# 2-move solves



## JediJupiter (Jun 21, 2014)

According to the WCA rules:
_4b3) Specification for the scramble program: An official scramble sequence must produce a random state from those that require at least 2 moves to solve._
Now, imagine that you're at a competition. They bring out your cube, and you see that you have a 2-move solve. You can solve it as fast as you can, or you can solve it slowly and try to take more than 5.55 seconds. What would you do? Of course, you only have 15 seconds to decide.
((If this counts as off topic, please feel free to move the thread.))


----------



## Goosly (Jun 21, 2014)

I would solve it and try to stop the timer at 1:00.00.


----------



## EMI (Jun 21, 2014)

I don't even get it, why should I wait five seconds?


----------



## pewpewrawr (Jun 21, 2014)

I'd do it as fast as I could, why would I purposefully be slow? :/


----------



## Ollie (Jun 21, 2014)

I'd DNF it. 

1. It requires no skill.
2. 3x3x3 single WR loses all merit.
3. The inevitability of having to explain to people just how unimpressive my world record is, which they'd certainly agree with.

However, everyone has an equal chance of getting a similar scramble at any competition at any time, I can understand if others will try and solve it as fast as possible. They shouldn't IMO, but it's kind of inevitable that one **** will do it.


----------



## 10461394944000 (Jun 21, 2014)

Ollie said:


> I'd DNF it.



i'd deliberately get a sub 0.5 WR to cause the biggest debate ever on speedsolving


----------



## pewpewrawr (Jun 21, 2014)

Ollie said:


> I'd DNF it.
> 
> 1. It requires no skill.
> 2. 3x3x3 single WR loses all merit.
> ...



You're taking things to seriously, I'd do it because 0.xx wr lol.


----------



## qqwref (Jun 21, 2014)

Excuse me, Ollie? If a competitor gets an easy scramble in competition, and solves it as fast as possible, it's _their fault_ that the time is too good, and we should look down on them for it?

If a scramble would be so easy as to render the event meaningless, it should not be used in competition. That's the whole point of scramble filtering, to prevent stuff like this. And this example is exactly why we need it.


----------



## Tim Major (Jun 21, 2014)

If this was E1 or E2 and I got the scramble but no one else would, I'd get 9.80+

If this was just a normal group's scramble, I'd go as fast as I could. Other people would so the 3x3 single would lose merit without me.


----------



## Ollie (Jun 21, 2014)

pewpewrawr said:


> You're taking things to seriously, I'd do it because 0.xx wr lol.



Would you rather have a sub-5.50 WR that you earned honestly or a sub-1 single which was only possible as a result of sheer luck (which virtually every non-cuber is capable of doing in a similar time?)


----------



## pewpewrawr (Jun 21, 2014)

Ollie said:


> Would you rather have a sub-5.50 WR that you earned honestly or a sub-1 single which was only possible as a result of sheer luck (which virtually every non-cuber is capable of doing in a similar time?)



Sub-1 because it would be funny.


----------



## JediJupiter (Jun 21, 2014)

EMI said:


> I don't even get it, why should I wait five seconds?



To respect the current world record holder who had to do _more_ than 2 moves.



qqwref said:


> Excuse me, Ollie? If a competitor gets an easy scramble in competition, and solves it as fast as possible, it's _their fault_ that the time is too good, and we should look down on them for it?



I'd at least have way more respect for someone who waited specifically to not get a WR on an easy solve, especially if they knew they would have no chance of breaking it otherwise.



qqwref said:


> If a scramble would be so easy as to render the event meaningless, it should not be used in competition. That's the whole point of scramble filtering, to prevent stuff like this. And this example is exactly why we need it.



I also agree. I'm also very confused about why a 7x7 can be just 2 moves away, but a 2x2 which can be done in under a second anyway has to be 4 moves away.


----------



## ryanj92 (Jun 21, 2014)

I'd probably pop or get a timer fail or something


----------



## Goosly (Jun 21, 2014)

JediJupiter said:


> I also agree. I'm also very confused about why a 7x7 can be just 2 moves away, but a 2x2 which can be done in under a second anyway has to be 4 moves away.



