Analysis of FMC Scrambles in Past Competitions

Billabob

Billabob

Regular
Joined
Jul 12, 2018
Messages
226
Hi all,

Apologies if this post is not appropriate for this subforum. Over the last few days I've been conducting a survey of the optimal solutions of FMC scrambles in past competitions. FMC is a unique event because, even if you find the best possible solution, not every scramble has the potential to be the world record - in fact it's become more and more unlikely with each successive record. The current single record is a 16 move solve by Sebastiano Tronto, set in 2019. According to cube20.org ~1/35 positions are solvable in 16 moves or less, ~1/432 positions are solvable in 15 moves or less, and ~1/5720 are solvable in 14 moves or less. So how do the official WCA scrambles compare?

The first competition with FMC scrambles available was HessenOpen2014, and the latest competition in my dataset is TaiwanOpen2022. In total I have scraped and used Cube Explorer to optimally solve 4286 scrambles. Here is the distribution of optimal solutions lengths:

Cubes solved optimally: 4286

15f*: 10
16f*: 110
17f*: 1157
18f*: 2871
19f*: 138

2014 - Cubes solved optimally: 301

16f*: 6
17f*: 75
18f*: 209
19f*: 11

2015 - Cubes solved optimally: 418

15f*: 2
16f*: 13
17f*: 103
18f*: 290
19f*: 10

2016 - Cubes solved optimally: 434

15f*: 4
16f*: 8
17f*: 123
18f*: 280
19f*: 19

2017 - Cubes solved optimally: 542

15f*: 3
16f*: 10
17f*: 147
18f*: 362
19f*: 20

2018 - Cubes solved optimally: 682

16f*: 25
17f*: 205
18f*: 433
19f*: 19

2019 - Cubes solved optimally: 881

16f*: 30
17f*: 230
18f*: 596
19f*: 25

2020 - Cubes solved optimally: 120

16f*: 1
17f*: 35
18f*: 80
19f*: 4

2021 - Cubes solved optimally: 80

16f*: 4
17f*: 16
18f*: 53
19f*: 7

2022 - Cubes solved optimally: 588

16f*: 6
17f*: 167
18f*: 399
19f*: 16

2023 - Cubes solved optimally: 240

15f*: 1
16f*: 7
17f*: 56
18f*: 169
19f*: 7

Yes, in the last 9 years of competitions there have only been 10 opportunities to set a 15-move FMC single record - and there has never been a scramble with a 14-move optimal solution! Here are all the 15-move positions and their solutions:

U2 R2 F' U2 D' L' D2 F' U F' R F' R2 F' L2 F' L2 B2 D2 - F2 L2 U' R U F' L2 D F' U2 L U B D' F2 DutchOpen2015 1
L2 B2 U2 B2 R2 U2 B' R2 U2 B2 F' L F' L2 F U' F2 L' R2 U' F - L' F' U D2 R2 U F2 U' L U' B' U' B R2 F' ThailandChampionship2015 1
R2 D2 F2 R' U R2 D' B U' F2 L F' D B F2 - F2 B' D' F L' F2 U B' D R2 U' R F2 D2 R2 PlentziaOpen2016 2
R' U' F D U2 B2 D F2 R2 U R2 B2 F2 U' B' D2 L F' U' R' B' U' L2 D' R' U' F - B U' D2 R L' D' B2 U L' B' L D' R L' F2 SydneyChampionship2016 1
R' U' F L' U2 L D2 F2 R2 D2 R2 D' L B2 D' L2 B' U R' D' B' U2 R' U' F - L' U2 D' L2 U' L' F' R B L D2 B2 D F2 U' JoaoCamara2016 1
R' U' F R2 U' B2 R2 U B2 D U2 B2 U R U2 R D L B D R' D U' R' U' F - D B R2 U2 B' R' L' B2 D' F2 B R B2 R2 U' Brasileiro2016 1
R' U' F D2 F2 L2 F2 U2 R' B2 F2 R' B' R B' F' D U B2 R' F D R' U' F - F B2 R' B2 R' B' U2 B L F2 L' B D L2 F2 PSKubing2017 1
R' U' F R2 D2 F2 L' F2 U2 B2 L' B2 F2 U' B R' B' D2 B' L U' R2 F2 U' R' U' F - B' U' L2 D2 F2 D B2 R B U2 F' U2 F2 R' U' SilentSwapOpen2017 3
R' U' F R2 U' R2 D B2 D U R2 U' F2 L' U' F' D2 L' D' L2 B R2 B' R' U' F - D' B2 R' B U' R' L2 F U2 D2 F' R' D2 B D' CobbCubes2017 1
R' U' F U' F2 L' R' B2 L2 R' D2 R' U' F2 R2 U2 F' L D U' F' R' U' F - L B2 U2 F D' R B R2 L2 F' U' R' L D' R' BFViennaDay2023 2

