Here is most of Richard's advanced method in one email, a total of 95
algorithms! These appeared in instalments over at speedsolving.

I have changed some values to make it more useful for me to see -- at a
glance -- probabilities. My thinking is that this is too much for one
person to memorize (though I would love it if someone proved me wrong) but
that the list can be used to assemble a shorter list (that is what I am
doing now). This could drastically cut down execution times for
blindfolding. All credit goes to Dr C., of course.
S.

Total average number of moves 94 21369829/28740096

Stage 1 / 2: Edge Orientation
75 Algorithms; Average number of moves: 15 257/512

Two Edges to Orient
Four algorithms; probability 66/2048 (0.03222)
1. Isomorphic to (1,2): L F' U L' B' F U R' F U' R B F' U' (14)
(probability 12/2048)
2. Isomorphic to (1,3): F U2 F2 D' U' L' U L D F2 U' F' U' (13)
(probability 24/2048)
3. Isomorphic to (1,6): L2 R2 D B' L D' B L2 R2 F' U L' F U' (14)
(probability 6/2048)
4. Isomorphic to (1,11): R' U' R U2 R2 D' U' F' U F D R2 U' (13)
(probability 24/2048)

Four Edges to Orient
Eighteen algorithms; probability 495/2048 (0.24169)
5. Isomorphic to (1,2,3,4): U' L2 F2 L2 D2 L' R B' R2 D2 R2 F2 L R' (14)
(probability 6/2048)
6. Isomorphic to (1,2,3,5): R2 D L' R F L' R U L' R B L' R' (13)
(probability 48/2048)
7. Isomorphic to (1,2,3,7): U2 F2 R2 F2 U' F2 R2 F2 U2 B' F R' B F' (14)
(probability 24/2048)
8. Isomorphic to (1,2,3,8): F2 L2 F2 U' F2 L2 F2 U2 B F' L' B' F U2 (14)
(probability 24/2048)
9. Isomorphic to (1,2,3,9): U F' U2 F R U B U' L U2 L' B' U' R' (14)
(probability 48/2048)
10. Isomorphic to (1,2,3,10): U F U' R U2 R' F' U' L' U B' U2 B L (14)
(probability 48/2048)
11. Isomorphic to (1,2,5,6): U B2 F2 U B2 F2 R2 B F' U2 R' U2 B' F R2 U'
(16) (probability 3/2048)
12. Isomorphic to (1,2,5,7): D L' R F L' R U L' R B L' R (12) (probability
48/2048)
13. Isomorphic to (1,2,7,8): B2 F2 D B2 F2 R2 B' F D2 R' D2 B F' R2 (14)
(probability 6/2048)
14. Isomorphic to (1,2,7,9): D' R2 B' L2 U' L' R' U' L2 F' R2 D' L R (14)
(probability 48/2048)
15. Isomorphic to (1,2,8,9): D R2 B' L2 U L' R' U' L2 F R2 D' L R (14)
(probability 48/2048)
16. Isomorphic to (1,2,9,11): F2 L2 D2 B' D2 L2 F2 U R2 U2 R' U2 R2 U' (14)
(probability 12/2048)
17. Isomorphic to (1,2,9,12): R2 F2 R2 D2 R2 B' R2 D2 R2 F2 L R' U' L' R'
(15) (probability 24/2048)
18. Isomorphic to (1,3,6,8): F2 R2 D' R2 F2 R2 U2 L R' B' L' R U2 R2 (14)
(probability 12/2048)
19. Isomorphic to (1,3,6,9): U' R2 U B R' B U R U2 R' B' U B' R' (14)
(probability 24/2048)
20. Isomorphic to (1,3,6,10): L B2 L2 U R2 B2 L' R U2 R2 B' L2 U2 R' (14)
(probability 24/2048)
21. Isomorphic to (1,3,6,11): U' B U' R' B2 R B U R' U B R2 B' R' (14)
(probability 24/2048)
22. Isomorphic to (1,3,6,12): L' B2 L2 U L2 R2 B2 L R' U2 B' R2 U2 R (14)
(probability 24/2048)

