I suck at 2x2
Session average: 4.82
1. 3.96 U R' U F' R F R2 F' R'
2. (3.46) F' U' F2 U' R U' F' U' R
3. (3.09) F' R U R' F2 R' U' R2 U2
4. 4.06 F' U R' U2 R U R2 F U'
5. 4.25 R2 U2 R' U R' F' R F' R' U'
6. 4.49 R2 U' F R U2 F' R' U F'
7. 5.52 U2 F U2 R' F' U F2 R2 U2
8. 4.76 F2 R' F2 R F' R F2 R' F2
9. 3.59 U F R F' U R2 U' F R2 U'
10. 6.80 R2 U' F U2 R' F U F2 U2
11. 4.88 U' R2 U' F R' F U' R2 U2
12. 5.23 U2 F' R U' R2 F U R F
13. 5.60 F2 U' R' U' R U' F' R' U'
14. 4.68 U2 F U2 F' R F2 R U' F'
15. 4.60 F2 U R' U2 R' U2 F U' R2
16. 5.18 U F U' R F2 R' U' R' U'
17. (7.47) U F2 R' U F U F' U F U'
18. 4.37 U' R F2 U' F U' R F R2
19. 5.60 F2 U R2 F' U' F' R F2 R'
20. 3.93 F2 R2 F R F' R U2 F U'
21. 4.94 F U R' U2 R' U2 R' U' F2
22. 5.81 U' R2 U R2 U F2 R F R2 U
23. (2.64) F U' F2 R' F' R2 F U R' U2
24. 3.55 R U F U2 F R U R2 U2
25. (7.21) U R F' R' U2 R2 F R' F'
26. 4.06 F R F R F2 R F2 R U
27. 5.19 F R2 F R' U2 R U2 R U2
28. 4.82 F2 R U' F' U2 R2 U' F' U
29. 5.41 U R U R' U F U R' U'
30. 4.18 U R2 U F' U' F U F2 R2 U2
31. 4.17 F' R U' R2 U F2 U' R' U'
32. 5.98 F' R2 F' U' R F2 U' F2 U'
33. 4.15 U' F2 R U' R F2 R U2 R' U'
34. 4.67 U2 F' U R' U F' U2 R U'
35. 4.71 R2 F' R F R U' F' U R
36. 4.52 F' U' R F' U' R F2 U' R
37. 5.15 U R2 F U' R2 F2 U F' U'
38. 5.28 F' U2 F2 R U' F U2 R' F'
39. 4.16 F2 R F R U' F R F2 U2
40. 5.82 F2 U' F' R2 U F' U2 F2 R U'
41. (6.83) F' U' F R2 F' U' R2 U2 R2
42. 5.43 U' R2 U F2 R' F2 R2 U2 R'
43. 5.11 R' F2 U2 R U' R F U R2
44. 5.41 F R' U F2 R' U' R2 U F' U
45. 4.92 U2 R F' U' R U2 F' U F'
46. 6.42 U2 F2 R2 U2 F' U' F' R' U'
47. 4.62 F' R2 U R' F U' F R2 U'
48. 4.19 F' U2 F R' U F2 R' F R
49. 3.47 F' R F' R2 F R2 U R2 U'
50. 4.56 F' U' R2 F2 U R F' R U2