PlentziaOpen2016's scramble is literally just the optimal 15-move solution in reverse. This is why all scrambles start and end with R' U' F these days. Notice that there was not a single 15-move position from 2018-2022.
Here are all the 16-move positions (note these are the optimal generators, invert them for the solution):

F' L' R' B' U' L2 F2 U2 F D' L' U B' L2 F2 D2 BrainStudio2014 2
R2 D' U' F L' R2 B U L' R2 B2 R' B R D' F' FinnishChampionship2014 2
L F2 L D2 R B R2 F2 R' U R2 F2 U L R F2 MontrealFall2014 1
F R2 B' U2 F2 R' F' U2 B2 L' D' L' U2 B' U' R' Euro2014 3
B D2 B2 L' D U2 B' U R' U' F U L2 R F' L2 TomskBlindWeekend2014 1
D2 U2 L' R2 B' F2 D2 F' D' U2 R2 B U' B D2 B CMIFiestaOpen2014 2
D2 U' B' F' L' F' D' U F' U2 L' U2 R2 U' R F FMCUSA2015 1
F U' L' B' D2 U2 F D' L B U R' D2 L' F' U' BeijingOpen2015 3
D L' R U F' U2 L2 B' L2 F D U' F L' R' F' VenezuelaNationals2015 3
R D B F R' B2 D' B L2 F' L' U L' D' B2 F' ArnoldClassicRubik2015 1
B' L' F2 D2 B2 U' F R' F2 R2 B2 F L' B F' L EstonianOpen2015 1
D L U' L2 U2 R U L R' D' B2 L' R' U' F2 R' N8W8Summer2015 2
R' F2 U' F U F L' D' U' F' U2 R' B2 L2 U' L2 Indiana2015 2
D2 L2 F' L D2 B' F2 L D F2 U2 R D' R' U2 B2 VelbertOpen2015 2
B F2 L' U L' U' B' F U2 L F U2 R' B D2 R2 CBNBC2015 3
F2 L D2 L B D2 U' B' L' B2 L2 B' L' R2 B R France2015 1
U' L D' F' U' L' F R B2 D R' F' R' D' F2 L2 FMCed2015 3
B D' R U2 L' B2 L2 R F' U2 L' B' F' L2 D' F2 WinterWestUkraine2015 1
L2 U2 B' D2 L' B' L2 B' L U' F' U2 L R2 D' U MazateOpen2015 2
R D2 L' U' F L' B R' D U' L' D2 R D' F U2 FMCAsia2016 1
D2 R F' U2 L2 F' U' F2 L' D B' D2 L2 F' D' U' PSKubing2016 1
B D' F2 D2 U L2 U2 L D B' F2 D R' D2 L R2 FMCBrasil2016 2
L' F2 U R2 U R' D' L' R B2 F R B L' D' U BelgorodOpen2016 3
F2 L' U B' U2 L' D F' R2 U2 R F D' R2 D' L' Singapore3332016 1
B2 U2 L2 B2 U F2 U' R2 F L' B2 U2 L B U2 B' SilentSaloonOpen2016 3
L' F2 L' F L D2 B F2 L2 B2 R' F L2 F' U B' CanberraAutumn2016 3
U B' D R' B2 D B2 U' B2 U' B D2 R D' L' B' France2016 1
L2 D' L U2 R' U' L' D R F L2 F R2 D2 L' F2 SwissNationals2017 1
L' B2 U' L F D' U2 L' B' D' B' R' B2 U2 R2 D' ClassicCity4Charity2017 1
R2 D2 U2 B D2 L2 U R2 D F2 D B F' L' F D BelgorodOpen2017 3
F' L' D' F L2 B F' D F' R2 D' R' F2 L F' D KirkkonummiOpen2017 2
D U R2 F2 D' B' R2 F L' B2 D2 U2 F' R2 D' R GLSCupIV2017 1
F2 R D U' R B' R2 U B D B' D' L' B' U2 B LanyangOpen2017 1
L' D L' B2 D2 U2 R' F U R2 D U2 B U' B L Brasileiro2017 1
