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Probability Thread

Altha said:
Excluding the buffer would it be that percentage multiplied by 7/8 or do I suck at maths
Click to expand...
You can't have just the the buffer twisted, then it would be unsolvable!
I just ignored the buffer, since it's determined by the rest of the 7 corners.

Basically, there are 7 corners. The probability for each corner of being twisted is 2/24. To find the probability of any one of them being twisted, you add them all up. But then you would be overcounting, because two corners could be twisted. So you subtract the probablity of any two combos of corners being twisted. But then you'd be undercounting, since three could be twisted. So you add the prob of three corner twists and so on...

EDIT: o wait i'm wrong. the buffer does matter. dangit why do i always mess up XD
 
Last edited by a moderator:
Altha said:
What's the chance of any scrambled cube having at least 1 twisted corner? (or 1-[no twisted corners])
Click to expand...

I tried it including the buffer and got an answer a little higher than Daniel's which ignored buffer
(!8)*(3^7) + 8*(!7)*(3^6) + (8 choose 2)*(!6)*(3^5) + (8 choose 3)*(!5)*(3^4) + (8 choose 4)*(!4)*(3^3) + (8 choose 5)*(!3)*(3^2) + (8 choose 6)*3 + 1

45,273,046 positions with no twisted corners

total positions = 3^7*8! = 88,179,840

so (88179840 - 45273046)/88179840

which is 48.658...%
 
Daniel Lin said:
The probability for each corner of being twisted is 2/24.
Click to expand...

Why 2/24?
Maybe I didn't understand the question but... why isn't the chance of at least one twisted corner (1 - (1/3)^7) ?

Also how could it ever be 44% or 48%? Almost half of the scrambles would have no twisted corners, which is clearly wrong.
 
Goosly said:
Why 2/24?
Maybe I didn't understand the question but... why isn't the chance of at least one twisted corner (1 - (1/3)^7) ?

Also how could it ever be 44% or 48%? Almost half of the scrambles would have no twisted corners, which is clearly wrong.
Click to expand...
Just pick a random sticker like UBR. There are 24 corners stickers, and UBR would be twisted if it were at RUB or BUR
 
What is the probability of using a random PLL generator (like the PLL option on csTimer) and not getting an E-Perm until the 46th PLL, and then getting the E-Perm 3 times in a row?
 
DELToS said:
What is the probability of using a random PLL generator (like the PLL option on csTimer) and not getting an E-Perm until the 46th PLL, and then getting the E-Perm 3 times in a row?
Click to expand...

Roughly (21/22)^45 * (1/36)^3, or .0002642%. So about to put it another way, you would get one of these occurences for every 20 LL skips

EDIT: I say roughly because I don't want to calculate the average PLL probability excluding E perm. 21/22 is close enough
 
obelisk477 said:
Roughly (21/22)^45 * (1/36)^3, or .0002642%. So about to put it another way, you would get one of these occurences for every 20 LL skips

EDIT: I say roughly because I don't want to calculate the average PLL probability excluding E perm. 21/22 is close enough
Click to expand...
I've probably done over ten to fifteen thousand solves (very rough estimate, cubing for 2.5 years) and I've never gotten a LL skip...
 
What is the probability of doing a 2 gen scramble by hand randomly and getting a 1 move solutions? 1 out of 146966400 if I'm correct?
 
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