Probability Thread

[TDM]

What are the odds of two OLL skips in a row?

(1/216)^2 = 1/46656 = 0.002%

 

[cashis]

(1/216)^2 = 1/46656 = 0.002%

Thanks. Happened yesterday.

 

[JediJupiter]

The human doesn't check anything, because clearly humans suck at checking scrambles
In some further stage, it should be possible to take a picture of the cube with your smartphone and have the app say "Yeah, I think this matches the scramble" or "You misscrambled".

Okay gotcha. So 3 faces correct, since that's the most with one picture, all adjacent. As a noob at probability calculating I think it's 54/(43*10^15) (I can't remember the actual number of possible states and my internet is too slow right now) which is tiny. But even so, that's from somehow randomly misscrambling the rest, and the amount of those states that could actually be achieved by misscrambling by one or two moves would be a lot smaller, I'd guess for most scrambles it's actually 0. By the way, will you actually make a timer with this function? If so, that's really cool.

 

[Goosly]

By the way, will you actually make a timer with this function? If so, that's really cool.

I don't think people want to take a picture of their cube after each scramble when practicing at home. What we do want is a more reliable way for checking scrambles at a competition.

 

[CubesOfTheWorld]

What is the chance of getting a cross skip on any side? on a specific side?

 

[TDM]

What is the chance of getting a cross skip on any side? on a specific side?

On a specific side,
1/(12*11*10*9*2^4) = 1/(11880 * 16)
= 1/190080.
For any side,
30942274/980995276800 = 0.00003154

 

[Isaac Lai]

This is probably around somewhere but I figured it might be easier to ask: What is the chance of a OLL skip?

 

[guysensei1]

This is probably around somewhere but I figured it might be easier to ask: What is the chance of a OLL skip?

1/216 assuming you don't use any LL control during F2L

 

[JustinTimeCuber]

lol your avatars are looking at each other XD

 

[IRNjuggle28]

I just got a LS+LL skip with no AUF and no parity on a 4x4, and no, that's not a typo of any sort. I solved my third pair, and the cube was solved. I'm completely in disbelief, and I feel pretty certain this is the most statistically unlikely thing that will ever happen to me with cubing, no matter how long I cube. I'm absolutely stunned that this happened. It'll be 1/8 as likely as a normal last layer skip, considering that I didn't get either parity or AUF, but I have no idea how unlikely skipping last slot in addition to all that is.

It was a seemingly normal scramble from a timer I know has decent scrambles, which I solved with Yau. I tried reconstructing, but it was hopeless. There was nothing notable about the solve until the very end; I don't remember anything about the beginning.

After reduction, I had solved the FR and BL pairs, and I did L' U L R' U2 R to solve the back right pair. In doing so, I accidentally solved the FL pair, as well as the last layer. There was no parity.

Someone who knows math: what are the odds of skipping last slot, OLL, PLL, OLL parity, PLL parity, and AUF on a 4x4?

 

[Logiqx]

I just got a LS+LL skip with no AUF and no parity on a 4x4, and no, that's not a typo of any sort.

Someone who knows math: what are the odds of skipping last slot, OLL, PLL, OLL parity, PLL parity, and AUF on a 4x4?

Wow. That's pretty crazy!

The probability of skipping the last slot is 1/150. It's a 1/15 chance of the corner being solved and 1/10 chance of the edge being solved.

The probability of skipping last slot, OLL, PLL, OLL parity, PLL parity and AUF is 1 / (150 * 216 * 72 * 2 * 2 * 4) = 1 / 37,324,800

That's almost 3 times less likely than a lotto win in the UK. All things considered, I think I'd prefer the lotto win.

 

[FailCuber]

Lol I just got a LL skip on 4x4. I never got a 3x3 LL skip when I timed my solves, but I got it on 4x4. The chances of getting an LL skip is (LL skip on 3x3) * 4 right?

 

[Logiqx]

Lol I just got a LL skip on 4x4. I never got a 3x3 LL skip when I timed my solves, but I got it on 4x4. The chances of getting an LL skip is (LL skip on 3x3) * 4 right?

Correct. 1 / 62,208 if you ignore the possibility of AUF.

 

[Stefan]

I feel pretty certain this is the most statistically unlikely thing that will ever happen to me with cubing

Nah, it's far less likely that you get the 4x4 scramble that you get next, and that will happen to you.

 

[rybaby]

What is the probability that, after first 2 blocks of Roux, the F2L is completely solved?
What about if the centers are always oriented in the last move of F2B (i.e. D/U center on U)?

 

[TDM]

What is the probability that, after first 2 blocks of Roux, the F2L is completely solved?
What about if the centers are always oriented in the last move of F2B (i.e. D/U center on U)?

First case: 6*5*4 = 120, so 1/120
Second case: 6*5*2 = 60, so 1/60

 

[Julian]

First case: 6*5*4 = 120, so 1/120
Second case: 6*5*2 = 60, so 1/60

The edges can be flipped, though.

 

[RomFrta33]

Taking orientation into account that'd just be 1/12*10 times two, so 1/60 seems to be good.

 

[GuRoux]

What is the probability that, after first 2 blocks of Roux, the F2L is completely solved?
What about if the centers are always oriented in the last move of F2B (i.e. D/U center on U)?

1/480 and 1/240

 

[IRNjuggle28]

Nah, it's far less likely that you get the 4x4 scramble that you get next, and that will happen to you.

Amusingly, I thought of that when writing that post, and assumed nobody would be ridiculous enough to point it out. Completely true, though.