B2 L2 U B R' D' L' F L' R2 F L2 F2 U R U KalmykiaOpen2017 1
U' B L B2 D2 B2 L2 B' L' U2 F D F' L2 B' F2 SCMUICTOpen2017 1
R' B2 F2 U2 F' R' U B' D2 B F2 D2 B2 R2 F' R CowboysFMCParty2017 3
U L2 D2 U' B2 F' L' U2 B' D U L' B' U L B GAChamp2018 2
B2 U2 L' D2 B2 R' B' U R2 U F L' U2 R' U' B' FMCAsia2018 1
D' B' U2 L' U B' U2 B' L D2 L2 D' F R2 D' L' PBQBerkeley2018 3
D2 B2 D2 F2 L2 R2 D' R' B L B L' R' D L' U2 SwisscubingFMC2018 3
D' F' R D R2 U L' B F2 R2 F U2 R' B2 L' R2 BelgorodOpen2018 1
R D2 U' R2 F D B2 D F2 U' R' D2 R' B' D2 B AnaheimFall2018 1
L' D' L2 F' D B D2 F' L F' D B F D2 U2 F Pennsylvania2018 2
D2 R' F' D2 L' U2 R2 D R' F2 R2 B R2 B' D' L DFWCubingFiestaAugust2018 2
B2 D' R' D2 L R2 D2 R F L U2 R F2 U F2 L' ItBetterBeSolvedNYC2018 1
B' D' L D2 F2 R2 U2 R' B2 D L F2 D R D2 R MentalBreakdownSummer2018 1
B' L D' B D2 R2 F D' R D L U2 F L2 D2 B OnlyMentalLyon2018 2
U B2 D2 F2 U2 R2 B' L2 D' R2 D U' L F L R ChennaiMindOverMatter2018 3
L D' L2 U R U L R2 D L F2 U R D2 B R Meadowlands2018 2
D' U2 B2 L B2 R2 D2 U L' R' F' D2 B2 L' U R' SchwandorfOpen2018 2
F D B' L2 D F R U2 B2 U' L D2 R U' F R2 SPBIsland2018 1
F2 D' B F L' D B2 L2 R D U' L D L B F AtomicCubingSpring2018 3
L' D' F' R2 F2 D2 B R' F' U F' L D' U2 F2 R France2018 2
R2 F2 U2 B' R2 U' B2 F' D2 U' L2 F U2 L B' F' MoreThanOneCube2018 1
R2 D2 U' L2 F D B2 U R F D2 U2 L2 U2 F2 L RockvilleQualifier2018 1
U' F' L' U2 R' B D B2 U2 L2 U L U L2 R U' Murcia2018 1
U' B' L R B D2 B' L' R2 U' B L B U F2 D GACubers2018 1
D2 L R D' B F2 D B2 R' D2 L U L2 F2 U L2 CarteBlancheKubeOpen2018 3
L2 F' L F2 L' U L2 B R' D2 L R2 B2 L' U B2 MedanOpen2018 2
D' L' D2 F U L U' R D' F D' B U R2 U F2 PleaseBeQuietWPIWinter2018 3
F' L F2 U' L2 B2 U2 F U2 B D' L R B L R SwisscubingMentalBreakdown2018 1
D B2 R2 B' R' U' F' U' B' D2 R2 U2 L F2 R' B' SelangorCubeOpen2019 3
F2 U2 L2 R' D2 U' L B U' L D' F' D2 B2 R' F PSTLukow2019 1
L F U L2 R2 F U B U' F' R F L2 R2 F2 D TapiolaWinterOpen2019 2
F2 D L' B U2 R B D' R' U F2 D' R2 B D L2 TaiwanChampionship2019 1
D B D' F D' U' L' R' D U' L D2 F2 D' B F2 BarbyCube2019 1
D' B' U R B D' U' L2 F2 D R U R' D2 L R2 ElistaLyceum2019 1
R B2 L U' L' D2 R2 B D2 R' U F2 R2 U' R' D2 Cubetcha2019 1
R2 U R B2 R2 B L2 R2 D F2 U' L2 U' F' L B' MusicCitySpeedsolving2019 1
F U' R' U L2 D2 F R2 F' R B' D B U2 B' F2 PolishChampionship2019 3
F2 L' F2 D2 R2 U L D' R F L2 F' D F2 L' U2 FacaMaispelasCriancas2019 2
B' U L' R2 F2 L2 F D R2 F' L U' L R2 D R2 WroclawSideChallenge2019 2
