Probability Thread

[Cyrus C.]

How many total F2L cases are there? Including misplaced edges, corners, etc. Mirrors, rotations, inverses, AUF included.

 

[qqwref]

If you consider allowing AUF & ADF, I calculate 5582 cases, not counting mirrors as the same; and 2909 cases if you count mirrors as the same.

Hang on. I'd want to allow AUF *after* the cross (as well as y rotations and mirrors), but I wouldn't want to allow any adjusting moves *before* the cross, just y rotations, since the full case must always be looked at during inspection. How many cases would we have then?

 

[Antcuber]

tough one:

Is there any possibility that with a random scramble the cube will solve itself? how about being 1 move away? or a u2?

 

[Cyrus C.]

tough one:

Is there any possibility that with a random scramble the cube will solve itself? how about being 1 move away? or a u2?

1 in 43 quintillion, right? There's only one state that the scramble will solve. I assume you mean scrambling a cube, then applying a different scramble to the cube.

 

[cuBerBruce]

Hang on. I'd want to allow AUF *after* the cross (as well as y rotations and mirrors), but I wouldn't want to allow any adjusting moves *before* the cross, just y rotations, since the full case must always be looked at during inspection. How many cases would we have then?

OK, I assume you want the number of cases for relative cross, without allowing AUF/ADF before cross.

I get 6138 cases (including solved). And by the way, only one of these cases requires 8 moves to make the relative cross.

If you count mirrors as separate cases, then it's 11916 cases (including solved).

 

[ben1996123]

OK, I assume you want the number of cases for relative cross, without allowing AUF/ADF before cross.

I get 6138 cases (including solved). And by the way, only one of these cases requires 8 moves to make the relative cross.

U R L F' B' D2 R L (8f*)

 

[cuBerBruce]

OK, I assume you want the number of cases for relative cross, without allowing AUF/ADF before cross.

I get 6138 cases (including solved). And by the way, only one of these cases requires 8 moves to make the relative cross.

U R L F' B' D2 R L (8f*)

Wrong! That's obviously wrong because the U move does not affect the relative arrangement of the cross pieces!

(You need to swap two adjacent cross edges.)

 

[hic0057]

Pyraminx probability question...

What the probability of having a corner-edge pair on a pyraminx?

What the probabiltiy of having a corner-edge-corner block like one on the first step of petrus made?
http://www.speedsolving.com/wiki/index.php/Pyraminx_Speedsolving_Methods

What is the probability of having a one move corner-edge-corner block?


Thank you so much if you can answer these.

 

[cuBerBruce]

Pyraminx probability question...

What the probability of having a corner-edge pair on a pyraminx?

[post=395400]See here.[/post]

What the probabiltiy of having a corner-edge-corner block like one on the first step of petrus made?

There are 48407 positions with at least one corner-edge-corner block.

So the probability is 48407/933120 or approximately 5.19%

What is the probability of having a one move corner-edge-corner block?

There are 174136 positions with no corner-edge-corner block that are one move from a position that does have such a block.

So the probability is 174136/933120 or approximately 18.66%.

The probability of needing zero or one move to get such a block is about 23.85%.

There are 445708 positions that require 2 moves to make a corner-edge corner block.

 

[Antcuber]

1 in 43 quintillion, right? There's only one state that the scramble will solve. I assume you mean scrambling a cube, then applying a different scramble to the cube.

no i mean for example having a 25 move random sequence that solves itself.

 

[irontwig]

5.19% seems way low, Bruce. It would be 1/24 for a specific corner-edge pair, which is over 4% by itself.

 

[cuBerBruce]

5.19% seems way low, Bruce. It would be 1/24 for a specific corner-edge pair, which is over 4% by itself.

I think you're thinking of a 3x3x3 cube, not a Pyraminx.

 

[irontwig]

Oops.

 

[clincr]

Probability of a 2x2 LL skip?

 

[Rpotts]

CP skip - 1/6 x CO skip 1/27 = 1/162

Is that correct? This probability counts a U2/U/U' LL the same as an AUF skip.

 

[ilikecubing]

Probability of a PLL skip?

 

[Andrew Ricci]

Probability of a PLL skip?

1/72

 

[toastman]

tough one:

Is there any possibility that with a random scramble the cube will solve itself? how about being 1 move away? or a u2?

I like this. Difficult, but a rough maximum to start the thinking: Assume a 20 move "naive" scramble. Probability that moves 11-20 are the inverse of 1-10 = 1 in 18^10 = 1 in 3.57 Trillion

The actual probability is likely way higher than this, as there's so many possibilities, e.g. where the scramble has junk like R L R' L' in it. I'm guessing by a factor of a hundred.

So, it *could* happen, given millions of cubers doing hundreds of thousands of solves in a lifetime. And I want to see the dude's face when it does. He'd be all like "Holy crap!"

 

[Rune]

Obviously, you are not Bruce?

 

[Cyrus C.]

Couldn't you also think of it as:

That scramble will only solve one state, probability that state is a solved cube: 1 in 43 quintillion.