WCA Scramble Algorithm

[okayama]

I have questions about the scramble-length.

The scramble-length is defined as:

(3x3: 25)
4x4: 40
5x5: 60
6x6: 80
7x7: 100
Mega: 70
Sq-1: 40

and I want to know

- History (how was the scramble-length defined?)
- Fact (is the length truly enough to get a random position?)

I'm interested in the Latch Cube, and I want to think/know the proper scramble-length for it based on the same idea as the puzzles above.

 

[FMC]

im interested in this latch cube....can you please tell me how different is this from 3x3x3 cube?
i think all anti clockwise turns can be replaced by 3 clockwise turns but there must be something
else that makes it different from normal 3x3x3..can i just use some arrow marks on my normal 3x3x3 cube
to simulate a latch cube or is it something more?thanks

 

[Lucas Garron]

- History (how was the scramble-length defined?)

Something that looks random enough and doesn't take too long.

- Fact (is the length truly enough to get a random position?)

(3x3: No)
4x4: No
5x5: No
6x6: No
7x7: No
Mega: No
Sq-1: No

No number of moves is enough; even if the distribution approaches the correct one, there will always be small deviations. The definition of "random" is subjective, and can be demonstrated to be quite high for some reasonable definitions of "random enough."

Although for the huge cubes what matters in practice is center distribution, and for Megaminx the star piece distribution (colors are solver-dependent).

 

[joey]

What if you don't start with centres or stars?

 

[qqwref]

I think the number of turns is enough to adequately scramble any piece type (centers, corners, edges (for star/cross), whatever). You will only notice a difference if you look at more complex things like block building (on centers, say), parity (on Square-1 it actually occurs well under 50% for our current scrambler, if you use optimal cubeshape), etc.

In all cases but Megaminx, there are more possible scrambles than possible positions. So at least that is good.

Lucas brings up a good point but also a useless one, because even though we would like to use a random position scrambler for all puzzles, it is not yet possible (computationally) to do this in a small number of moves for 5x5, 6x6, 7x7, and megaminx. (4x4 is debatable; there is a Thistlethwaite-like solver out there which almost has an acceptable movecount.)

 

[okayama]

im interested in this latch cube....can you please tell me how different is this from 3x3x3 cube?
i think all anti clockwise turns can be replaced by 3 clockwise turns but there must be something
else that makes it different from normal 3x3x3..can i just use some arrow marks on my normal 3x3x3 cube
to simulate a latch cube or is it something more?thanks

Big feature: If there are both (black and white) arrows on the same face, the face is locked!

- History (how was the scramble-length defined?)

Something that looks random enough and doesn't take too long.

Hmm, is there no theoretical ground?
For example, a friend of mine expects that there are 6 faces in 3x3x3, and
6^25 = 2.8 x 10^19 ~ 4.3 x 10^19 (approximately equals to the number of all states)
was probably the reason for 25 moves in the case of 3x3x3. (aside from the following fact)

- Fact (is the length truly enough to get a random position?)

No number of moves is enough; even if the distribution approaches the correct one, there will always be small deviations. The definition of "random" is subjective, and can be demonstrated to be quite high for some reasonable definitions of "random enough."

OK, aside from the fact, I want to know why WCA defined the following moves

(3x3: 25)
4x4: 40
5x5: 60
6x6: 80
7x7: 100
Mega: 70
Sq-1: 40

make the puzzle "looks random enough and doesn't take too long." Is there anyone who knows the (theoretical/mathematical) background?

 

[bcube]

It's not fair because the solves enter a database where solves are compared with people's who didn't get a chance at the same scrambles. "Fair" at the competition, not fair worldwide.

Do you know, by any chance, how WCA addressed this issue?

Since it is not solved yet, what were their arguments for keeping it worldwide unfair?

 

[stoic]

This is definitely my last post in this thread because I strongly believe that I have nothing more to add to what I said earlier

You're cheating by trying to keep your same argument going in a different thread from 14 years ago. Give it up man.

