Three random WCA related questions

[GloopyGum]

Just some random questions that I'd like to know the answer to.

1. Why do 4x4 scrambles take so long to generate?
2. If cutoff is say, 40 seconds for 3x3, and I get a 39 second solve, but +2 it, do I make cutoff?
3. What if the time limit is 40 seconds and I do the same thing? Do I DNF, or does the result get counted? (Unrealistic, but whatever)

 

[SkewbIsTheBestEvent]

Just some random questions that I'd like to know the answer to.

1. Why do 4x4 scrambles take so long to generate?
2. If cutoff is say, 40 seconds for 3x3, and I get a 39 second solve, but +2 it, do I make cutoff?
3. What if the time limit is 40 seconds and I do the same thing? Do I DNF, or does the result get counted? (Unrealistic, but whatever)

For 2 and 3, if it goes over then it will not count, so you will not make cutoff or time limit if you plus 2 over it.

 

[Mike Hughey]

For #1, the reason is that they switched to legitimate random state scrambles for 4x4x4. It takes quite a while to find a reasonably short scramble for a 4x4x4 random state.

Currently puzzles above the size of 4x4x4 are not done with random state scrambles because they would take too long to generate. Ideally, if it ever became possible to generate those in a reasonable amount of time, we would switch to those for the larger puzzles as well. But the time required to generate them is far too long to be justifiable for now. For now, we have settled on 4x4x4 being the largest size for an official random state scramble, and we make do with random move scrambles for the higher order puzzles.

 

[Tabe]

Just some random questions that I'd like to know the answer to.

1. Why do 4x4 scrambles take so long to generate?
2. If cutoff is say, 40 seconds for 3x3, and I get a 39 second solve, but +2 it, do I make cutoff?
3. What if the time limit is 40 seconds and I do the same thing? Do I DNF, or does the result get counted? (Unrealistic, but whatever)

Your final time is the time after all penalties. So you miss cutoff in #2 and get a DNF in #3.

 

[xyzzy]

1. Why do 4x4 scrambles take so long to generate?

Mike's post answers part of this question, but the other part is… do they really?

My crappy laptop takes about 1 second per scramble on average in csTimer, and only when I'm generating large batches of scrambles at once because csTimer automatically generates scrambles in the background. 1 second per scramble is slower than most other scramble generators (iirc the square-1 one is also kinda slow), but unless you need a large number of scrambles at once, it shouldn't be an issue.

Currently puzzles above the size of 4x4x4 are not done with random state scrambles because they would take too long to generate. Ideally, if it ever became possible to generate those in a reasonable amount of time, we would switch to those for the larger puzzles as well. But the time required to generate them is far too long to be justifiable for now. For now, we have settled on 4x4x4 being the largest size for an official random state scramble, and we make do with random move scrambles for the higher order puzzles.

It's not merely a matter of time. As far as I can tell, it's simply not feasible to solve 5/6/7/megaminx in around the same numbers of moves that we currently use for the random-move scrambles (60/80/100/70). (**) Longer scramble sequences also mean higher risk of misscrambling; allowing misscrambling also means you lose the key feature of random-state scrambles (that every legal state is provably equally likely (*)), and it is plausible that misscrambling random-state scrambles may introduce larger bias compared to misscrambling random-move scrambles.

This wasn't the case for 4, where the old scrambles used 40 moves (I think) and the random-state scrambles use around 45 moves, so switching wasn't a big deal. It didn't increase the risk of misscrambles much, and in fact might have reduced it.

(*) Modulo imperfections in the pseudorandom number generator used.
(**) (edit to add) Maybe 80-ish moves megaminx scrambles are possible (considering that the megaminx FMC ao12 UWR is a 96.5), but they'll also be 12-gen scrambles which extremely suck to do.

 

[abunickabhi]

Mike's post answers part of this question, but the other part is… do they really?

My crappy laptop takes about 1 second per scramble on average in csTimer, and only when I'm generating large batches of scrambles at once because csTimer automatically generates scrambles in the background. 1 second per scramble is slower than most other scramble generators (iirc the square-1 one is also kinda slow), but unless you need a large number of scrambles at once, it shouldn't be an issue.


It's not merely a matter of time. As far as I can tell, it's simply not feasible to solve 5/6/7/megaminx in around the same numbers of moves that we currently use for the random-move scrambles (60/80/100/70). Longer scramble sequences also mean higher risk of misscrambling; allowing misscrambling also means you lose the key feature of random-state scrambles (that every legal state is provably equally likely (*)), and it is plausible that misscrambling random-state scrambles may introduce larger bias compared to misscrambling random-move scrambles.

This wasn't the case for 4, where the old scrambles used 40 moves (I think) and the random-state scrambles use around 45 moves, so switching wasn't a big deal. It didn't increase the risk of misscrambles much, and in fact might have reduced it.

(*) Modulo imperfections in the pseudorandom number generator used.

Nice detailed answer. @GloopyGum did these answer clear all of your doubts related to the 3 questions?

 

[GloopyGum]

Yeah! thanks for the answers