L2 B' D' U' F' D' R2 U L2 U2 F' U R B2 R2 F2 BursaSummer2019 1
D F' R U L R' U2 B L2 U R U2 L2 D' R2 F2 Horsham2019 1
R B' D2 B U F' U F L F2 L' B' R D' U R' YJKazan2019 1
L U' B D F L2 B' U' R' U2 R D' B' L' D U NorthwestChampionship2019 2
D' U F L2 R B2 F' D' R2 D' L2 F D2 U2 F D2 FMC2019 1
D U' R2 U B' L2 U2 R2 U2 L' D' L2 R' U R2 U' MentalBreakdownMinnesota2019 1
D U2 F2 R2 D U' L B D' B' R' F R U2 B' D Pulmapelipaivat2019 1
U' B' D2 L' B L2 B' L' D' L U' F2 R B2 F U Pulmapelipaivat2019 2
B D' F' D R' B2 U' F' L' B' R' D2 B' L D' L WroclawFMCMasters2019 3
D R2 F D2 B' L U2 R' B' F' R U2 F L2 U2 L SilenceinTlaxcala2019 2
R' F2 D2 U F U L B R2 U2 F U' B2 R2 U' F' SilenceinTlaxcala2019 3
B' R2 B' U R U R F2 U' B' U F' R' D2 B2 L VirginiaQualifier2019 3
B' L F2 D' R D' R U2 F L' D2 B2 R' U B2 R SlowDownPerth2019 1
U2 B' D R' F2 R D' B' F2 U' F2 U' B2 U' L U' PleaseBeQuietKorea2019 1
R' U B D U2 R' B' F2 D2 R2 D2 L R D F D2 ChellesOpen2019 1
R B' F D2 L' D' F2 U2 F' L B' R D2 L' B D2 CFLGoesSideways2019 1
D' B' L' R' D L' R D2 L F R D U' L2 R' U PleaseBeQuietUtah2019 2
B' L' B' D F' D' F' R' D R2 U' B F2 D2 B R2 PSSFMCWarszawa2019 1
F2 L' R' D F' D2 L' R U B' R F D2 F' L' F AcarajeOpen2019 3
B' R U L F' L D' U' F U2 L R' U' B2 U' R' CebuOpen2020 1
D2 R U2 B' D2 B L' B U2 L2 U F' R U2 R2 B PolishChampionship2021 2
D2 L2 D' F2 L F' U F D U2 F D F R B R WelcomeBackAgainJkpg2021 1
U2 F' R U' F D' B D' B' L2 U' B2 F2 D F2 D TianjinSummerSolstice2021 2
U2 L' D2 B' F' D2 L U2 B2 D2 L2 B U' B' U2 F TianjinSummerSolstice2021 3
U2 F U2 F' L2 B F U' B F' L' F D L2 D F2 SwisscubingCupFinale2022 1
B' D' L R D' F D F' L2 F' L2 D2 L B R2 U DanishFMChampionship2022 1
U' L2 R2 U2 L D F D2 F' L' U2 R' U2 B L2 B' DanishFMChampionship2022 3
D' U R U2 B D' U' R2 F' R2 F2 U' B D' R B JaquecaDeFlorida2022 2
B2 D F' L' U2 L2 U2 B D F2 D2 B' U2 L' D' L2 UPPPoznanCubing2022 1
D2 L B D' U R2 U2 B' L2 D' L D F2 U2 L' U PBQtahWinter2022 2
U2 F2 L2 R D F' D2 R2 B' L F L U R' U2 F GuwahatiFMCChallenge2023 1
L' F2 U' F' L2 R D' R' D' F' R D L2 R2 D2 B' MartorellOpen2023 3
D R2 U L' B F2 D2 L D R2 F2 U' B2 D2 L' U BishopsStortfordSpringBBO2023 1
R F2 D' L R2 U' R' B' R' F U2 B' U2 R2 D2 B' YJKL2023 1
R' B2 D2 L' B' U' L2 R2 D L' B' R2 B D F2 R2 CambridgeSideEventsWinter2023 3
L2 F R' U' F U R F2 R' F' U' B R U2 L U' KyivFMCFriendsI2023 3
D B2 U2 R B F2 L2 B' U2 F' L F U' B' U R2 Mentallinn2023 1

