that the current WCA scrambler does not do it (the current WCA scrambler is optimal). Hence it is something I changed.



TomZ said:


> Secondly, setting a 11 move minimum is just a waste. Move count is a terrible indicator of difficulty. It would seem like a good idea to mask 4-move solves (if they remain) but there is no need to hide a solve is 8 moves. And (in theory at least) the solvers should not even be able to find this out in the first place.


You're right that making every scramble 11 moves is not necessary if all scrambles are guaranteed to be 8+ moves from solved anyway. The main reason I did this is because people tend to ask for it; it would be simple to remove.

Besides in practice there is no way to prevent people from finding out some data about the scrambles because the scramblers are in plain view at a table somewhere, as opposed to (say) in a completely different room. If they see a 4-move 2x2 scramble, they can't help but be a little excited... but, worse, if people solve a 4-move scramble, they tend to go tell their friends even if it is against the WCA regs to do so.


For those who are criticizing the idea of throwing out scrambles with <8 moves: do you at least agree that we need to remove very very easy scrambles? I think we need to discard ridiculously easy scrambles simply because they are massively unfair to anyone who does not get an attempt to solve them. You probably don't care about this issue but in my opinion having stuff like this makes cubing seem less like a carefully regulated sport and more like some kind of amateur club activity. I know most people treat the 2x2 single rankings as completely pointless, but I don't think it has to be that way; I think we treat it as useless because of the problem of insanely easy scrambles. As I said before, if you don't like the idea of discarding all scrambles under 8 moves, I would like to hear a better idea. TomZ's idea of discarding scrambles with 5 or fewer moves is a good one although it is still somewhat arbitrary.


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## TMOY (Oct 13, 2009)

DavidWoner said:


> 14	Erik Johnson	1.72	USA	US Nationals 2009
> 20	Phil Thomas 1.86	USA	Wisconsin Open 2008
> 
> maybe more.


IIRC Doudou's 1.66 solve at Toulouse Summer Open 2008 was 8 moves.


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## Kenneth (Oct 16, 2009)

qqwref said:


> Look at this: sub-1.5 single, 7 second average - is that fair, and is the single solve representative of that person's skill? No, it is not.



If you think that's the worst example then look at this: 

Kristianstad Open 2009 First 18 3.33 13.49 17.03 12.13 15.55 3.33 12.80 

That was my brother. In the same round Simon Westlund broke the NR with 3.00 but that's more fair, he is one of our best 2x2 cubers.


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## qqwref (Oct 16, 2009)

TMOY: Interesting. A 1.66 by Edouard would make a good single WR as the time is still beatable by a fast solver with a good (but non-ridiculous) solve, and as he is fast at the event and thus deserving of a record. (I don't mean offense to Erik, but rather to people who are slower than me at 2x2 but have had their lucky sub-2 single.)

Kenneth: Actually that IS the worst example I could find... your brother has a single/avg ratio of 0.296 and a single/avg rank ratio of 0.126, whereas Antoine has a single/avg ratio of 0.199 and a single/avg rank ratio of 0.006 (!!!). So I think Antoine's case is definitely more unfair to other competitors such as me.


I have heard that in Worlds there was one group of 2x2 competitors who had the extremely easy scramble, and another group which did not. This is an extremely unfair situation and I'd like to remind anyone who reads this topic that the whole purpose of removing extremely easy scrambles is to remove these unfair situations where people feel disadvantaged by not being in a particular competition or solving group. The single ranking for any event, even 2x2, should be determined more by the person's speed and luck than by the scrambles they are given.

I am sure it seems like I am making a big deal about nothing, but if the WCA's goal is to have "more competitions in more countries with more people and more fun, under fair conditions" then I think if an unfairness is found it needs to be corrected quickly, so we do not risk people feeling that we are as a whole amateurish and unprofessional.

