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How to determine if a Rubik's Cube is sufficiently scrambled?
Once I solve a Rubik's Cube I obviously want to start again. I just scramble it until it seems to be enough; however, sometimes when I then solve it, I can skip entire steps from the beginner's method. Is this normal or was the cube not scrambled enough? How can one determine if the cube is scrambled enough?
Each set of moves is designed to correct a parity error in the cube's layout, but each group of parity it corrects is essentially independent and random. Each step has a chance of already having the right parity. For instance, the way I do it is solve the bottom two layers and then attack the parity errors on the top one at a time
Make sure all the edges are rightsideup
3 possibilities
Make sure the corners are in the right order
3 possibilities
Make sure the corners are rightsideup
Not exactly sure. 5?
Make sure the edges are in the right order.
Not quite sure either. 5?
on a 4x4 there can be a flipped edge
2 possibilities
on a 5x5 there

Each set of moves is designed to correct a parity error in the cube's layout, but each group of parity it corrects is essentially independent and random. Each step has a chance of already having the right parity. For instance, the way I do it is solve the bottom two layers and then attack the parity errors on the top one at a time
Make sure all the edges are rightsideup
3 possibilities
Make sure the corners are in the right order
3 possibilities
Make sure the corners are rightsideup
Not exactly sure. 5?
Make sure the edges are in the right order.
Not quite sure either. 5?
on a 4x4 there can be a flipped edge
2 possibilities
on a 5x5 there are a couple other funny edge things
5?
Now, the probabilities probably aren't equal for each parity state, but at each step there is a fair chance at already being in the right state. That's just how randomness works.
I'd say if you need most of the steps most of the time, you're doing fine. After all, when you practic
20170320 23:38:45 
There are lots of places for scramblers, and provide a very good scrambler, because of the fact that the scrambles can reach all 44 quintillion positions. Here are scramblers, along with timers:
Here; and here.
Or, for an official scrambler, download TNoodle (No link, because not enough rep.)
20170321 00:17:17 
A good, scrambled Rubik's cube, in my opinion, has no lines of 3 of the same color on one side (green). It also has none of the same colors on a touching center and corner piece (red).
20170321 00:39:53 
Skipping steps (especially with the beginners method) is absolutely normal and happens all the time. As far as scrambles go, there isn't really a way to figure out a whether a hand scramble is good or not. It's best to use a scrambler (usually a part of timer software), such.as cstimer. The official WCA scrambler is called TNoodle.
20170321 01:08:16