When the Odds Are 1 in 241 Million

[@JonathonGraves-qr3fb]

While watching this video I got struck by an asteroid. I can guarantee I will not see another solve like this in my lifetime.

[@Battleatkursk_gd]

Are you going to eat the asteroid

[@lime-animates-2763]

@@Battleatkursk_gdHe needs to sanitise it first

[@thebe_stone_MC]

​@@lime-animates-2763don't use oil based soap.

[@jectlikeslearning2014]

hes rich now

[@AshrZ]

Did you skip the last layer of the asteroid?

[@speedcubingdotorg]

The 1 in 241 million odds are the odds of those two specific individuals both getting a last layer skip on one specific solve, the odds of any 2 individuals getting a last layer skip are far higher, especially when the solutions are somewhat similar, the thing is that there is a last layer skip possible on every scramble, it is just most of the time the F2L required to produce it would not be optimal and it wouldn't be predictable anyway. But two very impressive solves nonetheless.

[@goutgueule9197]

Yea theres this tool on speedcubedb that can find a ll skip in pretty much any scramble

[@vibhorgoel9774]

r/beatmetoit for odds are far greater than 1 in 241 million, but still low enough to be an extreme case.

[@jakerussell135]

62 people competed in the second round of 3x3. so all 62 would have gotten this scramble. so the real chance is (62 choose 2) * (15551/15552)^60 * (1/15552)^2. which is still extremely unlikely, but instead its closer to 1/128000

[@karanshome]

@@jakerussell135 This implies that there are only 62 solutions, and that all 62 solutions performed were necessarily unique, neither of which is necessarily the case.

[@tuurepaananen7729]

@@karanshome it doesn't imply that there are only 62 solutions. It's correctly calculated. It just assumes that the chance of a last layer skip is 1/15552, which according to the video is true.

[@AidanGrainger]

Awesome video, I cant believe you thought I was skilled enough to be thinking about what solution was optimal for last 2 pairs in that pause though,... in all honesty I was just looking for the pair to do next😅😅😅 Either way I cooked, absolutely ate, got the fries back out the bag and nommed them right up;

[@SatyaGala-m9q]

@@AidanGrainger nommed thrm right up is cold af

[@PoisonWaterFire]

funniest shi I read today

[@strawhatcuber]

Bro went from “in all honesty” to “nommed them right up” lmao

[@LiamFernandez-uc4b]

​@@SatyaGala-m9q i gotta use that term more now

[@SatyaGala-m9q]

@@LiamFernandez-uc4b real

[@pepkin88]

The odds in the title (1 in 241 Million) are incorrect, because those two events are not independent, as they came from the same scramble.

[@STUCUBE]

So what are the odds then? I realized that it’s much lower (probably) as I said but what exactly would they be?

[@Canyonpettitt]

@@STUCUBEit’s impossible to determine because how many solutions give a last layer skip is random But I don’t think it’s anywhere near 241 million

[@midaskiebert7933]

@@STUCUBE Assuming the two events are independent, the chance that this happened in this particular solve in this particular round (with 62 competitors) would be 1 minus the chance of either 0 or 1 last layer skips happening. The chance of 0 last layer skips is (15551/15552)^62, and the chance of 1 last layer skip is 62 * (1/15552) * (15551/15552)^61. Calculating this gives a chance of about 1 in 128232. But we don't really care on which particular solve this happened, so the chance that this happened in this particular round on any solve would be 1 minus the chance of it happening 0 times, which is about (128231/128232)^5. Calculating this we get that the chance of this happening in this particular round would be about 1 in 25647. I suspect that it is even more likely in reality, it seems likely to me that given the fact that there exists a "reasonable" F2L solution giving a last layer skip on some cross color on some scramble, that this would imply that the probability of there being a different "reasonable" F2L solution also giving a last layer skip on the same scramble on the same cross color is higher than the chance of any random scramble having a "reasonable" F2L solution giving a last layer skip. I have no way to prove this, but I suspect it's true because common moves in F2L usually preserve some blocks and orientations, or some other more complicated invariant which could potentially make the chance of seeing the same last layer case more likely. Calculating the exact probability is not feasible, since a "reasonable" F2L solution is not at all well defined, and depends on the solver.