2x2 scrambler is based on a random state. 7x7 scrambler is a big amount of random moves. It can't be 2 moves anyway.


----------



## Ollie (Jun 21, 2014)

qqwref said:


> Excuse me, Ollie? If a competitor gets an easy scramble in competition, and solves it as fast as possible, it's _their fault_ that the time is too good, and we should look down on them for it?
> 
> If a scramble would be so easy as to render the event meaningless, it should not be used in competition. That's the whole point of scramble filtering, to prevent stuff like this. And this example is exactly why we need it.





pewpewrawr said:


> Sub-1 because it would be funny.



A good case for scramble filtering methinks


----------



## JediJupiter (Jun 21, 2014)

I'm under the impression that it could; just because you're doing a large amount of moves doesn't mean it always becomes less 'solved'.


----------



## pewpewrawr (Jun 21, 2014)

Ollie said:


> A good case for scramble filtering methinks



I feel like that comment was a jab at me, but I'm going to let it go because I'm cool like that.


----------



## scottishcuber (Jun 21, 2014)

I agree with Ollie.


----------



## kcl (Jun 21, 2014)

I gotta say I'm with Ollie. I wouldn't feel right about a sub 1 3x3 single, it just seems wrong. I don't deserve WR single. I would still make it a good time, just probably not WR.


----------



## Kirjava (Jun 22, 2014)

Ollie said:


> A good case for scramble filtering methinks



Yes, we should ruin 2x2x2 because of highly probable cases like this.


----------



## WinterCub3r (Jun 22, 2014)

Just remember this, if you decide to solve it, you are that person that came up to you and said, "i can solve that super fast" then turns two sides and turns them back and laughs in you face. Don't be that person.


----------



## pewpewrawr (Jun 22, 2014)

I'll be whoever I want to, and I want to be sub-1 wr holder.


----------



## Ollie (Jun 22, 2014)

Kirjava said:


> Yes, we should ruin 2x2x2 because of highly probable cases like this.



I wasn't taking about 2x2x2, I think a 4 move minimum is fine. Besides, when this level of TPS is possible I can't see how having such a filter would ruin 2x2x2. But off topic


----------



## qqwref (Jun 22, 2014)

Please. We know the rough distribution of optimal movecounts for the 3x3x3. Let's say we forbid anything that can be solved in 13 or fewer moves; it turns out that that is 575,342,418,697,410 positions, or about one in every 75176 positions. So we can figure out exactly how much of an impact that would have on a typical competitor (answer: almost none).


----------



## pewpewrawr (Jun 22, 2014)

Either all solutions are ok or none of them are ok.


----------



## newtonbase (Jun 22, 2014)

Try to find any top level sportsman who would turn down a chance for an easy win*. There aren't many. If I could solve as fast as you guys then I'd go for any record available and I'd leave it up to the WCA to worry about whether it is legal or not.

* John Francome is an exception to the rule.


----------



## Petro Leum (Jun 22, 2014)

i would do it for the lols, seeing how low i could go considering all competitors of that round get the scramble; and if it's WR i would get the WCA to disqualify it afetrwards because it's lame.


----------



## Kirjava (Jun 22, 2014)

Ollie said:


> I think a 4 move minimum is fine



I really do not.


----------



## IRNjuggle28 (Jun 22, 2014)

Do you guys not understand the point of random permutation scrambles? Filtering scrambles completely ruins that. It's stupid enough to do it for 2x2. 



> I'm also very confused about why a 7x7 can be just 2 moves away, but a 2x2 which can be done in under a second anyway has to be 4 moves away.


The answer is pretty obvious. People think that the odds of getting a 2 move scramble on 7x7 are negligible. And they're right.

The singles don't matter that much compared to the community wide consensuses on who is actually fast. If someone gets a 2 move scramble, they are really not going to get that much recognition anyway. Do you hear people talking about Christian Kaserer? What about Chris and Rami? Yeah, that's what I thought. 

It's not just 2x2, either. People on here respect Mats Valk, but I don't think anyone thinks he's faster than Feliks. And that's considering that Mats _is_ actually one of the best in the world at 3x3. If someone sets a stupid record, the community doesn't take any recognition away from the people who really deserve it. 