For fun, here are the best competitions with more than one FMC scramble, by average solution length:

PlentziaOpen2016 - 2 scrambles, average: 16
DanishFMChampionship2022 - 3 scrambles, average: 16.3
Murcia2018 - 2 scrambles, average: 16.5
BFViennaDay2023 - 3 scrambles, average: 16.7
CanberraAutumn2016 - 3 scrambles, average: 16.7
JaquecaDeFlorida2022 - 3 scrambles, average: 16.7
Pulmapelipaivat2019 - 3 scrambles, average: 16.7
SydneyChampionship2016 - 3 scrambles, average: 16.7
TianjinSummerSolstice2021 - 3 scrambles, average: 16.7
WroclawSideChallenge2019 - 3 scrambles, average: 16.7

I hope you found my results interesting and that this puts the top FMC results into perspective. Finding the optimal solution of any scramble is still incredibly difficult for humans and requires a high level of understanding of the cube, as well as luck. There's no telling when the next 15-move position or the first 14-move position will show up, but when the time comes, will the right person be there to capitalise on it?

My scrape of FMC scrambles can be found here: https://pastebin.com/raw/45J5jS49
And their optimal generators* can be found here: https://pastebin.com/raw/MVRDgr7a

*Cube Explorer defaults to generators instead of solvers on its auto-run mode, sorry, couldn't find an option to change this!
 
Very interesting! If I recall correctly, someone also checked scrambles from all previous 3x3 rounds and found a scramble that had a 12 moves solution. Granted, there are a lot more 3x3 scrambles than FMC scrambles because of the difference in popularity, but you never know when such an FMC scramble pops up.

(I'm by no means experienced with FMC so please keep that in mind when reading the rest haha)

An interesting thought I had that might very well be wrong, but just going off of my intuition I feel like the shorter the optimal solution is, the more likely one is to find it. I think a 12 moves solution is easier to find than a 16 moves solution. I'm not sure this pattern extends all the way to 20 moves optimal scrambles too (in fact, I'm not sure if the pattern exists at all), because there would (again, going off of my intuition) be more 20 moves solutions possible than there are 12 moves solutions possible on a 12 moves optimal scramble. This would make it more likely to find one of those solutions than to find than one lucky solution on a 12 mover. Do these two factors -- shortness of the most optimal solution and the existence of multiple optimal solutions -- cancel out? In other words, is there any correlation to the length of the optimal solution and the likelihood that a pro FMCer finds an optimal solution?
 