[@grnarsch5287]

​@@STUCUBE yea hard to tell i would go with the 15000. id guess in real its even more likely. Even to see this independent at a few events seems kinda likely. Do you know the "birthday paradox". imagine there is a big event with 1000 solves. Its still unlikely but id guess 1/5000 or something. Im to lazy to look up the binomial. But you see that even this is much more likely than one in 241 Million

[@jakerussell135]

just considering that they are two people out of 62 people who competed in the second round, the chance is closer to 1/128000. but that's only for that specific scramble. if you apply it to all 5 scrambles in round 2, its closer to 1/25500. and if you expand it to the whole competition with all three rounds, it turns out to be around 1/8400

[@ashwynwadhawan7908]

bro doesn't understand the difference between independent and dependent probability

[@NetullaGD]

Title worked on us tho

[@wish9559]

Math ain't mathing

[@STUCUBE]

I’d say it’s still independent probability because they did entirely different solutions. Open to being wrong but 🤷‍♂️

[@AlanCondeSpeedcuber]

​@@STUCUBEnot that different solutions tbh

[@Someone-hi1nt]

@@STUCUBE not how it works bro

[@duvi9898]

That's not really how probability works. The chances of 2 people getting a last layer skip in a competition in the same scramble is not only the chances of two last layer skips but, in fact, that times the number of participants and the number of scrambles done. I would estimate the probability is about 1/1000, still pretty rare, but not even close to 1/275000000. This has probably happened before. What's actually crazy is that both competitors were able to take these opportunities and turn them into sub 4 solves. Unfortunately, that probability is impossible to calculate

[@duvi9898]

What you actually calculated is the probability of those exact two competitors getting the last layer skip, specifically in that one scramble, and it discounts all of other competitors and all of the other scrambles that were done in that same competition

[@ignDart]

@@duvi9898 and does not account for them having similar solutions with similar permutations of pieces that make skips hundreds of times more likely

[@asheep7797]

There were 575 solves of the 3x3x3 at the event that I found. The chance of a LL skip is 1 in 15,552. The chance of any two (or more!) people getting an LL skip in that competition is 1 in 1,502. Additional info: The chance of two people getting LL skip is 1 in 1,520. Three people? 1 in 123,808. Finally, four people? 1 in 13,463,425.

[@duvi9898]

@@asheep7797 Thanks for the numbers. I wanted to look them up but didn't know where to find them

[@OvejaGD]

Its crazy that i havent solved a cube in a few months and literally the only speedcubing channel that i watch is yours. You make this topic so entertaining that even non-cubers will find this entertaining

[@PieceByPiece1046]

thanks for this video!! i still can't believe all of this happened. can't speak to the probability of this but in a way, it doesn't matter, because however unlikely this was, it happened for real :D

[@Da_Rizzley_Bear]

WOW the UK be popping of this + FMC WR Congrats to these guys

[@RubiKubiK313]

Bro your editing and storytelling is soo good I can’t believe the high quality sometimes! You deserve so many more subs!🎉

[@MoreCubes]

If you were at that comp count yourself as one of the rarest people in the world, To be a cuber, in the uk, at that comp, while 1 in 24000000 chance solves happened

[@nickfarley3962]

Even more rare is to be taking a fat dump while reading this comment

[@MoreCubes]

@ lol

[@TheCubicWizard]

man this is just crazy, also we cant leave the good work he makes, loved the video, and especially those solves where its *exactly* 2 seconds from their previous pb, thanks for the great video!

[@curiousNic]

This is my favorite cubing story of the year. Getting a sub-4 out of the blue in the presence of two 3x3 World Champions has to be one of the best cubing dreams come true ever. PS: Not a fan of floccinaucinihilipilificationism.

[@steeveeboy51]

SOMEONE ELSE WHO KNOWS THE WORD OMG (you are officially my second favorite person now)

[@vibhorgoel9774]

@@steeveeboy51 i know the word too (from now on) thanks for calling me your third fav person

[@kerkare]

Such floccinaucinihilipilification my favorite word since 3rd grade

[@DrJohnners]

@@kerkare I always preferred pneumono­ultra­micro­scopic­silico­volcano­coniosis :)

[@kerkare]

@ it’s too known though

4:45 you can do a wide U exept for D and if you does the same solution he will have to do only one rotation and the solve will be the same.

[@daniel-kidd]

Aidan Grainger and Jake Brown my goats

[@EclipseGames]

Literally!