 

[tseitsei]

Do you know, by any chance, how WCA addressed this issue?

Since it is not solved yet, what were their arguments for keeping it worldwide unfair?

"worldwide fair" is not possible. Only fair way would be that everyone uses the exact same scrambles (that is why we do so in competitions to achieve "fairness" inside that competition). But obviously everyone can't use the same scrambles across the world since we have many competition at many different locations at many different times.

 

[Gecko777]

I tried searching for it in Google and in this forum before posting this thread, but no luck.
My question is, what is the algorithm that is used for generating scrambles in WCA competitions/Cube Explorer?
Is it just some random sequence of maneuvers, or some other sort of complex algorithm to avoid easy scrambles or something?
I need to know this because I'm going to make a Rubik's cube scrambler and timer for my PSP
to improve my programming skills and so that I can practice cubing anywhere (damn, I have no life ).

And hopefully, I'm posting in the correct category.

Crazy to think that this was 15 years ago

 

[Lucas Garron]

Do you know, by any chance, how WCA addressed this issue?

Since it is not solved yet, what were their arguments for keeping it worldwide unfair?

There isn't really an argument for having scrambles vary in difficulty across competitions. That's just what happens by default if you don't reuse scrambles (which would either change the nature of the event or cause huge potential for cheating), and there is no way to generate multiple random scrambles with objectively equal difficulty for all competitors across competitions.

That said, some things have happened in the 15 years since the post you quoted:

• We've adopted random-state scrambles for all puzzles where possible. This reduces bias compared to random moves. In fact, the ability to generate random-state 4x4x4 scrambles was a major motivation for adopting TNoodle over Mark 2.
• The closest to an objective process we have is our current scramble filtering, which avoids scrambles that take too few moves to solved. This was very controversial to implement, but I think we would be much worse off without it at this point.
• As you can see in the Incidents log, the WRC looks at mis-scrambles to figure out if they were unfairly easy compared to the proper random scramble.
• `xyzzy` has been doing some research into metrics to select scrambles that are less orderly (and therefore usually not "easier") from a human perspective. I would definitely like to evaluate techniques like this for WCA scrambles in the next few months. I'm not sure this is something we could ever apply to 3x3x3, but it's a first step to doing it for some puzzles.

 

[bcube]

Lucas, that's all nice and perfectly understandable, thank you for the summary. I am rather asking why is the WCA keep comparing the FMC worldwide results on their results page when all results are not mutually comparable (unlike the other WCA results in other events)? See e.g. this post (under the horizontal line), or basically the whole linked thread.

"worldwide fair" is not possible

For simplicity, let's consider FMC event, single attempt format. Regarding fairness, what's wrong with options #2 (which is outlined in the first post of that thread) and #3 outlined here? You might say option #1 doesn't use random state. I might say it uses "random state among all optimal 18-movers". So in terms of fairness, what's wrong with option #1?

Your argument "Having only 18 move optimal scrambles would not make all scrambles equal. Most of the optimal solutions are just unfindable for humans with current methods." seems to be irrelevant for me since I don't see why human methods should be considered at all (to my understanding, FMC is a method-less event).

 

[bldcuber314]

The closest to an objective process we have is our current scramble filtering, which avoids scrambles that take too few moves to solved. This was very controversial to implement, but I think we would be much worse off without it at this point.

By that you just mean rules like '2x2 scrambles must take at least 4 moves to solve' right? It's not like it's been made purposely hard to generate 4 movers?

 

[tseitsei]

For simplicity, let's consider FMC event, single attempt format. Regarding fairness, what's wrong with options #2 (which is outlined in the first post of that thread) and #3 outlined here? You might say option #1 doesn't use random state. I might say it uses "random state among all optimal 18-movers". So in terms of fairness, what's wrong with option #1?

Your argument "Having only 18 move optimal scrambles would not make all scrambles equal. Most of the optimal solutions are just unfindable for humans with current methods." seems to be irrelevant for me since I don't see why human methods should be considered at all (to my understanding, FMC is a method-less event).