About the 8 moves limit: Of course this can be changed at will (by modifying a single number in the code, it is not hard) but the question is then "to what?". On average a 2x2 takes 8.755 moves to solve so we do not want to pick something too far from this, but on the other hand we don't want to eliminate too many scrambles. I think discarding everything under 6 moves might be a good compromise, but this is after all still a bit subjective.


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## DavidWoner (Oct 16, 2009)

qqwref said:


> TomZ's idea of discarding scrambles with 5 or fewer moves is a good one although it is still somewhat arbitrary.



Uhh, it is neither TomZ's idea nor arbitrary... Did you not read what I wrote?



DavidWoner said:


> As I recall, Javier's 1.63, Patrick's NAR, Eric's current NAR, and this most recent scramble from WC were all FOUR moves. Not five or six or seven, but FOUR. So wouldn't discarding all positions <5 moves from solved make a _lot_ more sense?



<5 is not arbitrary because all of these slow people are getting their fast singles on 4 move scrambles.


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## AvGalen (Oct 16, 2009)

On the WR-scramble Erik got the WR because he is really good, not because it was a lucky scramble. Many other people got the same scramble but either don't possess the skill to see the solution or don't possess the speed to beat his time. Even on a 4 move scramble nobody has beaten that 7 mover (Erik and I are still both convinced we actually performed 8 moves although we have redone it many times and always used 7)

If a scramble would show up that has 1 layer done only some people would know how to solve it. Your scrambler would actually increase the chances of that happening compared to the current scrambler.

From a theoretical point of view I can see 2 problems:
- Not all positions might be reachable in exactly 11 moves. (I believe they can, but that's not proof)
- Deciding that "<8 moves scrambles" are easier and will result in faster times hasn't been proven for me.

Changing the scrambles in this way would make 2x2x2 a different event and would invalidate old results. I don't think that is needed. The solution is worse than the problem


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## hr.mohr (Oct 16, 2009)

qqwref said:


> I don't mean offense to Erik, but rather to people who are slower than me at 2x2 but have had their lucky sub-2 single.



So what you are saying is that it's OK to be lucky if you are faster than you?

I like that we all get a random state scramble and the chance to get lucky but should practice because the winner are found by average and not by a single lucky solve. Even if 5 lucky scrambles were to be found in the same round the winner would still be the one with the fastest fingers.


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## Cride5 (Oct 16, 2009)

qqwref said:


> I have heard that in Worlds there was one group of 2x2 competitors who had the extremely easy scramble, and another group which did not. This is an extremely unfair situation and I'd like to remind anyone who reads this topic that the whole purpose of removing extremely easy scrambles is to remove these unfair situations where people feel disadvantaged by not being in a particular competition or solving group. The single ranking for any event, even 2x2, should be determined more by the person's speed and luck than by the scrambles they are given.



I have to agree with qq on this one. If its in our power to make the system a fairer one then why not do it? While removing < 8-move scrambles won't guarantee against lucky solves, it will certainly vastly reduce their frequency.

Additional filters could be built into the scramble generator to remove known easy scrambles, for example: scrambles which only affect one layer, or result in solved orientation etc. However, the problem with going down this route, is that the design of the filter is likely to result in bias towards particular methods. For example: removing 1-layer scrambles will result in a penalty for CLL users, while Guimond users will be largely unaffected.


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## Pedro (Oct 16, 2009)

the single 2x2 ranking is indeed pointless, and so are almost all the other single solve rankings (except for the blds)

luck is part of the game and I don't think we should try to remove it.

It's not fair to just erase a lot of times. What happens with the averages?

the winner is decided by average, so even if someone gets a stupid scramble, they won't win if they're not good enough



> I have heard that in Worlds there was one group of 2x2 competitors who had the extremely easy scramble, and another group which did not. This is an extremely unfair situation and I'd like to remind anyone who reads this topic that the whole purpose of removing extremely easy scrambles is to remove these unfair situations where people feel disadvantaged by not being in a particular competition or solving group.



