WCA Scramble Algorithm

[mrCage]

Hi :-)

I see a possible future clash between the wca preferred scrambling notation and optimality. A random state optimal scrambler would (probably) use all notation tokens on larger cubes, not solely outer block notation. There are a few puzzles where random state scrambling is easy and feasible. So by all means go ahead and scramble like that. Noone has yet convinced me what is the gain in doing so. KISS

Per

[AvGalen]

For Clock I have had this feeling for quite some time that the scrambles aren't actually that good and certainly aren't "random state". Do you know of a study about this or do I have to do this research myself?

I just checked it (probably have before). I'm sure now. A proof is actually quite easy, at least if you know how to solve the clock. I can give my proof, but I'm sure you can do it as well and I'd like to see (how) you do it.

I am actually not quite sure that clock scrambles are indeed random state. I will look into this on sunday. I am especially worried about the quality of the scrambles when there are 0's in it. I hope that on Sunday I will realise that I shouldn't worry.

And Per: You should realise that for blind and FMC it is unfair if chances of 8 misoriented edges are smaller than 4 misoriented edges. For speed, this might also be an advantage if you use methods like EOLine. I am not saying this is a big problem, but if we have the capabilities to avoid it without big downsides...why not?

[qqwref]

The way the clock scramble should work is that it generates 14 random numbers (from -5 to 6 inclusive) and then does a specific set of 14 linearly independent moves with those amounts. That is, as there are 14 clocks, we should be able to solve every position by doing each of those moves once, and similarly we can scramble to any position by doing each of those moves once. As long as the function we use to generate the 14 numbers is truly random, the scrambles also will be.

[Cride5]

Looks like the simple idea of implementing Kociemba in Javascript wasn't to be. As I suspected, Javascript with its very loose type system made it difficult to store the lookup tables efficiently. The program consumed far too much memory to be usable. Looks like its back to the drawing board...

In the mean time, I've posted up a simple random state scramble generator as a Java applet if anyone's interested.

I'd still like to get an efficient solver (25 moves or less) working in Javascript, something with a much leaner memory footprint. Currently very short on time, so I'll put it on the back burner for now

[mrCage]

And Per: You should realise that for blind and FMC it is unfair if chances of 8 misoriented edges are smaller than 4 misoriented edges. For speed, this might also be an advantage if you use methods like EOLine. I am not saying this is a big problem, but if we have the capabilities to avoid it without big downsides...why not?

Have i misunderstood the concept of fairness?! As long as all competitors get the same scramble(s) it would be fair, right ???

Seriously, explain to me what is wrong with the occasional easy/lucky scramble as long as everyone get that same scramble??

Per

[Lucas Garron]

And Per: You should realise that for blind and FMC it is unfair if chances of 8 misoriented edges are smaller than 4 misoriented edges. For speed, this might also be an advantage if you use methods like EOLine. I am not saying this is a big problem, but if we have the capabilities to avoid it without big downsides...why not?

Have i misunderstood the concept of fairness?! As long as all competitors get the same scramble(s) it would be fair, right ???

Seriously, explain to me what is wrong with the occasional easy/lucky scramble as long as everyone get that same scramble??

Per

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.

Also, it's unfair because it changes the nature of the event. The idea is to assess the ability to solve any cube in few moves. With an uneven scramble distribution, we're giving competitors a chance to prepare to perform better in this event than their ability to solve arbitrary cubes.

[qqwref]

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.

This is the same reason that I have advocated removing scrambles that give a position which is too close to solved. Even if everyone in a competition has the opportunity to solve an incredibly easy scramble, not everyone in the world will, and so it's not fair to everyone who wasn't at that competition. For some events this is no problem at all, but for short events such as 2x2 and pyraminx it is a huge deal. I don't want to have to compete with someone who averages 8-9 seconds on 2x2 but got a 2-second solve because the scramble was 4 or 5 moves; unless I was world-class at 2x2, there's no way I could beat a time like that without also being lucky.

[mrCage]

And Per: You should realise that for blind and FMC it is unfair if chances of 8 misoriented edges are smaller than 4 misoriented edges. For speed, this might also be an advantage if you use methods like EOLine. I am not saying this is a big problem, but if we have the capabilities to avoid it without big downsides...why not?

Have i misunderstood the concept of fairness?! As long as all competitors get the same scramble(s) it would be fair, right ???

Seriously, explain to me what is wrong with the occasional easy/lucky scramble as long as everyone get that same scramble??

Per

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.

Also, it's unfair because it changes the nature of the event. The idea is to assess the ability to solve any cube in few moves. With an uneven scramble distribution, we're giving competitors a chance to prepare to perform better in this event than their ability to solve arbitrary cubes.

That is taking fairness a bit far ... Then one could say cubing contests are by nature unfair (unless online ... ) Would you also include method independence in your perfect fairness definition?

Per

[AvGalen]

...Would you also include method independence in your perfect fairness definition?

Per

Yes, that is exactly what this is about. If the number of oriented edges should be 6 on average, but it is 10 on average (these numbers are exagerated) then you could optimise training by learning all 2-flip algs but only 1 or 2 6 flip algs.

If a truly random puzzle state is generated first and then a scramble is calculated for it that would be the fairest way

[qqwref]

If a truly random puzzle state is generated first

Ah, Arnaud, didn't you know, that's the hardest part ;-)