Berd
Legend
Whats the odds of an X-cross skip in Yau? XX-cross!?
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Probability Thread
- Thread starter CubesOfTheWorld
- Start date
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- Tags
- cfop oll probability
TDM
Legend
No, actually. The probability of that outcome is 100%. To conclude that it is less you would have to ignore a fact already stated in the premise.
Stefan
Legend
I'm talking about that scramble. Not about "the scramble that you get next". Actually getting it is not part of what I'm talking *about*, it's just part of my talking.
But yeah, I'm not sure I have worded or am wording that well.
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What is the possibility of having the "cross" solved on one face of a clock after scrambling?
This means that you could be the only person this has ever happened to and will ever happen to in the cubing community.
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.
This means that you could be the only person this has ever happened to and will ever happen to in the cubing community.
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Logiqx
Veteran
Few of us will ever experience this skip but some cubers will be lucky enough to get it.
Tens of thousands of people doing hundreds / thousands of 4x4 solves a year adds up to a large number.
But 37 million? That number is huge.
Just to put this into context - There is a man who did nothing but count to try and break the World Record for the highest number counted to. He slept, obviously, but from the moment he woke up to the moment he went to sleep he counted. After 3 solid months of counting all day, every day, he broke the world record by reaching 1 million.
There are 12,498 people who have ever solved a 4x4 officially in a WCA competition (I'm going to use this number because it isn't too far off the actual number, because people who have never been to competitions and inactive cubers cancel each other out).
The probability of all the events described occurring is 37,324,800. Take that number and divide it by the number of people who have competed.
This would mean that 12,500 people would each have to do ~3000 (2986.46183 to be exact) solves a year for this to happen once in that year.
Now, how long would this take? The median of all people who have competed is 6249, and the time at that number is 1:24.72.
84.72 seconds multiplied by the 37,324,800 times the cube would have to be solved is 3,162,157,056 seconds, or 878,376.96 hours, or 36,599 days (100.5 years total solving time).
For each person that would be 253,013 seconds, or 70 hours.
tl;dr I would be VERY surprised if I saw another cuber here have the same luck.
EDIT- In other words, what you just did IRNjuggle, you had a 0.0000000267918381 chance of doing
Yeah.
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TDM
Legend
That seems like a long time to count to a million. Three months is 8 million seconds. Surely, even including sleep, it doesn't take 8 seconds to say each number?
Logiqx
Veteran
You're calculation is based on the WCA people doing it in one year. They have already been solving the 4x4 for many years and they will solve it for many years to come.
There are lots of people who cube for a hobby who don't actually compete, I know several amongst my friends. An example would be someone who does 12 solves on the 4x4 each week for an extended period of time... slightly over 600 solves in a year. You only need 60,000 of those guys (five times the WCA number) to do 37 million solves in a year.
Anyhow this logic is flawed because probability doesn't work in such a simple way. Doing 37,324,800 solves doesn't guarantee the outcome... you can equally say there is approximately 50% chance of the outcome by doing half the number of solves.
I think it unlikely for just one person in the community to have this happen.
Edit: There are 27,207 registered members on this forum.
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Isaac Lai
Veteran
What are the chances of getting a 4 mover in 2x2?
Logiqx
Veteran
I've re-done my calculation because I forgot to consider scramble filtering (i.e. minimum of 4 moves).
4 moves = 1847 / 3673775 = approximately 1 in 1989
Additionally...
5 moves or less = approximately 1 in 310
6 moves or less = approximately 1 in 59
7 moves or less = approximately 1 in 13
8 moves or less = approximately 1 in 3
I got the distribution from Wikipedia - https://en.wikipedia.org/?title=Pocket_Cube
4 moves = 1847 / 3673775 = approximately 1 in 1989
Additionally...
5 moves or less = approximately 1 in 310
6 moves or less = approximately 1 in 59
7 moves or less = approximately 1 in 13
8 moves or less = approximately 1 in 3
I got the distribution from Wikipedia - https://en.wikipedia.org/?title=Pocket_Cube
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1) Probability is always flawed in that case then. This is going off the idea that the last solve of the 37 million would be the desired one. You can never guarantee the outcome, for example you could buy 100 million lottery tickets and never win the jackpot.
2) I highly doubt the number of people who can solve a 4x4 and are currently solving at the required speed is anywhere near 60,000.
3) 27,207 forum members =/= 27,207 4x4 solvers. A lot of them may be inactive too.
June 18th 2007 - September 14th 2007
TDM
Legend
wat
Is there some limit for how slowly you have to count? Because it shouldn't take that long.
Stefan
Legend
Count out loud from let's say 374400 to 374500 and let us know how long it takes you.
TDM
Legend
Ok, I was wrong then, sorry.