[@orngng]

Not sure if this works but if we use your assumptions on squaring last layer skip chances you also have to multiply the "number of competitors choose 2" which means 62 choose 2 = 1891 (So this is saying for any two people getting a last layer skip, this could be 30th and 59th person) But this assumes that any competitor there can get a last layer skip which may depend on their solution and 62 because thats how many people competed 3x3 2nd round So we have to multiply the last layer skip calculation with that We assume combinations without repetition too, i got 1 in 127903 as a result

[@trumaneugene3769]

I’m not sure what’s nerdier, this video or the argument about the odds

[@ThanMG]

Bro, watching the rise in production quality is awesome. I can understand the the effort/energy it takes to put such a video together so I really appreciate how clean this video is 🙏🔥

[@franciscohamlin7544]

1:27 as a clear-up, Mats's 4.74 WR was a deliberate VLS, you can tell if you look at the reconstruction

[@ZaneDidIt]

Nice nail polish 💅🏼

[@Ackermanmedia]

As a kid who was alive for the invention of the Rubik's cube I find this totally amazing. I would sit around and try my hardest to solve that thing all day and not get it. Watching these guys do it in 4 seconds is not easy to comprehend.

[@_aquice]

New STUCUBE video, W!

[@TZ_Cubes]

One time my friend got a LL Skip and got a 12 on OH, then later in the competition, the Colorado state record was set with a LL skip on a 4.75. And I thought 2 in a whole competition was crazy, let alone in the same round

[@JordanMerrill-mx7cy]

I never would have thought I could get goosebumps while watching someone solve a Rubik’s cube haha 😂

[@DVSS77]

your solve breakdowns and the stats are the best.

[@thebeastbros9516]

Lol I remember you mentioning FLOCCINAUCINIHILIPILIFICATION on Dylan Millers stream. Great video btw!

[@PiercingSight]

The probabilities would be quite dependent rather than independent, so the probability is much smaller. Even though the F2L steps were done differently, because of the small number of moves and their efficiency, it was easily possible for most, if not all, of the last layer pieces to retain their existing parities and arrive at a similar if not identical configuration. Add to that the number of competitors attempting the same scrambles, and also the number of scrambles, and the probabilities come down even further. Fantastic video though!

[@Abdullahalmaharmeh]

putting resonance as the ending song is pure beautiful

[@CardinalCityRecords]

me: I have absolutely know idea what's going, what the lingo is, what's so special about me: gonna go now, it was nice tho, I feel more cultured, liked and subscribed

[@Dhavin_the_cube_explorer]

I really appreciate it stucuber. Thanks for showing me something that would never happen again in my life

[@nc6390]

I was at a comp in Ireland when this happened I was scrambling and the delegates came over and told us what just happened

[@SerKubos]

1:20 how you got that rankings??!?

[@STUCUBE]

Inspect element

[@SerKubos]

@STUCUBE omg that's so smart

[@jonah.leonard]

@@STUCUBEbruhhhh no way

[@humzini]

the description gets me every time

[@_aquice]

This competition is the main character

[@Minimus408]

I downsolved it with Aidan's solution at 2.87!

[@ignDart]

i meann the odds are very misleading because yk specific permutation stuff about the scramble lmao but nice vid

[@STUCUBE]

I’m interested in what the actual odds are bc people keep talking about how they were boosted but I can’t find anything that actually proves that

[@FlyingDaddy721]

Thanks for bringing up my asteroid fear. Im more of a super localized meteor hits just me kind of fear, but still... triggered

[@_isititc_]

The reaction describes it all, man cubing is can be so unpredictable haha, who would've thought there would be two different solutions for a last layer skip

[@dylan_1313]

When I was 10, I was doing a challenge with my brother, whoever got the most sides solved. We both didn’t know how to solve one. On my turn I got one side, three turns later, LITERALLY THREE, I solved it, I was shocked. Now that I know how to solve it, I’m even more mind blown by that.

[@jaycubing]

love the vid, keep it up

[@justinmanser7525]

I was once dealt A 2 3 4 of spades in a hi-low 7 card stud poker game, that is probably pretty comparable odds considering the vast number of different games I was playing at the time, getting the perfect cards for that particular style of poker...didn't get to see the 5th street as all other players folded, but I think even the odds of losing with that hand also are pretty astronomical with 3 cards to come. I also once saw a sparrow fly under an oncoming speed train and the hop onto the platform before the train had completely passed, meaning the amazing little fella actually flew between it's wheels.... *_''Never tell me the odds!''_* - Han Solo, Trigger Happy Nerfherder

[@danilocruz747]

very nice analisys...regards from Costa Rica

[@PotatoesAreUs]

The whole room was electric after this 5 minute period of everyone realising what had happened. Being the Delegate in charge of verifying these scrambles was both the most exciting and nerve wracking moment of my whole cubing career.