Everyone who goes to a competition, anywhere, has an equal chance of getting a scramble that stupid. And if Feliks got that scramble, and got a sub 1, I would think it was every bit as stupid as if someone else did. People have no obligation to not solve it as fast as they can.


----------



## XTowncuber (Jun 22, 2014)

oh dear can we please not do this again? I'm tired of this discussion.

I would probably pop if I got a 2 move scramble. That's just my luck.


----------



## goodatthis (Jun 22, 2014)

Rocky0701 said:


> You would get 5 LL skips by the time it would ever take affect in a compeition. It isn't much to ask for, it just pregents people who average like 20 seconds to get a record that they don't deserve because of luck. Do you really count 10 moves a "solve"? Chill out.



5 LL Skips? No. The amount of possible positions that are solved with 15 moves or less compared to all possible positions is 1/400, compared to the much greater number that would be 5 LL skips. The probability that you would get 5 LL skips in a row is more than the possible positions on the cube, by a lot. ((1/15552)[SUP]5[/SUP])

Also, if you meant over a long period of time, unless I've done my math wrong, you would have about a 1 in a billion chance of having 5 LL skips in 1000 solves. (Doing binomial probability is kinda tough when you have to find a calculator high powered enough to do exponents that high)


----------



## Tim Major (Jun 22, 2014)

newtonbase said:


> Try to find any top level sportsman who would turn down a chance for an easy win*. There aren't many. If I could solve as fast as you guys then I'd go for any record available and I'd leave it up to the WCA to worry about whether it is legal or not.
> 
> * John Francome is an exception to the rule.



A lot of Australian cricket players, following in the footsteps of Adam Gilchrist, walk (showing they're out) regardless of whether the umpire calls them out or not.

I think you're underestimating the sportsmanship of professionals.


----------



## qqwref (Jun 22, 2014)

Tim Major said:


> A lot of Australian cricket players, following in the footsteps of Adam Gilchrist, walk (showing they're out) regardless of whether the umpire calls them out or not.
> 
> I think you're underestimating the sportsmanship of professionals.


Not a cricket player, but I assume an out is a "your turn's done" type of thing that happens many times every single game - which would mean it's a pretty basic politeness move. That's more like when a cuber points out a +2 penalty or DNF that the judge didn't notice - you lose a few seconds or one solve out of the many that you do each competition. Not really comparable to giving up a one-in-more-than-a-trillion lucky scramble.


----------



## Rocky0701 (Jun 22, 2014)

goodatthis said:


> 5 LL Skips? No. The amount of possible positions that are solved with 15 moves or less compared to all possible positions is 1/400, compared to the much greater number that would be 5 LL skips. The probability that you would get 5 LL skips in a row is more than the possible positions on the cube, by a lot. ((1/15552)[SUP]5[/SUP])
> 
> Also, if you meant over a long period of time, unless I've done my math wrong, you would have about a 1 in a billion chance of having 5 LL skips in 1000 solves. (Doing binomial probability is kinda tough when you have to find a calculator high powered enough to do exponents that high)


I was basing it off of qqwref's statement that it was one in 75,000 chance for a 13 move or below solution. I can see the huge difference between 15 and 13 move solutions now.


----------



## Tim Major (Jun 22, 2014)

qqwref said:


> Not a cricket player, but I assume an out is a "your turn's done" type of thing that happens many times every single game - which would mean it's a pretty basic politeness move. That's more like when a cuber points out a +2 penalty or DNF that the judge didn't notice - you lose a few seconds or one solve out of the many that you do each competition. Not really comparable to giving up a one-in-more-than-a-trillion lucky scramble.



It has changed entire games before, and potentially series before. This was the semi-final at a World champs: https://www.youtube.com/watch?v=X8vmRKOEcCY

If Mats' +2 wasn't called by the judge (even though it should've been) and Mats won worlds instead of Feliks. Walking would be the equivalent of saying "no that WAS a +2" after the cube was already realigned.

There are plenty of sportsman who would turn down an unfair chance at an easy win.