EDIT: OH Average of 50: 20.16
I was swearing and very angry at the last few solves. Could have been sub-20...
1. 17.06 D' U' L2 B2 L2 F2 U F2 U B2 R2 F' D L' F D B' R F' R D'
2. 22.67 B2 U2 B' D2 L2 F D2 B2 U2 L2 D2 R' F2 D B' U2 L2 D L2 F2 L
3. 17.18 R F2 L D2 L' U2 F2 D2 L' B2 R D' B F2 L2 R B U' L B' U2
4. 20.63 D2 R B2 R' U2 R D2 B2 F2 L F2 D' R' F U2 F R U' F' R' D2
5. 17.73 B2 U L2 U' L2 U2 R2 B2 U' F2 D R B D' B U B2 U B2 D2 R'
6. 19.95 L' F2 L B2 R2 F2 L D2 R F2 U2 F D F' R' B2 D2 F' D2 L' B
7. 20.09 D2 L2 D' L2 D' F2 L2 R2 D R2 D2 B' L' B2 U' B' D F' U L2 F'
8. 20.47 U2 B' D2 B D2 F D2 B R2 D2 B' D' F2 L D2 F R2 F2 R' B2 U2
9. 22.01 F' L2 D2 F' L2 B2 D2 B D2 F2 L2 U R D2 B D B D' R B2
10. 21.51 U2 F2 R2 D2 U2 L U2 L D2 L' F D B' F L' F2 L2 U B L
11. (16.53) F2 R2 U' L2 F2 D' B2 D' L2 B2 R2 F L U2 B2 R' B F' U' L' B
12. 19.79 U2 B2 D' R2 F2 U' B2 U2 B2 F2 U2 F' R' D' F' L' D' R' D' B' R
13. 17.13 R2 B2 D2 U2 B' U2 F U2 F R2 F2 D' F R B2 L2 D L R2 D U2
14. 18.18 F' L' D2 B2 R' L F' U' D' B' L2 F2 R D2 L' F2 R F2 L' U2 B2
15. 17.81 F2 D L2 B2 F2 U F2 L2 U' B2 F2 L' F U2 B R B' L' F2 D U'
16. (15.29) D' F R F' U F' U2 B D' R L2 F2 U2 L2 U2 D F2 B2 L2 B2 D
17. 22.84 R B2 R' B2 D' L' D' F' R' B D B2 R2 U' L2 D F2 D2 L2 B2 L2
18. 19.50 U L2 D2 F U F U2 F2 R D' L2 F2 R2 D2 R2 U R2 B2 U2
19. 22.25 U2 B U2 F R2 U2 R2 B2 R2 F2 U' R B' U2 L2 D' L2 F2 L' B2
20. 17.69 F2 D2 B' U' B L' B R L U B2 L2 F2 D2 F2 U L2 U' L2 B2
21. 23.49 B2 R2 F2 U' L2 U' F2 D L2 D' U2 F' D2 B U2 R2 F' L D' F R'
22. 21.42 U F2 R2 B2 R2 U' L2 D' F2 D2 F2 L F U' L' B2 R2 D' B' U' R2
23. (25.36) D2 B2 R' F2 R2 U2 F2 L' F2 R2 F' D2 U L2 F D2 R' B2 R'
24. 19.78 F2 U' F2 U F2 U L2 F2 D L2 D2 R U' F2 L B' U R2 U' B'
25. 22.30 F2 U' F D' R' B2 L D' F U' D2 F R2 U2 B D2 L2 F' D2 R2
26. 18.36 R2 F2 D2 B2 R' U2 L' F2 R D2 B2 U' F' R U B U' F2 R' D
27. 18.35 L2 U' R' B' U B2 D L D L D2 B U2 R2 U2 R2 F' D2 B2 R2 D2
28. 23.96 D' L2 D L2 U2 B2 D F2 R2 B2 R2 F' R2 D U L' D2 B U B2
29. 19.72 F2 R2 B2 L2 U2 L B2 R' D2 B2 L B L2 U R D F L B2 D U2
30. 20.85 F2 L2 U2 L2 D2 B' D2 U2 F2 U2 F' R B' F2 D' U B U2 B' L' U2
31. 18.02 R2 F2 D' L2 B2 D L2 U F2 L2 U L U' F L' F2 L2 R U' B L'
32. (15.94) F2 U2 R B2 F2 R' U2 L B2 L2 B' U L F2 R2 B2 F R2 U2 L' U'
33. 19.77 U' R2 D' F2 D' F2 R2 U B2 F' L2 R' F' U' B U2 B' D' L2
34. 24.24 B' L2 R2 B' L2 F' L2 B2 U2 F' R2 D' L2 D L' F2 D' U R2 D' B'
35. 19.56 F2 U' L2 D' L2 B2 D2 U' B2 L2 B2 L' B D2 L' F2 D L' D' R2 D2
36. 16.81 F2 R' U2 L F2 L U2 R B2 F2 R' D' B L' F U' R2 D L' F2 L'
37. 19.64 R' F2 R F2 L F2 D2 R' U2 R2 D' L2 F' D2 L2 D2 R D' R2 F
38. 21.97 B L2 F' R2 U2 R2 B L2 B F D2 R' F' D' B F L' R' D' B F2
39. 21.05 B2 D F' U2 R' F' B U R L U2 R2 B2 U B2 U' L2 F2 U' L2 U2
40. 17.23 R2 B2 R2 D F2 R2 D' F2 U' R2 B' L' D2 U2 L' F R2 F' D'
41. 19.64 R2 U2 F2 U2 B D2 F' U2 L2 U2 F' U B D' U F R2 U R
42. 21.81 F L2 U' D' F R U' F U2 B' R F2 R L D2 F2 R B2 L F2 L
43. 19.70 U' B2 R L2 U L' F2 U2 B' L' D2 F L2 F D2 F' R2 B' D2 B
44. 18.72 D R2 B L U2 R' L' B R F2 U' L2 F2 U' L2 F2 U' D B2
45. 22.13 F2 R2 F2 L2 D2 B F2 L2 D2 F L2 R B2 F R' F2 L D L R2 U
46. 18.32 L' F2 D' R U2 R2 F2 L' F' D F2 U2 D' B2 D' F2 L2 F2 B2 U'
47. (24.59) L2 U2 B' U2 R2 B L2 B2 F U2 R2 D' F2 U' B U2 F U2 L' R' F'
48. 23.52 L2 U2 F2 R' U2 L U2 B2 D2 R' D2 U B' R2 D R' U B D2 R2
49. 22.19 D2 L2 D R2 U L2 R2 U R2 B2 R2 F' D U2 B2 R D2 B' D' U2 F2
50. (25.75) R L2 U' R2 D2 R F' D R B2 R2 U B2 D B2 D' L2 F2 U' B2
Rolled to 20.09 and I gave up. Sub-20 will come... soon.
 
