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If I wanted to solve a physical Rubik's cube multiple times, for practice, what is the best, most random way, to scramble the solved cube?
The best way I can think is to hold it behind my back and turn randomly until, when I look at it, it looks random enough.
Is there a better way?
If you're willing to take the time: The World Cube Association has a specific method for shuffling their cubes. They use a program called TNoodle to do the scrambling; the program generates a "scramble sequence" which can be followed to produce a scrambled cube.
Their code actually features a nice interface to generate the scrambles:
I have yet to figure out what the "Adjust Events" options do, but producing the scramble sequences just comes down to clicking the "Scramble!" button.
Here's the result of running their program:
There is also an online interface here. I used it to scramble my new 30x30x30 Rubik's cube:
If the goal is to have a truly random cube, holding behind your back and scrambling it is as good as any other method, as long as you do ~20 twists or so.
People often intuitively think that if you scramble a cube for a really long time, it will make it harder to solve. Beyond the first few twists, this is not so. Not only can any amateur solver demonstrate a cube scrambled for half an hour is as easy to solve as a cube scrambled for 10 seconds, there is a proven upper bound on the "hardest" possible Rubik's cube state: 20 moves from scrambled to solved.
Naturally it's possible to produce a scramble using any method where, by random chance, there is less work needed at some point (As in, you solve the first two layers, and lo and behold, the third layer required only one operation!). This is a perfectly fair random occurrence though, and a good scrambler wouldn't discriminate against such scenarios, even if it could detect them.
One more thing: for most solvers, as few as six random twists is enough to scramble a cube. It is a fun puzzle to have a friend perform 4, 5, or 6 random twists on a solved cube, and then see if you can undo the twists without messing up the cube. 4 is usually easy, 5 is quite hard for me, and I can't do 6 without getting lucky : )
Bottom line is, unless you're a savant or a supercomputer, don't overthink cube scrambling!
There are 2 popular methods used to scramble a cube. The first being to apply a certain number of random moves until you are satisfied. The second method is to physical take apart the cube and assemble it again in any solvable state.
The second is known as random state scrambling, and is what is now used in official Rubik's Cube competitions. See more here
The official scrambling program can be found at https://www.worldcubeassociation.org/regulations/scrambles/
This is advantageous over the first method, as it has no statistical bias towards 'easy' scrambles.
As a speedcuber myself, I often find that when I am just applying random moves myself, I end up with the same scrambles as before. This is probably nothing statistical and is likely due to the fact that I am used to performing fast algorithms over and over, but is the main reason why I use generated scrambles myself.
The best tool to generate scrambles for all WCA puzzles is http://ruwix.com/puzzle-scramble-generator/
It supports cubes from 2x2x2 up to 11x11x11, Square-1, Rubik's Clock, Megaminx, Pyraminx and Skewb. You can customize the scramble in many ways and there's a built-in stopwatch to measure your times.
