Probability Thread

[Underwatercuber]

I was wondering if anyone was able to generate a large number of skeletons and find average optimal insertions. More details if someone is actually up for this.

If anyone can write up the program for it then i can run it in my computer for you

 

[Max_Hult]

Hello

Today this CRAZY thing happened. I first got a green cross skip and the next solve was just a 1 move cross.
I really need the answer to what the odds for this to happen is.
So if your good at math please give me the answer.
Heres the scrambles. btw the scrambles were generated on cstimer so OMG!!!!!!!!!!!!!!!!!!!!!!!!!!!


4. 9.87 L2 D2 R2 D B2 F2 R2 D' F2 D L' R B L' U' F2 L B2 L
5. (8.16) F2 B2 D2 F2 L' F2 R2 U' L' F2 U2 L2 F' U2 L2 B2 U2 B R2 D2

 

[xyzzy]

Today this CRAZY thing happened. I first got a green cross skip and the next solve was just a 1 move cross.
I really need the answer to what the odds for this to happen is.
So if your good at math please give me the answer.

The probability of getting two ≤1-move crosses in two specific solves is about (0.05%)^2 ~ 0.000025% ~ 1/4000000.

(Source: CubeZone cross study.)

 

[WoowyBaby]

Hmm......
Thinking thinking thinking.....

If you get two of a specific VLS case in a row in two specific solves, chance is 1/46656

If you get any two VLS case in a row in two specific solves, chance is 1/216

If you get any two VLS case in a row within a session of 216 solves, chance is about (may not be exactly) 1/2

You get widely different numbers even though all of them are the chance of getting a VLS case in two consecutive solves.
1/46656 vs. 1/216 vs. ~1/2
(it doesn’t have to be VLS, I just picked a set where each human case is equally likely)

 

[WillyTheWizard]

If a pll skip is 1/72 would 2 pll skips in a row mean 1/144? And what are the odds of an entire ll skip because that is literally what happened on my first ever solve

 

[Etotheipi]

If a pll skip is 1/72 would 2 pll skips in a row mean 1/144? And what are the odds of an entire ll skip because that is literally what happened on my first ever solve

Th e chance of 2 pll skips in a row is 1/72 x 1/72 = 1/5184 the odds of a ll skip are 1/15552 you got very lucky.

 

[Etotheipi]

So i was doing a solve, and when i got to LSE it was all correctly permuted but the UL and BD edges were misoriented. I calculated that the chance of 2 edges being misoriented but permuted and the rest solved to be about 1/940 including aufs. Correct me if im wrong.

 

[whatshisbucket]

So i was doing a solve, and when i got to LSE it was all correctly permuted but the UL and BD edges were misoriented. I calculated that the chance of 2 edges being misoriented but permuted and the rest solved to be about 1/940 including aufs. Correct me if im wrong.

1/360 chance of correct permutation
15/32 chance of exactly 2 flipped edges
1/768 total.

 

[Etotheipi]

1/360 chance of correct permutation
15/32 chance of exactly 2 flipped edges
1/768 total.

Ok lol i screwed up.

 

[cubeshepherd]

What are the odds of a single, Ao5 and Ao12 all being the same time? I was just doing a little 3x3 and trying to practice it again, and I got a 15.56 single which helped lead to the Ao5 and Ao12 being the same.

Spoiler: Single, ao5 and 12 times/scrambles

Generated By csTimer on 2019-4-12
avg of 5: 15.56

Time List:
1. 15.18 F' L2 R2 U R2 U' L2 U' F2 D' B2 D' L B2 D2 B F' U2 L' R2 D'
2. (14.62) R' F L2 F U' L' U2 F D' F2 U' R2 B2 L2 U2 L2 D' L
3. 15.93 D2 F2 L2 R U2 L2 F2 L B2 R' U2 D' R' D F' L B L B D2
4. (17.28) L F2 L2 U B2 U' F2 U' R2 B2 L2 D R F L D' R B D F' U'
5. 15.56 D F2 L' B' U F2 D2 R2 L B D L2 D' F2 U F2 L2 F2 R2 D' F2


Generated By csTimer on 2019-4-12
avg of 12: 15.56

Time List:
1. 15.52 F2 L2 F2 R2 D2 F2 R2 D' L2 F2 U2 R' B2 F' L F' D F2 D2 U'
2. (19.56) U' L2 D2 U' L2 U F2 U' F2 L2 U' R' U' B2 L F2 U B' D' U2
3. 17.51 U2 R2 D2 R2 B D2 U2 L' U' B U R B D' L' U' F'
4. 16.58 L2 D2 R' D2 U2 L' R D2 R' D B2 F2 D B2 R F D' B' U'
5. (13.28) L2 F' L2 D2 B2 F' D2 F L2 D2 L' B D F2 R U B' F' L
6. 13.62 U' L2 D' F2 D' B2 R D F' B2 U2 R2 D' F2 U B2 R2 D2 B2 U
7. 13.78 F2 B R' D L' B2 R B' U L' R2 U2 R2 U' R2 B2 D R2 F2 D L2
8. 15.18 F' L2 R2 U R2 U' L2 U' F2 D' B2 D' L B2 D2 B F' U2 L' R2 D'
9. 14.62 R' F L2 F U' L' U2 F D' F2 U' R2 B2 L2 U2 L2 D' L
10. 15.93 D2 F2 L2 R U2 L2 F2 L B2 R' U2 D' R' D F' L B L B D2
11. 17.28 L F2 L2 U B2 U' F2 U' R2 B2 L2 D R F L D' R B D F' U'
12. 15.56 D F2 L' B' U F2 D2 R2 L B D L2 D' F2 U F2 L2 F2 R2 D' F2

 

[aerocube]

What are the odds of a single, Ao5 and Ao12 all being the same time? I was just doing a little 3x3 and trying to practice it again, and I got a 15.56 single which helped lead to the Ao5 and Ao12 being the same.