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10.822 single
-full step
-f perm
-6 move oll
-3 move x-cross

Reconstruction:

Time:10.822
Scramble: L2 U' L2 D' U' B2 D U2 L' U2 L2 B' L' B2 L2 R' F' U2

y // inspection
L F R' // x-cross
y' U' R' U' R // second pair
y' U' R U R' y' R U R' // third pair
R' U R U R' U R U' R' U R // last pair
U R' U2 R U R' U R // OLL
R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R // PLL

52 moves
2 cancellations

50/10.822= 4.620 tps
 
Reconstruction:

Time:10.822
Scramble: L2 U' L2 D' U' B2 D U2 L' U2 L2 B' L' B2 L2 R' F' U2

y // inspection
L F R' // x-cross
y' U' R' U' R // second pair
y' U' R U R' y' R U R' // third pair
R' U R U R' U R U' R' U R // last pair
U R' U2 R U R' U R // OLL
R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R // PLL

52 moves
2 cancellations

50/10.822= 4.620 tps

Y
L F R' (3/3)
U' Y' R' U' R (4/7)
U2 L U L U' L2 U L2 (8/15)
U' L U2 L' (4/19)
F R' F' R U2 R U2 R' U2 (9/28)

6.90 (not counting as PB because it's not my scramble)
 
5x5 stackmat

1:01.31, 1:03.22, (1:11.68), (1:01.02), 1:04.16 => 1:02.90 avg5

1:01.31, 1:03.22, (1:11.68), (1:01.02), 1:04.16, 1:04.00, 1:10.56, 1:06.46, 1:06.69, 1:01.66, 1:09.05, 1:02.06 => 1:04.92 avg12
 
3x3 Full-step singles 8.25 D2 B2 F2 U L2 B2 R2 U' F2 U R2 B R' B2 F' U' B2 F' R F2 U' and 7.84 F2 U2 B2 D' L2 B2 U F2 U2 L2 R U2 B' F' U B' D2 R' B2 R2 . avg of 5: 10.74, avg of 12: 10.71 and avg of 50 PB 11.67 :D
 