Jorian Meeuse said:
Very interesting! If I recall correctly, someone also checked scrambles from all previous 3x3 rounds and found a scramble that had a 12 moves solution. Granted, there are a lot more 3x3 scrambles than FMC scrambles because of the difference in popularity, but you never know when such an FMC scramble pops up.
Click to expand...

I've scraped all the scrambles for the 3x3 speedsolving category from 2023 so far. It'll likely take a few days to run them all and there's no real reason to spend all that computer power, but there's already a surprising result from the first pass with the two-phase algorithm...

Number of Cubes: 25326
Cubes not solved yet: 0
---------------------------------------------------------------
Cubes solved optimally: 13

16f*: 2
17f*: 10
18f*: 1
---------------------------------------------------------------
Cubes solved with Two-Phase-Algorithm: 25313

13f: 1
14f: 3
15f: 37
16f: 227
17f: 1385
18f: 5915
19f: 12007
20f: 5414
21f: 324

Feel free to attempt this scramble to test your hypothesis: B2 U' B2 R2 D2 F2 L2 D F2 D' F2 L2 U L' D F U' F D L2

It's from group B in the second round of Pickering D 2023. The scramble given in the competition was 13 moves long so I generated a longer one so as not to give it away. I wouldn't be surprised if the scramble was input to the database incorrectly, it's absurdly easy.

I'm not going to exhaustively check every 3x3 scramble but I wouldn't be surprised if there were 12 move positions in there - it's only 1 in every million scrambles :)
 
Billabob said:
I've scraped all the scrambles for the 3x3 speedsolving category from 2023 so far. It'll likely take a few days to run them all and there's no real reason to spend all that computer power, but there's already a surprising result from the first pass with the two-phase algorithm...

Number of Cubes: 25326
Cubes not solved yet: 0
---------------------------------------------------------------
Cubes solved optimally: 13

16f*: 2
17f*: 10
18f*: 1
---------------------------------------------------------------
Cubes solved with Two-Phase-Algorithm: 25313

13f: 1
14f: 3
15f: 37
16f: 227
17f: 1385
18f: 5915
19f: 12007
20f: 5414
21f: 324

Feel free to attempt this scramble to test your hypothesis: B2 U' B2 R2 D2 F2 L2 D F2 D' F2 L2 U L' D F U' F D L2

It's from group B in the second round of Pickering D 2023. The scramble given in the competition was 13 moves long so I generated a longer one so as not to give it away. I wouldn't be surprised if the scramble was input to the database incorrectly, it's absurdly easy.

I'm not going to exhaustively check every 3x3 scramble but I wouldn't be surprised if there were 12 move positions in there - it's only 1 in every million scrambles :)
Click to expand...
Found this document with some interesting stats:
 
Jorian Meeuse said:
Found this document with some interesting stats:
Click to expand...
OK so I just realized something very weird. According to this document, there has never been an official 3x3 scramble that needed 20 moves to solve (not considering MBLD scrambles at least). My PB for FMC was done with this scramble:
R' U' F R B' L2 R2 D L2 B2 U' B2 R2 U2 B2 R B D' L D B L2 F' R' U' F
My solution was 27 moves (F D' B R B2 D F2 D' F' U' L' U L F U' F' L F U2 F' L' F2 U' F' L U' L) although I could have replaced F2 D' F' U' L' U L F with F U' L' U L F D' to make it 26 moves, which I realized later.
But here comes the strange part, if I put this scramble in the Kociemba Optimal Solver, it gives me a 20 moves solution! This seems very strange to me, especially considering the big block you can see on the scramble (although big blocks obviously don't really mean as much lol)

If you are wondering, this is the optimal solution it gave me: F D B' D' R2 B' L2 U L B D2 R2 L U' B2 U2 F2 B2 L2 D'
 
Jorian Meeuse said:
Ok so does the Kociemba Optimal Solver not give optimal solutions? I've tried the solver twice and it gave 20 moves twice.
Click to expand...
I have no idea what software you're using, but I got the 17-move solution above with Cube Explorer.