[@AntiPomni]

Wait, this is neither a video about Yiheng nor was he mentioned 😮What were the odds of that?

[@cubinglab]

Am not a colour neutral, but I wanna try colour neutral scrambles. How do I scramble for each colour when I'm doing only white cross?

[@STUCUBE]

Put whatever color you want to solve on in white’s place

[@Ozymandias-Gaming]

Credit to you for using Resonance as outro music

[@azurev2258]

It's unlikely for a lucky event to happen at a specified point in time, but it's even more unlikely for a lucky event to never happen over a prolonged period of time.

[@Donut_Face_111]

The fact I was a witness of this in real life and knew STUCUBE would make a video on this 😂😂😂

[@MigaFerreira-fg5nk]

Broooo. What are the odds that my math module right now is about probability and odds🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯

[@Alex-mq7fb]

you would need the independent probabilities that a given cuber finds that certain solve of the scramble to arrive at a final probability. unfortunately, it's impossible to measure the probability that person A does solve X, as opposed to solve Y, as too many confounding variables affect the situation after the first time solving. and what makes this even more trickier to measure is the infinite amount of scrambles that have a near zero probability of being executed (due to length), or the probability that one messes up the solving. tl;dr you need to factor in the participant's individual probabilities of coming up and executing the solves they did, which is impossible, so we can just say "yeah this was really crazy wtf, props to them"

[@MafuyusZoloft]

As someone who has never even looked at the rubix cube solving community I'm watching this like "wow yeah! So cool! I understand exactly what you're saying!!" 😭 Its interesting tho There's always something that you wouldn't expect to see that someone is so skilled in

[@crazyiwascrazyoncetheylocked]

man i can't even solve one and here are these ppl solving it in under 4 seconds 💀

[@DanRblx-qo8pj]

1:41 Any of the approximately 4 quadrillion Rubix Cube positions are solvable in 20 moves or less 😅

[@Barrio02]

Yes, but while speedsolving you just remember and don't have time to think, that's why 29 is a low move count for speedsolving.

[@jasonhatfield3084]

Although I agree that each of two solvers getting a LL skip on the same scramble is a very rare event, I don't agree with your odds calculation. For your calculation to be correct, the event for solver A has to be independent of the event for solver B. Since they have a scramble in common, they are not independent. There is a simple scenario where your calculation is correct, but the common scramble surely violates the assumption of independence.

[@creecha5766]

I was thinking the same thing

[@texashookem22]

The odds of me giving up after 5 minutes and asking where the bar is are 1:1. This is crazy.

[@Sempermac]

Never even solved a rubic once in my life and yet here I am.

[@JamesOhara-yd6ez]

When the odds are 1 in 241 million, they aren't mine 😢😂

[@jakerussell135]

just considering that they are two people out of 62 people who competed in the second round, the chance is closer to 1/128000. but that's only for that specific scramble. if you apply it to all 5 scrambles in round 2, its closer to 1/25500. and if you expand it to the whole competition with all three rounds, it turns out to be around 1/8400

[@Cuber9921]

Nice video, keep it up!

[@mattj7245]

the fact that they both broke their pr singles by exactly 2 seconds is insane

[@andrejbogdanov2816]

Imagine being one of the 2 kids behind that 3.69 solve and for the rest of your life you'll be able to tell the story: I was there! But I was looking at my phone instead so I didn't actually see it happen.

[@-ZH]

3:37 Ever seeing it again, or ever experiencing it?

[@AlixJack]

For the odds calculation, you can’t really square the odds of 1/15000, since it was not back to back LL skips but rather 2 LL skips among the 62 competitors from that round.

[@SatyaGala-m9q]

Okay this is already crazy enough but something else which is actuslly just insanely unlikely, to the point where we cant even come close to comprehending it, is that there were actually *twenty five* LL skip solutions actually crazy and theoretically if 25 of the people in that group found a didferent LL skip solution the chance would be 1 / 15552^25 which is actuslly crZzzyyyyyy (im aware that it technically wouldnt be 15552^25 cuz thats just not how probability works but shhhhh)

[@cookierobber]

Wdym there were 25 LL skip solutions?

[@SatyaGala-m9q]

There were 25 different solutions to solve f2l that wouldve given a last layer skip

[@cookierobber]

@@SatyaGala-m9q There are infinite solutions that give last layer skips on every scramble...