We are talking about an event where HUMANS try to solve cubes in as few moves as possible. So obviously human methods and what kind of solutions are easier for humans to find is incredibly relevant. 17 mover with only some weird non-human findable computer solutions is obviously much much harder than an 18 mover where an optimal solution follows EO->DR->HTR logic with reasonable step lengths. And obviously not all 18 movers are even close to equal either in terms of human FMC.

And your understanding of FMC is just wrong. Literally ALL the top solvers nowadays use the same exact method which is:
Edge orientation (reduce the cube to <F2, B2, R, L, U, D> movegroup)
Domino reduction = DR (reduce the cube to <F2, B2, R2, L2, U, D> movegroup)
Half-turn reduction = HTR (reduce to <F2, B2, R2, L2, U2, D2>)
Solved

 

[Lucas Garron]

Lucas, that's all nice and perfectly understandable, thank you for the summary. I am rather asking why is the WCA keep comparing the FMC worldwide results on their results page when all results are not mutually comparable (unlike the other WCA results in other events)? See e.g. this post (under the horizontal line), or basically the whole linked thread.

I think you're making assumptions that don't apply here. It's not like we sit down every year and decide whether to keep the FMC ranking mechanism the same or not. Things change when someone identifies an issue, proposes a solution, and the tradeoffs are weighed for adopting it.

But I think you're also getting up in arms about something that I haven't seen competitors be particularly upset about. I don't think there's much of a practical difference between the "unfairness" of a 16-move FMC scramble (compared to ≈18 moves) and the "unfairness" of a 4-move 2x2x2 scramble (compared to ≈10 moves). I certainly wouldn't call 10-move 2x2x2 scramble more fair than an 18-move FMC scramble just because a WR wouldn't automatically break the laws of physics/mathematics. Both events are very mature, so a single record will always have a factor of luck and most top competitors will presumably be focused on averages.

To be clear, I'm not saying the current system should stay. In fact, I've been doing some research to see how feasible it is to implement FMC scramble filtering, and I would like to see more community discussion and research on this topic. As competitors push the FMC WR average close to optimal, we may yet reach the point where it's worth looking at ways to make FMC attempts and means "more fair", but I don't think we know right now whether basing this purely on the optimal solution move count is intrinsically guaranteed to solve more problems than it could cause.

 

[bcube]

And your understanding of FMC is just wrong.

We can agree that I don't know (or really care about) what methods are used for FMC by the best FMC-ers nowadays. What difference would it make it for me? Another methods were being used 15 years ago, another methods might be used after 15 years. That's why I see FMC event as a method-less event.

17 mover with only some weird non-human findable computer solutions is obviously much much harder than an 18 mover where an optimal solution follows EO->DR->HTR logic with reasonable step lengths.

So? The competitor is welcome to use any method to find the shortest solution. It is his choice to use shorter or longer, just like any other competitor could choose shorter if he can find it.

And obviously not all 18 movers are even close to equal either in terms of human FMC.

So? Getting luck is not a crime. Otherwise I don't know how luck is defined in FMC.

Things change when someone identifies an issue, proposes a solution, and the tradeoffs are weighed for adopting it.

As stated here, I don't believe I am the first one bringing this issue up to the WCA. I expected dessisions for keeping the issue have been made in the past, looking for their arguments.

But I think you're also getting up in arms about something that I haven't seen competitors be particularly upset about.

Do you see doping cycling racers objecting about fair play? There is not even needed a discussion between cycling governing body and racers because it is just clear some racers are being discriminated. To me, it is just clear, no discussion between WCA and cubers is really needed in this case (don't get me wrong, I would love to see meaningfull discussion between WCA and cubers about it).

Anyway, I can live with whatever rules is WCA applying. Just wanted to make the world a little bit better for everyone.