The previous Square-1 single holder was laughed at by the community (and doubted). I'm sure many people in this community would take their average solve time to solve a 2 move scramble. At the end of the day, what's the point in getting a 0.5 solve? Unless you have some sponsorship, you're;
-not making money
-potentially losing respect
-getting a (meaningless) title that everyone won't care about


----------



## brian724080 (Jun 22, 2014)

I would solve it as fast as I can, pop the cube on the last move, and reset the timer.


----------



## guysensei1 (Jun 22, 2014)

I would do the 2 moves, put the cube down, then stride around the competition area for around the same time as my global average, then stop the timer.


----------



## Carrot (Jun 22, 2014)

XTowncuber said:


> oh dear can we please not do this again? I'm tired of this discussion.
> 
> I would probably pop if I got a 2 move scramble. That's just my luck.



Pyra scrambles should definitely be 10 moves as minimum :3


----------



## Bindedsa (Jun 22, 2014)

Carrot said:


> Pyra scrambles should definitely be 10 moves as minimum :3



Than should would we DQ you WR single?


----------



## mark49152 (Jun 22, 2014)

Sportsmanship has nothing to do with it. If it's legal, it's legal. I would do the solve as fast as I could, laugh about my meaningless single WR, and let everyone tie themselves in knots about how dumb the rules are


----------



## CriticalCubing (Jun 22, 2014)

I would solve it at 0.XX TPS and in the end a timer fail or DNF. But I will not try to get a WR using sheer luck.


----------



## Renslay (Jun 22, 2014)

mark49152 said:


> Sportsmanship has nothing to do with it. If it's legal, it's legal. I would do the solve as fast as I could, laugh about my meaningless single WR, and let everyone tie themselves in knots about how dumb the rules are



Completely agree.

Also, wouldn't the delegate or the main judge has the right to change a scramble before it goes out? I highly doubt that they let a 2 move scramble be an official one. "Hey, look, a 2 move scramble!" "Nah, let it man, it's what the software generated..."


----------



## Cubeologist (Jun 22, 2014)

I think I would just go for the NAR haha.


----------



## EMI (Jun 22, 2014)

Well many of you are arguing that 3x3 single would be worthless then, but also saying you should not solve it because someone else deserves it more than you. That doesn't make sense to me. When I have super lucky cards at Poker, and play against a better player, I don't let him win because he deserves it. Same goes for cubing because luck always plays a role. (Not as much as in Poker, but it still is part of the game.)
That's why I don't care for 3x3 singles, and that's why I don't have a problem to use whatever luck I get. And yes that is totally legit and fair.


----------



## Antonie faz fan (Jun 22, 2014)

i would probably do a 0.xx solve but really no reaction.


----------



## goodatthis (Jun 22, 2014)

Carrot said:


> Pyra scrambles should definitely be 10 moves as minimum :3



Isn't 11 the Pyra God's Number?


And anyway, maybe we should just stop taking this thread so literally and realize how incredibly small the chances are of a 2 move solve. It would be 1/176 quadrillion compared to the 1/286 million chance of winning the lottery. It's also still even less that winning the lottery twice in your lifetime. It would be even less than the chances of winning the lottery 3 times in your lifetime. Or even a 3 move solve, which would be 1/13 quadrillion, that's just a little more common than getting the lottery 3 times in your lifetime. So yeah it's great to have "moral" discussions on what you would do, but we need to think within the reasonable realm of probability.


----------



## VeryKewlName (Jun 22, 2014)

pewpewrawr said:


> I'd do it as fast as I could, why would I purposefully be slow? :/



You would be purposefully slow so that it didn't seem like you got an unfair scramble.


----------



## Rocky0701 (Jun 22, 2014)

dsbias said:


> I think I would just go for the NAR haha.


But you would have to do good with the other solves too. you said: nAr.


----------



## TMOY (Jun 22, 2014)

Renslay said:


> Also, wouldn't the delegate or the main judge has the right to change a scramble before it goes out? I highly doubt that they let a 2 move scramble be an official one. "Hey, look, a 2 move scramble!" "Nah, let it man, it's what the software generated..."