[@SatyaGala-m9q]

bruh i meant reasonable and findable solutions

[@cookierobber]

@@SatyaGala-m9q What's the source on there being 25 haha? Just seems like a really specific number

[@Gladiator6]

This is why I love cubing

[@bonthecuber]

same here

[@Soph_252]

THE GOATSSSSS

[@szithaanu9934]

44 years and I have yet to solve a Rubiks Cube

[@its_lucky2526]

so in an alternate universe we were crushed by an asteroid

[@matk5728]

14,5 tps for a 29 moves solution is 2 seconds flat, which means theoretically a sub 2 solve is also doable 0_0 ( like a 1.99)

[@GlassMelon]

Love this channel

[@GoldenPotato888]

when you click the video less than 22 seconds after upload

[@XERTU]

you forgot about the "on" buddy

[@pixelation_yt]

@@XERTUbrother, he does not have to add the “on”

[@XERTU]

@@pixelation_yt bro i i was sleeping

[@pixelation_yt]

@@XERTU mb brah

[@lockupcubing]

No way Stu introduced Feliks as a two time world champ as if there was a single person watching who didn’t already know him

[@mushroomscav]

i have no idea what any of these terms mean but fire video 🔥🔥

[@Yurio]

People pointing out the odds aren’t that low but I think it would be interesting to see how many LL skips you can get doing different solutions with the same scramble

[@limepelt2348]

I had no idea what you were talking about for like half of that (I don't know anything about Cube). Also my what now of subscribing??

[@The_speedcuber-Tperm]

Another guy called mrcube made a vid about this, but this is better. Well done!

[@WaterboyCuber]

british yusheng

[@CubingForEveryone]

Waterboy???

[@WaterboyCuber]

@@CubingForEveryone yooo

[@CubingForEveryone]

@@WaterboyCuberyoo

[@somenygaard]

Power ball odds are even higher, 1:292,200,000 , and people hit the jackpot multiple times every year.

[@ubern3rd]

Saving this video for 2027 for when the asteroid maybe hits us 3:30

[@MHanes-m4f]

When ever i need a humble.. i watch this... im lost

[@roiel5153]

I watched the vid of the 3.69 and knew the that it had low probably but I had no idea what just went down

[@RemyMS]

Thats actually crazy 🤯

[@Matt-Speedcuber]

just thought id mention 3:45 you said jake and aidan are both dual nuetral, but jake is fully colour nuetral

[@megaapple1233]

w video as always ❤

[@lucahermann3040]

The weirdest thing that ever happend to me when cubing was three PLL skips within 5 consecutive solves. (The probability is 1:864) Too bad nobody else witnessed it.

[@Lolll_Cattt]

3:12 It sounds like someone just got shot and everybody is screaming.

[@obbispeedrunsgames9573]

i got last layer skip and next solve pll skip in a row the thing is i did it at school and didnt record the time nor the scramble since its just a random moves which is a 1 in 1,119,744 chance.

[@occubing]

Where did you get that cool cube graphic you used for the cube solving?

[@STUCUBE]

I made it in blender

[@occubing]

Dude that’s really impressive!

[@teriww]

0:39 radosław marcinek?

[@SamuelLandveld]

Guiness world record for worlds most attracting titles😂

[@thecubeisalie413]

Both improved their pr by 2.00 seconds ☠️

[@HenryZhoupokemon]

I learned how to spell floccinaucinihilipilification when I was 10 (cuz it was in some facts book as the longest word) and the definition is the act of estimating as worthless... never thought I'd see someone else use the wrod

[@Cloudsurfer69]

i subbed after checking your math :)

[@nicolasgoossens]

"It's not a crime to get lucky" 🤣😂

[@esjelly]

20 seconds ago!

[@ReubenBBX]

The scream 💀

[@gbamfs]

Everyone is all worried about the math when what really matters is the win. Who cares how rare it is? Very impressive

[@xporterx18x]

Do I know how to solve a cube? No. And I interested in it? Also not really. Did I watch this entire video excited and knowing I'm watching history? Well yes, yes I did.

[@yinyangsepticruski]

LITERALLY a Keaton Ellis & Lucas Etter moment, but in a fraction of the time difference between the two NRs occurring. Also, never a bad time to add a hate comment: I hate GAN cube (prices, I actually really love using them)... So get yours this week with Black Friday sales event (sorry for solicited advice and this is NOT an ad).

[@Untoldanimations]

By the way, you just squared 1/15552 to get the probability but there were more than those 2 people competing in that round for someone else to also have a chance at getting a LL skip

[@mr.tv001]

reminds me of chris moneymaker (yes his real name) who had consecutive increadible logic defying luck