IRNjuggle28
Veteran
That's exactly my thoughts--it felt absolutely surreal. Without thinking about the exact math, it occurred to me that I may be the only person in the world this has ever happened to. It seemed so unbelievable that I wondered if I'd remembered the solve wrong, and done more of the solve than I thought before getting a skip, but I clearly remember the final moves of the solve being L' U L R' U2 R, which guarantees that I'm right about it being a LS+LL skip as it affects more than one F2L slot.
When it comes to massive skips, I've been quite lucky. I've been cubing for less than two years, and I have at least 5 LL skips on 3x3, not even counting this one on 4x4, and not counting the one or two I've gotten on big cubes. I don't get lucky in other ways too often; I don't get an abnormally large number of PLL or OLL skips, but I've had a few incredibly lucky solves. Some people go 5 years without getting a single one of what I must have close to 10 of by now.
JustinTimeCuber
Legend
Chances of getting an (x) skip at a competition for 1-4 rounds of 5 solves:
1 round: 3.049%
2 rounds: 6.004%
3 rounds: 8.870%
4 rounds: 11.648%
100 solves: 46.162%
2 rounds: 6.004%
3 rounds: 8.870%
4 rounds: 11.648%
100 solves: 46.162%
1 round: 59.812%
2 rounds: 83.849%
3 rounds: 93.509%
4 rounds: 97.392%
100 solves: 99.999999%
2 rounds: 83.849%
3 rounds: 93.509%
4 rounds: 97.392%
100 solves: 99.999999%
1 round: 17.197%
2 rounds: 31.436%
3 rounds: 43.227%
4 rounds: 52.990%
100 solves: 97.704%
2 rounds: 31.436%
3 rounds: 43.227%
4 rounds: 52.990%
100 solves: 97.704%
1 round: 13.138%
2 rounds: 24.551%
3 rounds: 34.464%
4 rounds: 43.074%
100 solves: 94.022%
2 rounds: 24.551%
3 rounds: 34.464%
4 rounds: 43.074%
100 solves: 94.022%
1 round: 0.513%
2 rounds: 1.024%
3 rounds: 1.532%
4 rounds: 2.038%
100 solves: 9.781%
2 rounds: 1.024%
3 rounds: 1.532%
4 rounds: 2.038%
100 solves: 9.781%
1 round: 0.042%
2 rounds: 0.084%
3 rounds: 0.126%
4 rounds: 0.168%
100 solves: 0.838%
2 rounds: 0.084%
3 rounds: 0.126%
4 rounds: 0.168%
100 solves: 0.838%
1 round: 0.168%
2 rounds: 0.336%
3 rounds: 0.504%
4 rounds: 0.671%
100 solves: 3.311%
2 rounds: 0.336%
3 rounds: 0.504%
4 rounds: 0.671%
100 solves: 3.311%
1 round: 6.754%
2 rounds: 13.052%
3 rounds: 18.925%
4 rounds: 24.401%
100 solves: 75.306%
2 rounds: 13.052%
3 rounds: 18.925%
4 rounds: 24.401%
100 solves: 75.306%
1 round: 2.293%
2 rounds: 4.534%
3 rounds: 6.724%
4 rounds: 8.863%
100 solves: 37.126%
2 rounds: 4.534%
3 rounds: 6.724%
4 rounds: 8.863%
100 solves: 37.126%
1 round: 3.049%
2 rounds: 6.004%
3 rounds: 8.870%
4 rounds: 11.648%
100 solves: 46.162%
2 rounds: 6.004%
3 rounds: 8.870%
4 rounds: 11.648%
100 solves: 46.162%
1 round: 0.032%
2 rounds: 0.064%
3 rounds: 0.096%
4 rounds: 0.128%
100 solves: 0.641%
2 rounds: 0.064%
3 rounds: 0.096%
4 rounds: 0.128%
100 solves: 0.641%
1 round: 76.270%
2 rounds: 94.369%
3 rounds: 98.664%
4 rounds: 99.683%
100 solves: 99.9999999999%
2 rounds: 94.369%
3 rounds: 98.664%
4 rounds: 99.683%
100 solves: 99.9999999999%
1 round: 0.097%
2 rounds: 9.537e-5%
3 rounds: 9.313e-8%
4 rounds: 9.094e-11%
100 solves: 6.223e-59%
2 rounds: 9.537e-5%
3 rounds: 9.313e-8%
4 rounds: 9.094e-11%
100 solves: 6.223e-59%
1 round: 99.902%
2 rounds: 99.9999%
3 rounds: 99.9999999%
4 rounds: 99.9999999999%
100 solves: 99.999999999999999999999999999999999999999999999999999999999%
2 rounds: 99.9999%
3 rounds: 99.9999999%
4 rounds: 99.9999999999%
100 solves: 99.999999999999999999999999999999999999999999999999999999999%
1 round: 23.730%
2 rounds: 5.631%
3 rounds: 1.336%
4 rounds: 0.317%
100 solves: 3.207e-11%
2 rounds: 5.631%
3 rounds: 1.336%
4 rounds: 0.317%
100 solves: 3.207e-11%
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