That happened at Phalsbourg Open 2012; when we (the scramblers) noticed that the last solve of the 2^3 group we were scrambling for had a 2-move solution (scramble filtering for 2^3 was not in effect yet). The delegate told us to replace it by the first scramble of an extra group he had generated just in case.

And this kind of discussion always makes me laugh. It is very easy to say "of course, I would naturally decline it" while comfortably sitting on a chair at home in front of a computer. If those righteous guys actually got faced with such a scramble at an official comp, how many of them would resist the temptation of getting a superfast PB ? Probably not that many. Come on, guys, getting lucky is not a crime.


----------



## Antonie faz fan (Jun 22, 2014)

TMOY said:


> That happened at Phalsbourg Open 2012; when we (the scramblers) noticed that the last solve of the 2^3 group we were scrambling for had a 2-move solution (scramble filtering for 2^3 was not in effect yet). The delegate told us to replace it by the first scramble of an extra group he had generated just in case.
> 
> And this kind of discussion always makes me laugh. It is very easy to say "of course, I would naturally decline it" while comfortably sitting on a chair at home in front of a computer. If those righteous guys actually got faced with such a scramble at an official comp, how many of them would resist the temptation of getting a superfast PB ? Probably not that many. Come on, guys, getting lucky is not a crime.



what event? like 2x2 pyra or skewb? cuz if anything else it would crazy...


----------



## TDM (Jun 22, 2014)

Antonie faz fan said:


> what event? like 2x2 pyra or skewb? cuz if anything else it would crazy...


2x2.


----------



## JediJupiter (Jun 22, 2014)

goodatthis said:


> Isn't 11 the Pyra God's Number?
> 
> 
> And anyway, maybe we should just stop taking this thread so literally and realize how incredibly small the chances are of a 2 move solve. It would be 1/176 quadrillion compared to the 1/286 million chance of winning the lottery. It's also still even less that winning the lottery twice in your lifetime. It would be even less than the chances of winning the lottery 3 times in your lifetime. Or even a 3 move solve, which would be 1/13 quadrillion, that's just a little more common than getting the lottery 3 times in your lifetime. So yeah it's great to have "moral" discussions on what you would do, but we need to think within the reasonable realm of probability.



It's not that it's unlikely to happen. It's that it could happen. Just because it's unlikely that you'll win the lottery doesn't mean it won't happen.


----------



## goodatthis (Jun 22, 2014)

JediJupiter said:


> It's not that it's unlikely to happen. It's that it could happen. Just because it's unlikely that you'll win the lottery doesn't mean it won't happen.



Sure, but there's only been about 2 million solves done in the WCA's history. And honestly I'm just going to leave you to ponder the number 176 quadrillion. That's 176,000,000,000,000,000. And I'm not aware of anyone who has won the Mega Millions lottery more than 3 times in their lifetime. And there's also a lot more people who have played the lottery than have competed in a WCA competition. There are some things that are so infinitesimally small a chance of happening that sometimes it's not even worth it to wonder. And I never said it wouldn't happen, but there are some things, such as the Infinite Monkey Therorem (http://en.m.wikipedia.org/wiki/Infinite_monkey_theorem) that bring up the question, how low is too low? Obviously something like 167 quadrillion is no where near is great as in the infinite monkey theorem, but it's still a very low probability.


----------



## mark49152 (Jun 22, 2014)

JediJupiter said:


> It's not that it's unlikely to happen. It's that it could happen. Just because it's unlikely that you'll win the lottery doesn't mean it won't happen.


I don't think probability is the point. It's a hypothetical question. Everyone's aware that a 2-move 3x3 solution will almost certainly never happen. Perhaps it would be more interesting to consider where people would draw the line. For example, of those saying here that they would forego a 2-move solution, I wonder what they would do with say a cross skip and LL skip? Wait until the clock passes 5.55 before hitting the timer?


----------



## JediJupiter (Jun 22, 2014)

Still, there will continue to be competitions held for years from now. If they go on long enough, it's hard to imaginr there not being a 2-move solve. Also, just because my chance of being mugged on the way home are extremely low, it doesn't mean the police say "oh, it's too unlikely to happen." They take measurements to stop it anyway.