Six Edges to Orient
Thirty algorithms; probability 924/2048 (0.45117)
23. Isomorphic to (1,2,3,4,5,6): L F' L' U L2 R2 D2 L' R F L D' L2 R2 U2 R'
(16) (probability 12/2048)
24. Isomorphic to (1,2,3,4,5,7): U L2 R2 D' B2 R2 D L2 F2 U L R' F' L2 B L
R (17) (probability 24/2048)
25. Isomorphic to (1,2,3,4,5,9): L2 F2 U B2 L' R2 D' F' U2 F2 L' B2 D2 U R
F (16) (probability 48/2048)
26. Isomorphic to (1,2,3,4,5,11): U' L2 B L B L2 R' B2 F' R2 D R D L' R2 D2
(16) (probability 48/2048)
27. Isomorphic to (1,2,3,4,9,10): U F2 U2 B2 F' D R D B' F2 D2 F2 D L' D'
B' (16) (probability 24/2048)
28. Isomorphic to (1,2,3,4,9,12): R2 D2 U F2 L' B2 U2 B' D' L' R2 F2 U B2
L2 B R' (17) (probability 12/2048)
29. Isomorphic to (1,2,3,5,6,7): F2 L2 D U' R2 U' L R F' U2 R2 U2 B F2 L R
U' (17) (probability 12/2048)
30. Isomorphic to (1,2,3,5,6,8): L B2 L2 R2 F' L D L' R F2 L2 R2 B L' D' R'
(16) (probability 12/2048)
31. Isomorphic to (1,2,3,5,6,9): L2 R2 D' L B L' R D2 L2 R2 U L' B' L R' U2
(16) (probability 24/2048)
32. Isomorphic to (1,2,3,5,6,10): U2 L2 R2 D R' B' L' R D2 L2 R2 U' R B L
R' (16) (probability 24/2048)
33. Isomorphic to (1,2,3,5,7,8): D' B2 L2 U' R2 F2 U L2 R2 D' L' R' F' L2 B
L' R (17) (probability 24/2048)
34. Isomorphic to (1,2,3,5,7,9): B2 L2 D R2 F2 R B D U2 L2 F' R2 D2 R' U'
F' (16) (probability 48/2048)
35. Isomorphic to (1,2,3,5,7,10): B L2 F2 L' D L B R' F2 R2 B2 F L' U' L'
F2 (16) (probability 48/2048)
36. Isomorphic to (1,2,3,5,7,11): R2 B2 L' B R B2 L2 F L' U' L F2 L' B2 R2
B U' (17) (probability 48/2048)
37. Isomorphic to (1,2,3,5,7,12): L2 F' L2 U2 B2 R' B' L F L2 D2 B R D B2 L
U' (17) (probability 48/2048)
38. Isomorphic to (1,2,3,5,8,9): F2 U B2 L' R2 D' F' U2 F2 L' B2 D2 U R F
L2 (16) (probability 48/2048)
39. Isomorphic to (1,2,3,5,8,10): D' L2 D B L B' F2 U' B L2 B' D' L' D U2 F
(16) (probability 48/2048)
40. Isomorphic to (1,2,3,5,8,11): L2 D2 U L R2 D' R' D' R2 B2 F L2 R B' L'
B' (16) (probability 48/2048)
41. Isomorphic to (1,2,3,5,8,12): L2 D2 U' R2 F R F L' R2 B' F2 L2 D L D R'
(16) (probability 48/2048)
42. Isomorphic to (1,2,3,5,11,12): U' B2 F2 R D' B L D' F' D2 U2 L B' D R
B' (16) (probability 48/2048)
43. Isomorphic to (1,2,3,7,8,10): U B2 F2 D2 B' F L B D' B2 F2 U2 B F' L'
B' (16) (probability 48/2048)
44. Isomorphic to (1,2,3,7,9,10): D2 L' F' R2 F2 U' B2 L2 R D F U2 F2 R B2
U' (16) (probability 16/2048)
45. Isomorphic to (1,2,3,7,9,12): B' F2 R' B U2 B' L' U' L R2 F L' U2 L B U
(16) (probability 48/2048)
46. Isomorphic to (1,2,3,7,10,12): R2 D U2 R' B' R' D2 U L2 U2 L' D R F R'
U2 (16) (probability 27/2048)
47. Isomorphic to (1,2,3,8,9,11): R2 D2 R2 D F' D' L' U R2 U2 L2 R' D B D
L' (16) (probability 12/2048)
48. Isomorphic to (1,2,3,8,9,12): L2 R' F R D F2 D' L D U2 F' D' R' F2 R U'
(16) (probability 45/2048)
49. Isomorphic to (1,2,3,8,10,12): L2 D2 U R' F' R' D U2 R2 U2 R' B R D L'
U2 (16) (probability 12/2048)
50. Isomorphic to (1,2,7,8,9,12): L B' D2 U2 R U B' L' U F' L2 R2 D L F' U'
(16) (probability 12/2048)
51. Isomorphic to (1,3,6,8,9,12): F2 D B2 L2 D2 F2 U B' R' F R2 U F2 L2 D L
F R' (18) (probability 4/2048)
52. Isomorphic to (1,3,6,8,10,11): R2 B2 F2 D F R' U' F L' D2 U2 B U L' F'
U R (17) (probability 4/2048)