Spoiler: Single, ao5 and 12 times/scrambles

Generated By csTimer on 2019-4-12
avg of 5: 15.56

Time List:
1. 15.18 F' L2 R2 U R2 U' L2 U' F2 D' B2 D' L B2 D2 B F' U2 L' R2 D'
2. (14.62) R' F L2 F U' L' U2 F D' F2 U' R2 B2 L2 U2 L2 D' L
3. 15.93 D2 F2 L2 R U2 L2 F2 L B2 R' U2 D' R' D F' L B L B D2
4. (17.28) L F2 L2 U B2 U' F2 U' R2 B2 L2 D R F L D' R B D F' U'
5. 15.56 D F2 L' B' U F2 D2 R2 L B D L2 D' F2 U F2 L2 F2 R2 D' F2


Generated By csTimer on 2019-4-12
avg of 12: 15.56

Time List:
1. 15.52 F2 L2 F2 R2 D2 F2 R2 D' L2 F2 U2 R' B2 F' L F' D F2 D2 U'
2. (19.56) U' L2 D2 U' L2 U F2 U' F2 L2 U' R' U' B2 L F2 U B' D' U2
3. 17.51 U2 R2 D2 R2 B D2 U2 L' U' B U R B D' L' U' F'
4. 16.58 L2 D2 R' D2 U2 L' R D2 R' D B2 F2 D B2 R F D' B' U'
5. (13.28) L2 F' L2 D2 B2 F' D2 F L2 D2 L' B D F2 R U B' F' L
6. 13.62 U' L2 D' F2 D' B2 R D F' B2 U2 R2 D' F2 U B2 R2 D2 B2 U
7. 13.78 F2 B R' D L' B2 R B' U L' R2 U2 R2 U' R2 B2 D R2 F2 D L2
8. 15.18 F' L2 R2 U R2 U' L2 U' F2 D' B2 D' L B2 D2 B F' U2 L' R2 D'
9. 14.62 R' F L2 F U' L' U2 F D' F2 U' R2 B2 L2 U2 L2 D' L
10. 15.93 D2 F2 L2 R U2 L2 F2 L B2 R' U2 D' R' D F' L B L B D2
11. 17.28 L F2 L2 U B2 U' F2 U' R2 B2 L2 D R F L D' R B D F' U'
12. 15.56 D F2 L' B' U F2 D2 R2 L B D L2 D' F2 U F2 L2 F2 R2 D' F2

is it even possible to get odds on that? that seems incalculable as someone could just solve before the end and wait till the timer hit a certain number

 

[cubeshepherd]

is it even possible to get odds on that? that seems incalculable as someone could just solve before the end and wait till the timer hit a certain number

That is true that someone could do that (although I am not sure why someone would purposely do that, unless they were bored), but that is not what happened from me and I was just checking to see if there is a way to calculate my questions above. Does anyone have any idea what the probability is (if there is a way to find out)?

 

[whatshisbucket]

That is true that someone could do that (although I am not sure why someone would purposely do that, unless they were bored), but that is not what happened from me and I was just checking to see if there is a way to calculate my questions above. Does anyone have any idea what the probability is (if there is a way to find out)?

Obviously information about the probability distribution of your times is necessary. If each time is 12.00 with probability 1, then obviously all your averages will also be 12.00. If you somehow know your distribution, a Monte Carlo simulation would probably be the best way to compute the probability.

 

[iLikeCheese]

Chance of 2 sune PLL skips in a row? Just got it.

 

[WoowyBaby]

1/72*4/216*1/72*4/216=0.00003%

If you did more than 2 solves or influenced LL or count antisune/fat sune as sune, any of these three things would make that number go way up.
If you did 200 solves then the chance of that happening is ~1% (not sure tho)

Just wondering, were those two solves faster than average?

 

[iLikeCheese]

1/72*4/216*1/72*4/216=0.00003%

If you did more than 2 solves or influenced LL or count antisune/fat sune as sune, any of these three things would make that number go way up.
If you did 200 solves then the chance of that happening is ~1% (not sure tho)

Just wondering, were those two solves faster than average?

Idk I was just doing some solves (around 30) and it happened. I have gotten many low probability occurrences before, such as 3 Pll skips in a row, or 2 Oll skips in a row, those are easier to calculate. Also it wasn’t fat sunes or antisunes, so pretty rare The two solves were both sub 7 btw, I think one was ~6.5 seconds.

 

[2x2 is fun]

chances of having a four mover 2x2 at a comp?

 

[rubik2005]

Oh! I forgot to post this a couple weeks ago. I just wanted to know what's the probability of getting a LL skip on a kibiminx because I actually got one.

 

[whatshisbucket]

chances of having a four mover 2x2 at a comp?

1847/3673775 for each scramble, which is about 1 in 1989.

Oh! I forgot to post this a couple weeks ago. I just wanted to know what's the probability of getting a LL skip on a kibiminx because I actually got one.

There is a 1 in 81 chance of skipping OLL and a 1 in 12 chance of skipping PLL for a 1 in 972 chance of a full LL skip.

 

[Miklopy]

The chances of a cross skip is 1/15840
The calculation is:
1/24 x 1/22 x 1/20 x 1/18 x 6