5x5

(58.34), 1:04.73, 1:01.98, (1:07.28), 1:04.89, 1:07.25, 1:04.34, 1:06.04, 1:04.75, 1:00.95, 1:05.33, 59.20 = 1:03.95 ao12
 
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Wow crazy solves.

avg of 5: 20.567

Time List:
1. 18.858 L B' U' R2 D R2 B' U' L F' D2 R2 B' U2 B2 L2 F L2 F'
2. 23.234 D2 B2 L2 B2 R2 D L2 U' B2 R2 U' F' L' B2 R D L2 B D' R' U2
3. 19.610 R2 U2 L2 B2 D' U B2 U F2 U' F' L U' B' D' B' R' U2 B L2
4. (17.093) B2 D2 B2 L2 D2 F2 L' D2 U2 B2 D' R F L' R2 D' R' U F2
5. (23.512) U' R2 U' F2 U F2 L2 D L2 U L2 B R D U2 B F R2 D

*gets 18*

"Very nice."

*gets 19*

"Yay, a counting 19."

*gets 17*

"o.O"

avg of 12: 23.100

Time List:
1. 27.031 R2 U B2 L2 F2 R2 U' B2 R2 D U2 B L U' R2 B' L' F2 D F L'
2. 23.229 L' F2 D2 L' U2 B2 F2 R' F2 L' D2 F' D' L U F U2 F2 R D U'
3. 22.009 F D2 B U2 F' U2 B2 U2 L2 F L U B2 D2 U' R2 U R
4. 26.045 U L2 U' L2 U R2 D2 L2 B2 D R2 B D L' U R B D B' R2 B
5. (30.260) F2 U L2 D' F2 D2 U' R2 U B2 U' F' U B2 R' D2 R B' U2 F R'
6. 18.858 L B' U' R2 D R2 B' U' L F' D2 R2 B' U2 B2 L2 F L2 F'
7. 23.234 D2 B2 L2 B2 R2 D L2 U' B2 R2 U' F' L' B2 R D L2 B D' R' U2
8. 19.610 R2 U2 L2 B2 D' U B2 U F2 U' F' L U' B' D' B' R' U2 B L2
9. (17.093) B2 D2 B2 L2 D2 F2 L' D2 U2 B2 D' R F L' R2 D' R' U F2
10. 23.512 U' R2 U' F2 U F2 L2 D L2 U L2 B R D U2 B F R2 D
11. 25.996 L' D2 F2 L2 F2 L D2 L2 F2 R' D F U2 R F' L R F' L B2 D'
12. 21.475 L2 U2 B2 U L2 F2 R2 U2 L2 R2 B2 R' B2 D' L2 U' F' R2 U B F

Augh messed it up after this.
 
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Barely an achievement, more luck but today throughout my non-timed solves I have achieved a total of 3 LL skips.
These were all hand-scrambles for a decent amount of time so the cube already being partly solved had nothing to do with it.
I think also although I cannot confirm that all of the gave me an AUF of U2.
What topped it was that when I got my most recent one, I was even thinking about LL skips and what illustriousness they hold and then BAM.

Probability of getting 3 LL skips + U2 AUF:

p(1LL skip-any AUF) = 1/72 * 1/216 = 1/15552
p(U2 AUF) = 1/4
p(1LLS + U2) = 1/15552 * 1/4 = 1/46656
p(3xLLS + U2) = 1/46656^3 = 1/101559956668416

Note: This model applies to getting 3 LL skips + U2 AUF in 3 consecutive solves.

Note 2: This will never happen again in my life.
 
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Those numbers aren't valid because:
- You didn't just get 3 LL skips with U2 AUF in a row, you got them in some number of solves, so you have to take that into account - for example if I flipped 6 coins and got 3 heads the probability is not 1/8
- Hand scrambles are not random: they're not independent (people tend to do the same thing over and over, so you probably used the same move sequences several times) and each one is not necessarily properly scrambled (you may have done a sequence of moves over an over, having very little effect or doing the equivalent of only a few moves).
- 15552*4 = 62208
 
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