Eight Edges to Orient
Eighteen algorithms; probability 495/2048 (0.24169)
53. Isomorphic to not (1,2,3,4): L2 R2 D' B' F' L' R' D' U' B' F' L' R' U'
L2 R2 (16) (probability 6/2048)
54. Isomorphic to not (1,2,3,5): U' B2 D' L' R' B' F' D' U' L' R' B' F' U'
B2 U (16) (probability 48/2048)
55. Isomorphic to not (1,2,3,7): U2 L2 D' B' F' L' R' D' U' B' F' L' R' U'
L2 U2 (16) (probability 24/2048)
56. Isomorphic to not (1,2,3,8): R2 D' B' F' L' R' D' U' B' F' L' R' U' R2
(14) (probability 24/2048)
57. Isomorphic to not (1,2,3,9): U' B2 F2 L2 F' U2 L' D U L' U2 B' L2 B2 F2
U' L' R' (18) (probability 48/2048)
58. Isomorphic to not (1,2,3,10): L R2 D' B' F' L' R' D' U' B' F' L' R' U'
L' R2 (16) (probability 48/2048)
59. Isomorphic to not (1,2,5,6): B' F' L' R' D' U' B' F' L' R' D' U' (12)
(probability 3/2048)
60. Isomorphic to not (1,2,5,7): F D B' L' R' D' U' B' F' L' R' D' U' F' D'
F' (16) (probability 48/2048)
61. Isomorphic to not (1,2,7,8): D' B' F' L' R' D' U' B' F' L' R' U' (12)
(probability 6/2048)
62. Isomorphic to not (1,2,7,9): F' L D' B' F' L' R' D' U' B' F' L' R' U' L'
F (16) (probability 48/2048)
63. Isomorphic to not (1,2,8,9): R' D' B' F' L' R' D' U' B' F' L' R' U' R
(14) (probability 48/2048)
64. Isomorphic to not (1,2,9,11): B U2 L' R' D B2 L2 D2 B F R2 F2 L' D U F'
(16) (probability 12/2048)
65. Isomorphic to not (1,2,9,12): B' F D' U' L B2 L2 B' F' U2 R2 F2 D' L R
U2 (16) (probability 24/2048)
66. Isomorphic to not (1,3,6,8): D F2 L R B D2 L2 F2 D' U' R2 U2 R' B' F' U'
(16) (probability 12/2048)
67. Isomorphic to not (1,3,6,9): U2 L B' L' R' D' U' B' F' L' R' D' U' F' L'
U2 (16) (probability 24/2048)
68. Isomorphic to not (1,3,6,10): U' R' B' L' R' D' U' B' F' L' R' D' U' F'
R U (16) (probability 24/2048)
69. Isomorphic to not (1,3,6,11): U R' F2 D' L' R' B' F' D' U' L' R' B' F'
U' F2 R U' (18) (probability 24/2048)
70. Isomorphic to not (1,3,6,12): R D2 B' D' U' L' R' B' F' D' U' L' R' F'
D2 R' (16) (probability 24/2048)