It also finds this 19-move two-phase solution in a few seconds: U' R2 D2 B2 D B L B2 U' L B2 U2 B D2 L R2 U' B' F (19f)
 
Jorian Meeuse said:
Ok so does the Kociemba Optimal Solver not give optimal solutions? I've tried the solver twice and it gave 20 moves twice.
Click to expand...
I don't know what program you're referring to here, but if you're using Cube Explorer you have to tick "optimal" next to the cube to get it to find the optimal solution for you. Otherwise it'll do a quick pass with the two-phase algorithm and generate a "good enough" solution.

20-move positions are roughly 1/88,269,394,437 so it's likely no one has ever gotten one in any category.
 
Decided to analyze some of these scrambles for fun to see if any of them seem reasonably findable with DR. These could of course be analyzed with blockbuilding as well, but hopefully this gives some idea of how rare findable 15's truly are!

For the 15's, the only one that seems humanly findable with DR is the 15 from PSKubing2017

R' U' F D2 F2 L2 F2 U2 R' B2 F2 R' B' R B' F' D U B2 R' F D R' U' F

(F2 L2 D') // EO 3/3
F (B') // DR-4C2E 2/5
(L F2 L' B' U2 B) // DR 6/11
(R B2 R B2) // Solved 4/15

Hard to say if this is likely to be checked since there's a good amount of nice DR triggers in less than 5 moves on this scramble, but this double NISS technique where the first move does nothing isn't completely crazy & is something I've done on some scrambles (it's also a necessary technique if you want to guarantee finding every nice DR trigger in 5 or less moves off of your 3 move EO's).

On this scramble you would need to perform this blind premove 8 times to cover all of the options due to the 3 move EO's all being HTR equivalent with another 3 move EO. It's also plausible that maybe you're checking F as a premove for the inverse scramble for some reason and find this DR accidentally as a result, though there doesn't seem to be something reasonable on this scramble that would lead to this premove being checked.

I don't know if I want to go through all of the 16's or not since there seems to be a lot of them & there's only 3 which have been shown to have findable 16's that I'm personally aware of (the WR, and 2 of Yiwei Liu's solves from her 21.67 AsR mean).
 
ottozing said:
Decided to analyze some of these scrambles for fun to see if any of them seem reasonably findable with DR. These could of course be analyzed with blockbuilding as well, but hopefully this gives some idea of how rare findable 15's truly are!

For the 15's, the only one that seems humanly findable with DR is the 15 from PSKubing2017

R' U' F D2 F2 L2 F2 U2 R' B2 F2 R' B' R B' F' D U B2 R' F D R' U' F

(F2 L2 D') // EO 3/3
F (B') // DR-4C2E 2/5
(L F2 L' B' U2 B) // DR 6/11
(R B2 R B2) // Solved 4/15

Hard to say if this is likely to be checked since there's a good amount of nice DR triggers in less than 5 moves on this scramble, but this double NISS technique where the first move does nothing isn't completely crazy & is something I've done on some scrambles (it's also a necessary technique if you want to guarantee finding every nice DR trigger in 5 or less moves off of your 3 move EO's).

On this scramble you would need to perform this blind premove 8 times to cover all of the options due to the 3 move EO's all being HTR equivalent with another 3 move EO. It's also plausible that maybe you're checking F as a premove for the inverse scramble for some reason and find this DR accidentally as a result, though there doesn't seem to be something reasonable on this scramble that would lead to this premove being checked.

I don't know if I want to go through all of the 16's or not since there seems to be a lot of them & there's only 3 which have been shown to have findable 16's that I'm personally aware of (the WR, and 2 of Yiwei Liu's solves from her 21.67 AsR mean).
Click to expand...
OMG FUNNY CUBE DROP MAN!!1!!!1!!

But in all seriousness great summary, shows how hard it will be to break the FMC WR Single.
 