----------



## Lucas Garron (Jun 22, 2014)

JediJupiter said:


> Still, there will continue to be competitions held for years from now. If they go on long enough, it's hard to imaginr there not being a 2-move solve.



I'm very much imagining it. In fact, I *believe* it.

(Unless humans keep cubing for at least a few *million* more years. I think they'll have had enough time to think about it by then.)


----------



## goodatthis (Jun 22, 2014)

JediJupiter said:


> Still, there will continue to be competitions held for years from now. If they go on long enough, it's hard to imaginr there not being a 2-move solve.



Actually it is very hard to imagine. You would have to have 167 quadrillion solves total just to have your odds of getting a 2 move scramble be statistically "more probable than not." If there were 4 competitions a day, 7 days a week, 365 days a year, with 300 scramble sequences for each, so basically a national championship 4 times a day, it would take 381 billion years to accomplish that many solves (or scramble sequences rather). Compare that to the age of the universe, 13 billion years, and you understand how what you're saying doesn't make sense. Earth will be burnt to a crisp by the sun in much much much less time than the time it would take for it to be statistically more probable than not that we will find a 2 move scramble in a competition.

Please do a little bit of thinking before posting a claim that ludicrous. I doubt the WCA will outlive the Sun.


----------



## DeeDubb (Jun 22, 2014)

JediJupiter said:


> Still, there will continue to be competitions held for years from now. If they go on long enough, it's hard to imaginr there not being a 2-move solve. Also, just because my chance of being mugged on the way home are extremely low, it doesn't mean the police say "oh, it's too unlikely to happen." They take measurements to stop it anyway.



There's a lot more realistic things to worry about than a scramble leading to a two move solve. For example, the event being hit by a meteor.


----------



## Carrot (Jun 23, 2014)

Bindedsa said:


> Than should would we DQ you WR single?


Your argument is invalid, my WR is already below filter limit ^_^



goodatthis said:


> Isn't 11 the Pyra God's Number?



14 (tips..)


----------



## 10461394944000 (Jun 23, 2014)

JediJupiter said:


> It's not that it's unlikely to happen. It's that it could happen. Just because it's unlikely that you'll win the lottery doesn't mean it won't happen.



it won't happen.


----------



## Dane man (Jun 23, 2014)

Woah, what happened here? Well, I'd say no. A sub 1 WR would be fun, but also kinda.... I dunno, I'd put myself on a guilt trip 'cus it'd feel like cheating even if it wasn't.

But that sub-1 WR would be very, VERY tempting... I'm not sure 15 seconds is enough to decide. I think instinct would kick in and I'd get a sub 1 just because it's there... then I'd feel bad forever.. or at least unless they discounted it our had someone else beat it for real. ;P

Maybe they'll change the rule to require at least 6 moves on 3x3 (so that intuiting a direct solution isn't all that simple).


----------



## Bunyanderman (Jun 23, 2014)

The real question is how many two move solutions can come from a 25 move scramble?


----------



## goodatthis (Jun 23, 2014)

Bunyanderman said:


> The real question is how many two move solutions can come from a 25 move scramble?



The scramble length doesn't matter, if it's a random state scramble, then 243. Approximately 1/167 quadrillion of all possible combinations. I posted it on the last page, along with some interesting statistics


----------



## Bunyanderman (Jun 23, 2014)

goodatthis said:


> The scramble length doesn't matter, if it's a random state scramble, then 243. Approximately 1/167 quadrillion of all possible combinations. I posted it on the last page, along with some interesting statistics



Thank for the reply, but doesn't answer my question. I would think that a 25 move scramble has a lower chance to have a 2-move solution that a 100 move scramble.


----------



## Julian (Jun 23, 2014)

Bunyanderman said:


> Thank for the reply, but doesn't answer my question. I would think that a 25 move scramble has a lower chance to have a 2-move solution that a 100 move scramble.


Random-state means that a position of the ~43 quintillion available is chosen at random. Then a scramble is generated which will give the chosen position. Each position has an equal chance of being chosen. Like goodatthis said, the scramble length doesn't matter.


