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Probability Thread

Scollier

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I am designing an app that calculates the number of permutations in a certain amount of edges, corners, or edges corners combined.

So it would be greatly appreciated if someone could tell me how to calculate the number of permutations in x amount of edges, and how to calculate the number of permutations in x amount of corners. This would be GREATLY appreciated.

And for finding the number of permutations in x amount of edges and x amount of corners, I believe you just multiply both of the number of permutations together?

Thanks.

And Note: This is finding the number of solvable permutations of course, e.g., not finding permutations of flipped pieces as well.

And also, I should have clarified, This is for 3x3.
 
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Jam88

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I am designing an app that calculates the number of permutations in a certain amount of edges, corners, or edges corners combined.

So it would be greatly appreciated if someone could tell me how to calculate the number of permutations in x amount of edges, and how to calculate the number of permutations in x amount of corners. This would be GREATLY appreciated.

And for finding the number of permutations in x amount of edges and x amount of corners, I believe you just multiply both of the number of permutations together?

Thanks.

And Note: This is finding the number of solvable permutations of course, e.g., not finding permutations of flipped pieces as well.
surely there would be less than multiplied together? bc parities etc. idk tho
xyzzy can prob provide an answer
 

Kit Clement

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I am designing an app that calculates the number of permutations in a certain amount of edges, corners, or edges corners combined.

So it would be greatly appreciated if someone could tell me how to calculate the number of permutations in x amount of edges, and how to calculate the number of permutations in x amount of corners. This would be GREATLY appreciated.

And for finding the number of permutations in x amount of edges and x amount of corners, I believe you just multiply both of the number of permutations together?

Thanks.

And Note: This is finding the number of solvable permutations of course, e.g., not finding permutations of flipped pieces as well.

And also, I should have clarified, This is for 3x3.

The total number of permuations of a 3x3x3 is:

12! - ways to permute edges
2^12 - ways to orient edges
8! - ways to permute corners
3^8 - ways to orient corners

However, we have to divide by:

2 - since the last edge's orientation is determined by the previous 11
3 - since the last corner's orientation is determined by the previous 7
2 - since the permutation parity of the puzzle is always even (i.e. can't swap only 2 corners)

This gives:

12! * 2^(12-1) * 8! * 3^(8-1) / 2

So if you want to do this for a subset of x edges and y corners, fixing the rest, this function could be used to find the number of permutations of those pieces:

f(x, y) = x! * 2^(x-1) * y! * 3^(y - 1) / 2

Note that this is not the same as cases for LL, as counting specific cases takes symmetries and AUF into account. So if you're looking for literal permutations this will work, but it gets trickier if your purpose is for counting specific cases for a given alg set.
 
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Sorry if this was asked before, but what's the chances of L2C skip on 5x5? I just got one lol
 

xyzzy

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Sorry if this was asked before, but what's the chances of L2C skip on 5x5? I just got one lol
Previous page!

 
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Deleted member 55877

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turns out i actually had answered the very question i am asking (attempted to, at any rate) ... brain fart
 

rubik2005

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I don't think there's really a way to figure this out, but for some reason a lot of the misscrambles in comps result in really fast times like Max's OH solve at Nats. If someone who isn't really world-class has a misscramble, technically nobody would know about it since no one would notice an average solve. So that chances that someone like Max or Felik's 1: gets a misscramble cubed, and 2 solves it in WR or extremely close to it would be astronomical right? But it has happened multiple times, so I maybe wrong scrambles happen more often than we think?
 

xyzzy

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So that chances that someone like Max or Felik's 1: gets a misscramble cubed, and 2 solves it in WR or extremely close to it would be astronomical right?
While 1 is moderately unlikely in a well-run competition, 2 isn't all that unlikely for those two people! There's also some reason to believe that misscrambles caused by misreading a single move in a scramble sequence (as opposed to misscrambles caused by accidental move done in transit, misscrambles with 2 or more misread moves, etc.) are slightly biased towards being easier than typical.

Also:
someone like Max or Felik's
[…]
WR or extremely close to it
Introduce enough fudge factors and you can get something that sounds like it should be unlikely, but in reality is very likely. This is something you have to be very wary of when doing statistics.
 

Kit Clement

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Yeah, this is the classic blade of grass paradox. In a pre-COVID world, world class solvers were each often doing upwards of 100 solves across all events every month. Additionally, there are hundreds of world class cubers whose solves are closely followed by the community. So it may seem like a one-in-a-million occurrence to happen at that very point in time, but with the frequency that official solves happen at a high level, it's almost certain for it to happen in a way that is noticed eventually.
 
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coll is 42algs so instead of learning full oll i can learn EOLL which is 3 algs, COLL at 42 and EPLL at 4 algs vs OLL with 57 alone. also coll has about an 8 move count average. im also using pure eoll which changes nothing except corners so recognition wont even be that bad.

theres probably somthing im missing but i think COLL is better than oll in every way.
 

OreKehStrah

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coll is 42algs so instead of learning full oll i can learn EOLL which is 3 algs, COLL at 42 and EPLL at 4 algs vs OLL with 57 alone. also coll has about an 8 move count average. im also using pure eoll which changes nothing except corners so recognition wont even be that bad.

theres probably somthing im missing but i think COLL is better than oll in every way.
A lot of COLL is slower than OLL on average. Why not just do CFCE? It’s what I use.
 

Pyjam

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You may complete your set of COLL with easy cases of ZBLL.
So, if you know 3 algs per COLL case, the odds for EPLL skip are 1/4.
 

Athefre

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You may complete your set of COLL with easy cases of ZBLL.
So, if you know 3 algs per COLL case, the odds for EPLL skip are 1/4.

If going this direction, it is only two algs per COLL case that is required to always have that skip chance. Ua, Ub, or a skip.
 

LukasCubes

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does anyone know the odds of skipping eoll when using coll?
if you get a COLL for every solve, you get a 1/12 chance of a PLL skip or 8.3333333333333333333333333333333333333333333333% chance (8 1/3%)

I know because I know full COLL and use ZB as my main method while also knowing almost a quarter of full ZBLL even though I am currently in a break right now.
 

xyzzy

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also coll has about an 8 move count average.
It's more like 9.8 moves with move-optimal algs, 11-ish with speed-optimal algs.

theres probably somthing im missing but i think COLL is better than oll in every way.
It's worse in terms of overall move count.

6 moves for EO + 10 moves for COLL + 9 moves for EPLL = 25 moves (add 2 moves if you're using corner-preserving EO algs)
9 moves for OLL + 11 moves for PLL = 20 moves

It's better to just do the standard OLL/PLL (78 algs, ~20.5 moves), 2-look OLL with full PLL (31 algs, ~23 moves), or CLL/ELL (71 algs, ~20.5 moves). The logic is simple: less steps means less moves (usually).

(Move counts reported above are for FTM-optimal, which is a good (but imperfect) proxy for execution time with speed-optimised algs. Execution time is highly subjective, but optimal move counts aren't.)

---

does anyone know the odds of skipping eoll when using coll?
Also two people upthread answered this for EPLL, but the probability of skipping EO when using COLL is the same as if you're not using COLL, i.e. 1/8 assuming no edge control. The cube has no brain and can't possibly know that you're about to use a COLL alg, so EO can't possibly depend on that.
 
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