Billabob said:
the latest competition in my dataset is TaiwanOpen2022
Click to expand...

That competition seems to be the last for 2022 in your dataset, nevertheless, there are also scrambles from 2023 in your dataset.

For us with crappy CPU/RAM, could you please update your statistics for FMC scrambles? In my dataset from several days back I see 5613 scrambles, so it would take "only" 1327 scrambles to solve/generate optimally.

Billabob said:
FMC is a unique event because, even if you find the best possible solution, not every scramble has the potential to be the world record - in fact it's become more and more unlikely with each successive record.
Click to expand...

I would rephrase it like what has become more and more unlikely is getting the WR potential scramble, not the WR solution itself (which is, on contrary, more and more likely to get in my opinion).

Billabob said:
So how do the official WCA scrambles compare?
Click to expand...

I am sure you are aware of frequency distribution. I bet a lot of people is not. For them, the scrambles/solutions are simply not comparable at all.

Billabob said:
The first competition with FMC scrambles available was HessenOpen2014
Click to expand...

I was quite shocked to find it out. Does anyone know the reason why WCA doesn´t have 3x3x3 scrambles before 2014? Edit: I didn't realize I asked already in 2010.
 
Last edited:
bcube said:
I am sure you are aware of frequency distribution. I bet a lot of people is not. For them, the scrambles/solutions are simply not comparable at all.
Click to expand...

I might be stating the obvious, but getting familiar with the frequency distribution of scrambles is not enough unless the optimal move count of solutions is known as well (at the bare minimum, WCA should provide such data but it's not priority for them).
 
bcube said:
I was quite shocked to find it out. Does anyone know the reason why WCA doesn´t have 3x3x3 scrambles before 2014?
Click to expand...

Scrambles have only been necessary to include with results since 2013 (1c3a). Where 2013-2014 are I'm not sure.
 
bcube said:
I might be stating the obvious, but getting familiar with the frequency distribution of scrambles is not enough unless the optimal move count of solutions is known as well (at the bare minimum, WCA should provide such data but it's not priority for them).
Click to expand...
Please can you keep this weird crusade to its own thread and not derail mine with it. I might scrape & solve the new scrambles, it has been just over a year since my original post... I'd have to dig up my original code.

TaiwanOpen2022 being the latest competition in my set while including 2023 competitions is a bit confusing - I don't remember exactly why that happened - perhaps its results were only published in 2023. It takes a while for scrambles etc to become available on the site.
 
bcube said:
Hmm, I am wondering how exactly Stefan came up to these 304 scrambles back in 2011.
Click to expand...

I checked a database export from 2010 and they aren't there. Wasn't mentioned in the readme until mid 2014. Stefan probably had access to the real database which might have stored them somewhere. He also seemed to keep some results page of his own.

World Cube Association

The World Cube Association governs competitions for mechanical puzzles that are operated by twisting groups of pieces, commonly known as 'twisty puzzles'. The most famous of these puzzles is the Rubik's Cube, invented by professor Rubik from Hungary. A selection of these puzzles are chosen as...
www.worldcubeassociation.org www.worldcubeassociation.org

2013 scrambles should really be available though. Maybe Lucas or Stefan know.
 
You must log in or register to reply here.

Similar threads

O
Automatic F2L Pair Analysis for solver solutions
Replies
3
Views
304
abunickabhi
abunickabhi
J
Carsen, Magnus (13) (2482) vs. Dolmatov, Sergey (45) (2591) Game Analysis
Replies
0
Views
217
J-EZ_Music
J
Isaiah Scott
Free Square-1 Solve Analysis from a 13 second solver!!!
Replies
5
Views
1,211
eeeeeeeee
eeeeeeeee
Arcanist
WRC Statement on Frame-by-Frame Analysis
4 5 6
Replies
101
Views
12,919
siwoo
siwoo
abunickabhi
  • Poll Poll
Preference: Live Pack splits or post attempt video analysis splits
Replies
0
Views
341
abunickabhi
abunickabhi
Back
Top