----------



## Bunyanderman (Jun 23, 2014)

Julian said:


> Random-state means that a position of the ~43 quintillion available is chosen at random. Then a scramble is generated which will give the chosen position. Each position has an equal chance of being chosen. Like goodatthis said, the scramble length doesn't matter.



I think we are all confused (probably me more,) yes I get that now, but is it more likely to have a 2-move solution out of 25 random moves, or more than that (100 moves?)


----------



## guysensei1 (Jun 23, 2014)

Hmm, doesn't the random state scrambler generate optimal (or near optimal) scrambles? So a 2 move state would have a 2 move scramble right?


----------



## Julian (Jun 23, 2014)

guysensei1 said:


> Hmm, doesn't the random state scrambler generate optimal (or near optimal) scrambles? So a 2 move state would have a 2 move scramble right?


They can be told to generate optimal or sub-optimal scrambles.


----------



## DeeDubb (Jun 23, 2014)

Bunyanderman said:


> I think we are all confused (probably me more,) yes I get that now, but is it more likely to have a 2-move solution out of 25 random moves, or more than that (100 moves?)



After you get past a certain point, it becomes pretty much the same likelyhood. 100 moves, 1000 moves, 10000 moves, all have the same chance of having any given random state, including the 2 move solution. 20 moves might be SLIGHTLY more likely because it is under God's number for 3x3, but I don't really know for sure.


----------



## elrog (Jun 23, 2014)

DeeDubb said:


> After you get past a certain point, it becomes pretty much the same likelyhood. 100 moves, 1000 moves, 10000 moves, all have the same chance of having any given random state, including the 2 move solution. 20 moves might be SLIGHTLY more likely because it is under God's number for 3x3, but I don't really know for sure.


I would like to clarify something in your post. You said that X moves have the same chance to give a random state, but some states are more likely to occur than others due to symmetries. On a supercube, every state has equal probability. I think what you were meaning though is that X moves and Y moves both have the same chance to come up with the same state.

Lets say you start at any particular random state on the cube. If you apply exactly 20 moves to the cube, there may be cases that are still unreachable. Take a state that is 19 moves optimally from the state you started at. That state is only reachable if it is solvable in 20 moves as well as the optimal 19 moves. I am fairly certain that there are 19 move optimal solutions that cannot be solved in exactly 20 moves because there are also 5 move solutions which cannot be solved in 6 moves.

It is true that the probability would eventually be the same, but to define the point, you would have to find a number big enough that every state can be solved in exactly that many moves. There may also be a few numbers of moves above this number of moves which cannot cover every position, but it seems that eventually you would reach a point where any number of moves above this number, whatever it may be, would be able to cover every position. I cannot be to sure though as prime numbers would seem the same way, but they really only become further and further apart.


Oh, and to answer the original question disregarding the point that the chances are so small, I have not and may not ever attend a competition, and that the scramble would surely be thrown out, I would solve the cube in 1 move STM if possible and give up if it wasn't possible.


----------



## goodatthis (Jun 23, 2014)

Bunyanderman said:


> I think we are all confused (probably me more,) yes I get that now, but is it more likely to have a 2-move solution out of 25 random moves, or more than that (100 moves?)



Basically the way it works is a computer program randomly picks a position, (out of 43 quintillion, 243 is the amount that are 2 moves away) let's just say it's the checkerboard pattern. Then the computer tries to solve that position, and yields a solution, which would be something like R2 L2 U2 D2 F2 B2. After that, the computer inverts the solution to instead of solving a given position, it turns a solved cube into that given position, and that's what a scramble is. Move length of the scramble has nothing to do with it when we are talking about random state scramblers.

Does that answer your question? Since Gods Number is 20, if you scramble a cube with 20 moves, and that scramble is sure to yield a random state, (not just random moves) anything over 20 moves is completely useless and wastes moves. Therefore, if you had a random state scrambler (random moves scramblers aren't used anymore) that was really inefficient and gave 100 move solutions to given positions, it wouldn't matter. *Because it's the position on the cube that matters, not the moves being done to it.*


----------