If I remember correctly, there were like 4 groups for 2x2 at Worlds.

Not everybody is going to be at all competitions, so some people will always get an "advantage". It just happens like that. If everybody got the same easy scramble at Worlds, would it be more "fair" with all the thousands of people which weren't there?


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## Kenneth (Oct 17, 2009)

qqwref said:


> Kenneth: Actually that IS the worst example I could find... your brother has a single/avg ratio of 0.296 and a single/avg rank ratio of 0.126, whereas Antoine has a single/avg ratio of 0.199 and a single/avg rank ratio of 0.006 (!!!). So I think Antoine's case is definitely more unfair to other competitors such as me.



Yes, maybe so, but the span between single and average for my brother is over 10 seconds and that is a bit... lolable 

_I'm not making jokes on his behalf here, he nows he sucks at 2x2, it is the scrambler that is funny, not he._


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## qqwref (Oct 17, 2009)

hr.mohr said:


> qqwref said:
> 
> 
> > I don't mean offense to Erik, but rather to people who are slower than me at 2x2 but have had their lucky sub-2 single.
> ...


Not quite, but I am saying that people who are slower than me (and I am not even fast) do not really deserve such a fast single time. If someone is much faster than me, maybe a sub-2 single can be gotten on a normal solve.



Pedro said:


> the single 2x2 ranking is indeed pointless, and so are almost all the other single solve rankings (except for the blds)
> 
> luck is part of the game and I don't think we should try to remove it.
> 
> ...


But that is the thing, I don't think the 2x2 single ranking HAS TO be pointless. Anyway, I don't want to 'erase' the times, just mark them somehow so that they don't show up on the single ranking. A lucky single does not affect an avg5 much if at all.


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## tim (Oct 17, 2009)

qqwref said:


> A lucky single does not affect an avg5 much if at all.



Why does this thread exist then?


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## qqwref (Oct 17, 2009)

tim said:


> qqwref said:
> 
> 
> > A lucky single does not affect an avg5 much if at all.
> ...





qqwref said:


> I think this could restore some legitimacy to the 2x2 single solve event.


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## esquimalt1 (Oct 17, 2009)

I'm still with qqwref on this. I think it's much more fair, and it's much nicer to not have an event (such as 2x2 single) that has to be about luck.


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## hr.mohr (Oct 17, 2009)

You guys do know that there is no single solve event? 

There's only an average event and a wall of fame for people that are lucky and skilled. The same scramble at Geneva where handed to several people and yet only one a few were able to break the current wr at the time. Luck is a big part of records but not the largest part.


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## hawkmp4 (Oct 20, 2009)

qqwref said:


> http://mzrg.com/miniSites/scramblers/222 11moves.html
> 
> I'd like to propose for this to become WCA-official but this type of thing isn't under consideration right now so there is no point in posting it in the WCA forum yet. Anyway this is a modification of the current WCA-official scrambler. Here are the changes:
> - The official scrambler does 500 moves to find the random position, but this one is better because it simply picks a random position directly.
> ...



In order of your points-
-I think that this is the right way to go. No reason we shouldn't be doing this, especially if we're doing it for 3x3. Makes no sense not to for 2x2.
-While I agree that 2x2 SHOULD have something like this, implementing it...well. I think throwing out 20% of the scrambles is a bad idea. I'd rather see more like 5%, MAYBE 10%. A lot of these scrambles are short movecount wise but as many people have said, it may not be easy to see. I think everyone can agree though, a 3 move scramble isn't really representative of anyone's abilities. (More on this in the conclusion) Also, though unfortunate I think, there ARE already records and rankings, and without a reaaalllly compelling reason I find it hard to either take away records and such from people who have already solved, or take the opportunity to break records away from future solvers. For better or for worse, 2x2 single is ruled by luck. It's due to the nature of the puzzle, and if we mess around too much with removing scrambles from the pool...well, it just doesn't seem right to me.
-With all due respect, what's the point? If this is intended for competition, scramble length won't matter. Competitors will never see the scramble algorithm nor see their cubes being scrambled so I don't think this is really necessary unless I'm missing something. I think in general, less moves is better for scrambles. Less moves to screw up leads to better consistency.
-Not much to say on the last two points. Good work.