Ten Edges to Orient
Four algorithms; probability 66/2048 (0.03222)
71. Isomorphic to not (1,2): D U' B2 L2 B2 L2 D2 R' B2 U2 B' F' D' B2 U' L
R' F' (18) (probability 12/2048)
72. Isomorphic to not (1,3): D' U' R2 D' U2 B2 L2 B2 U' L R F D' U R B F R2
(18) (probability 24/2048)
73. Isomorphic to not (1,6): D2 B2 L2 B2 D' L2 D U L2 B' F' L' D U' B' L' R'
U' (18) (probability 6/2048)
74. Isomorphic to not (1,11): L2 B2 D U' B2 R2 D2 R B F' D' L' R' B L2 U2 R2
F' (18) (probability 24/2048)

Twelve Edges to Orient
One algorithm; probability 1/2048 (0.00048)
75. Isomorphic to superflip: U' R2 U' F2 D' R2 U' B F U2 L' B2 R2 F2 D' U F'
U2 L' R' (20) (probability 1/2048)

Stage 4: Finishing the Middle Layer
Average number of moves 6.5
(Need to reflect some algorithms (these are not noted) and to invert some
(noted))

76. D2 B2 D2 U2 F2 U2 (Probability 1/12)
77. D B2 F2 D' U L2 R2 U' (Probability 1/24)
78. D R2 D' U F2 U' (Probability 1/3 - need to know inverse)
79. F2 U2 F2 U2 F2 U2 (Probability 1/6 - disturbs U layer too)
80. F2 D' U' L2 D U F2 U2 (Probability 1/12 - disturbs U layer too)
81. D2 B2 D' U' R2 D' U' F2 (Probability 1/12 - disturbs U layer too, needs
inverse)
82. B2 D' U' R2 D2 L2 D' U' (Probability 1/6 - disturbs U layer too, needs
inverse)

Stage 5 / 6: Edges to Correct Layer
Eleven algorithms; average number of moves 7 17/35

One Edge to Move
Two algorithms; probability 16/70 (0.22857)
83. Isomorphic to (1 5 2) (the inverse gives (1 2 5)): L R' F2 L' R U2 (6*)
(probability 8/70)
84. Isomorphic to (1 5 3): B2 L2 D F2 L2 B2 U R2 (8) (probability 8/70)

Two Edges to Move
Six algorithms; probability 36/70 (0.51428)
85. Isomorphic to (1 5)(2 6): L2 B2 L2 R2 F2 R2 (6) (probability 2/70)
86. Isomorphic to (1 5)(2 7): L2 B2 R2 D' B2 L2 F2 U' (8) (probability
16/70)
87. Isomorphic to (1 5)(3 7): F2 R2 F2 R2 F2 R2 (6) (probability 4/70;
effectively the same as one of the Stage 4 algorithms, 2 both adjacent
straight)
88. Isomorphic to (1 5)(3 8): R2 B2 L2 D2 B2 R2 F2 U2 (8) (probability
8/70)
89. Isomorphic to (1 6)(3 8): U2 B2 R2 F2 L2 F2 R2 U2 (8) (probability
4/70)
90. Isomorphic to (1 7)(2 8): U' R2 F2 B2 L2 F2 B2 U (8) (probability 2/70)

Three Edges to Move
Three algorithms; probability 16/70 (0.22857)
91. Isomorphic to (1 5 2 3)(3 7): L' B2 L2 F2 L' R' U2 R' (8) (probability
4/70)
92. Isomorphic to (1 5 2 6)(4 8): R2 D B2 L2 R2 F2 U' L2 (8) (probability
4/70)
93. Isomorphic to (1 6 2 7)(3 8): L2 U F2 R2 F2 U L2 B2 (8) (probability
8/70)

Four Edges to Move
One algorithm; probability 1/70 (0.01428)
94. Isomorphic to (1 5)(2 6)(3 7)(4 8): L2 F2 R2 B2 F2 R2 F2 R2 (8)
(probability 1/70)

Stage 7
One algorithm; probability 1/2 (0.5); average number of moves 3
Same as (or at least is isomorphic to) an algorithm from Stage 4 (from a
different angle)

95. L2 R2 U2 L2 R2 D2

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