 

[cubenerd74]

We can agree that I don't know (or really care about) what methods are used for FMC by the best FMC-ers nowadays. What difference would it make it for me? Another methods were being used 15 years ago, another methods might be used after 15 years. That's why I see FMC event as a method-less event.

That same logic can be applied to every single event. Please at least make sure your arguments make sense before posting them.

 

[tseitsei]

We can agree that I don't know (or really care about) what methods are used for FMC by the best FMC-ers nowadays. What difference would it make it for me? Another methods were being used 15 years ago, another methods might be used after 15 years. That's why I see FMC event as a method-less event.

Of course human methods make a huge difference for evaluating "easiness" and "fairness" of a scramble. Humans don't just find solutions using brute force. We need a well structured method to follow and that method determines if a given scramble is considered "easy" or "hard". At least it affects "easiness" of the scramble much more concretely and tangibly than some weird computer findable optimal solution.

So? The competitor is welcome to use any method to find the shortest solution. It is his choice to use shorter or longer, just like any other competitor could choose shorter if he can find it.

You wanted FAIR scrambles worldwide. Obviously it wont be fair if optimal solution is much easier to find on some scrambles than others.

So? Getting luck is not a crime. Otherwise I don't know how luck is defined in FMC.

Exactly. Getting lucky is and always necessarily will be a part of cubing since everyone can not use the exact same scrambles. That is what I have been trying to say.

 

[bcube]

human methods make a huge difference for evaluating "easiness"

Agreed. In other words, the same scramble may be seen as easier for competitor 1 using method A than for competitor 2 using method B. I don´t have any problem with this "easiness" difference among competitors/methods.

You wanted FAIR scrambles worldwide. Obviously it wont be fair if optimal solution is much easier to find on some scrambles than others.

We may be saying the same thing, using different vocabulary. As you pointed out, "absolute fair" scrambles are not possible. I would like to see "relative fair" scrambles being introduced. Or as Lucas calls it, "more fair" scrambles. I have a problem with Adam running 110 metres, Bob runing 90 meters, both timing 55 seconds and both being ranked in the same ranking list based on their clocked times without any type of correction factor or category involved. I don´t have a problem with Adam running by his feet (method A) while Bob running by his hands (method B) if both competitors chose it that way.

Getting lucky is and always necessarily will be a part of cubing since everyone can not use the exact same scrambles. That is what I have been trying to say.

If it was not obvious, I didn´t have a problem with competitors being lucky (in the meaning of "luck" I am operating on) since beginning.

 

[tseitsei]

Agreed. In other words, the same scramble may be seen as easier for competitor 1 using method A than for competitor 2 using method B. I don´t have any problem with this "easiness" difference among competitors/methods.

Say we have competitors A and B. Both are top level FMC solvers and thus use the before described method of DR/HTR. A goes to a competition X and B goes to competition Y. Both get an 18 move optimal scramble. The scramble A got has an optimal solution that is very easy to find with the method that EVERY SINGLE top level competitor uses. B gets a scramble where only 18 and 19 move solutions are practically impossible for any human to find. How is that fair in your opinion?

We may be saying the same thing, using different vocabulary. As you pointed out, "absolute fair" scrambles are not possible. I would like to see "relative fair" scrambles being introduced. Or as Lucas calls it, "more fair" scrambles. I have a problem with Adam running 110 metres, Bob runing 90 meters, both timing 55 seconds and both being ranked in the same ranking list based on their clocked times without any type of correction factor or category involved. I don´t have a problem with Adam running by his feet (method A) while Bob running by his hands (method B) if both competitors chose it that way.

As I have said before, optimal move count not really that good of an indicator if a scramble is easy or hard. And thus using only 18 move scrambles will really not add fairness nearly as much as you seem to think it does. I will say it once again: Structure of the short solutions for the scramble matter MUCH more than the move count of absolute optimal solution.

If it was not obvious, I didn´t have a problem with competitors being lucky (in the meaning of "luck" I am operating on) since beginning.

Ok, then you just have different meaning for luck than I do.