I think that the best and most fair we can do is rely on a truly random solver and the distribution of move counts for optimal solutions. Besides the practical implications of cutting out certain scrambles and the effects of that on records, we still have the issue of judging which scrambles are 'too easy' or not. And I think that's better left alone. That's just my thoughts. Good work on the scrambler though- I think I'll be using it for practice now.


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## Tim Major (Oct 20, 2009)

hr.mohr said:


> You guys do know that there is no single solve event?
> 
> There's only an average event and a wall of fame for people that are lucky and skilled. The same scramble at Geneva where handed to several people and yet only one a few were able to break the current wr at the time. Luck is a big part of records but not the largest part.


True, which is why introducing this would mean introducing a whole new event, due to the almost impossibility of breaking Erik's record with proper scrambles.


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## qqwref (Oct 20, 2009)

ZB: Erik's solve was 7 moves. If we keep 7-move scrambles, we will clearly not need a new event because anyone who got a faster solve would be able to break Erik's record. Besides, do you think we need a new 3x3 event because 7.08 is impossible to break? Clearly not, even though nobody else has done a sub-8 yet.


hawkmp4: I said 20% because the number of scrambles up to 7 moves is <20% while the number of scrambles up to 8 moves is >20%. The number of scrambles up to 7 moves is under 10%. The 20% number was just used because that is our definition of what constitutes lucky.

For the purposes of math:
if we discard every scramble up to 7 moves we discard 7.89% or about one in 12;
every scramble up to 6 moves, 1.70% or one in 60;
every scramble up to 5 moves, 0.33% or one in 300;
every scramble up to 4 moves, 0.06% or one in 1600.


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## Dirk BerGuRK (Oct 21, 2009)

I would be interested in seeing a poll about this subject. I think this is certainly a topic worth discussing. I seem to remember a discussion on TwistyPuzzles a while back about removing lucky scrambles for a 3x3 that didn't receive much favor, although this is a different scenario since entire solutions can be seen during inspection.

I have seen a few one and two move solutions appearing on hi-games, but I have never heard about any appearing in a competition. If these appear are they thrown out?


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## Tim Major (Oct 21, 2009)

qqwref said:


> ZB: Erik's solve was 7 moves.


Timer start, pick up cube, execute 7 moves, drop cube, stop timer. This was done in 0.96? WTF?!?! Did someone recreate the solution? I would be interested to see it. I can barely do 4 moves in that time, and that is 4 random moves. Insanity.


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## Anthony (Oct 21, 2009)

I'm not really for or against using this scrambler, whatever happens happens. But, I can think of one situation where easy scrambles definitely influenced an average. Check this out.

Michal Robaczyk is ranked 17th in the world with a 3.97 average. Here are his times. 1.66, 5.48, (1.55), (6.63), 4.77.


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## DavidWoner (Oct 21, 2009)

I think it's a little weird that Erik and Lucasz were the only other people to even sub4 on the third scramble.


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## Anthony (Oct 21, 2009)

DavidWoner said:


> I think it's a little weird that Erik and Lucasz were the only other people to even sub4 on the third scramble.



I know. I mentioned that to some people on msn and we agreed that there's a good chance they didn't scramble his cube properly. :/


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## hr.mohr (Oct 21, 2009)

ZB_FTW!!! said:


> qqwref said:
> 
> 
> > ZB: Erik's solve was 7 moves.
> ...



Eriks own post about the solution: http://www.speedsolving.com/forum/showpost.php?p=100915&postcount=9


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