<r2,U>

[deepSubDiver]

A few optimal blocks. Note: Random-move scrambles, not random state!

U' r2 U2 r2 U2 r2 U r2 U' r2 U' r2 U2 r2 U2 r2 U' r2 U2 r2 U r2 U r2 U' 
[False, [1, 3, 0, 5, 2, 6, 4], [4, 2, 3, 1, 5, 0]]
solving block
SOLUTION: r2 U2 r2 U2 r2 U' r2 U2 r2 U2 r2 U' r2 U r2 

U' r2 U r2 U2 r2 U' r2 U2 r2 U2 r2 U r2 U r2 U2 r2 U r2 U2 r2 U2 r2 U' 
[False, [1, 5, 6, 2, 0, 4, 3], [1, 4, 5, 0, 2, 3]]
solving block
SOLUTION: r2 U r2 U2 r2 U' r2 U r2 U r2 U' r2 U2 r2 
SOLUTION: r2 U r2 U' r2 U' r2 U r2 U2 r2 U' r2 U2 r2 
SOLUTION: r2 U2 r2 U r2 U2 r2 U2 r2 U r2 U2 r2 U2 r2 
SOLUTION: r2 U2 r2 U' r2 U2 r2 U2 r2 U' r2 U2 r2 U2 r2 
SOLUTION: r2 U' r2 U2 r2 U' r2 U2 r2 U r2 U' r2 U' r2 

U r2 U' r2 U2 r2 U2 r2 U' r2 U' r2 U r2 U2 r2 U2 r2 U r2 U' r2 U r2 U' 
[False, [6, 5, 0, 2, 1, 4, 3], [5, 2, 0, 1, 3, 4]]
solving block
SOLUTION: r2 U' r2 U r2 U2 r2 U r2 U r2

U' r2 U r2 U2 r2 U' r2 U2 r2 U' r2 U2 r2 U r2 U2 r2 U r2 U2 r2 U2 r2 U2 
[False, [1, 0, 3, 2, 5, 6, 4], [3, 0, 2, 4, 5, 1]]
solving block
SOLUTION: U' r2 U r2  (wat?)

U r2 U r2 U2 r2 U' r2 U r2 U r2 U r2 U r2 U2 r2 U' r2 U2 r2 U r2 U 
[False, [6, 3, 0, 2, 5, 1, 4], [1, 2, 0, 4, 5, 3]]
solving block
SOLUTION: U' r2 U' r2 U2 r2 U r2 U2 r2 U2 r2 

U r2 U r2 U2 r2 U2 r2 U r2 U' r2 U' r2 U' r2 U' r2 U r2 U' r2 U' r2 U' 
[False, [3, 5, 2, 4, 0, 1, 6], [1, 5, 4, 2, 0, 3]]
solving block
SOLUTION: U' r2 U2 r2 U2 r2 U' r2 U' r2 U' r2 U r2 U' r2 

U r2 U2 r2 U2 r2 U r2 U2 r2 U2 r2 U' r2 U r2 U' r2 U2 r2 U' r2 U r2 U 
[False, [2, 0, 1, 6, 3, 5, 4], [5, 1, 2, 4, 3, 0]]
solving block
SOLUTION: U r2 U' r2 U2 r2 U2 r2 U' r2 U' r2 

U' r2 U r2 U r2 U2 r2 U' r2 U r2 U2 r2 U' r2 U r2 U2 r2 U2 r2 U' r2 U 
[False, [1, 6, 0, 2, 3, 5, 4], [1, 0, 5, 4, 3, 2]]
solving block
SOLUTION: r2 U' r2 U' r2 U r2 U r2 U r2 U' r2 U' r2

So, nice blocks don't mean short blocks.

Average of 1,000 for the block was around 13 moves.
Average of 100 for optimal solutions was around 22 moves.
During that average I encounterd 6 positions which were not solvable in 25 moves - thus, 25 move scrambles don't do it for us.

When I implemented a more efficient algorithm (not even using transition or pruning tables... Ugh!) I will do a more detailed analysis.

 

[keemy]

finally had time to actually try this so I did 25 timed solve (improved by 2nd half XP)
best avg5: 14.12 (σ = 0.65)
best avg12: 16.80 (σ = 3.53)
session avg: 21.55 (σ = 5.64)

not sure about method I have been doing something very limited but reco was easy.(note i am doing <l2,U> because i'm cool like that >_>)
1. join (DF and DLF) or (DL and DLF)
2. join (D center) and edge (DF or DL) not used in step one to the block formed by step one
3. pick up last corner (DBL) onto the 2x2x1 formed and place entire block on D.
4. put in the DB edge (algs are really fast for this, but I am bad at executing the mirror for DF so that's why I always do it this way)
5. LL (I need to work on this my reco and execution are pretty slow)

I may have some time again tomorrow so watch out qq.

 

[deepSubDiver]

Depth distribution table for optimal solutions:
9: <0,1%
10: <0,1%
11: <0,1%
13: <0,1%
14: 0,1%
15: 1%
16: 2%
17: 4%
18: 5%
19: 11%
20: 11%
21: 18%
22: 23%
23: 13%
24: 9%
25: 2%
26: 0.4%
27: 0.2%
28: <0.1%

 

[Stefan]

A few optimal blocks.

Nice, looks like I'm not that bad at it after all. Would've done it optimally several times, near-optimally the other times. I should learn looking for the dangling corner earlier, and know solutions for some ugly special cases where I need to look and think way too much.

thus, 25 move scrambles don't do it for us.

Damn... guess I'll use 30 if I try this again and there's no random-state scrambler by then (which should be easy to do, there's just a few hundred thousand states, right?).

 

[Johannes91]

deepSubDiver: Cool, our programs seem to agree.

Damn... guess I'll use 30 if I try this again and there's no random-state scrambler by then (which should be easy to do, there's just a few hundred thousand states, right?).

Ask and ye shall receive: http://laire.fi/t/r2U.pl.

I can easily generate any statistics if there's interest.

 

[Stefan]

Before I forget it: A while ago I improved further (just couldn't steal Michael's single record, grrr):

best time: 3.64
best avg5: 9.43 (σ = 0.34)
best avg12: 10.78 (σ = 2.10)
best avg100: 12.27 (σ = 3.10)
Still used 30 random moves scrambling...

Details:

Spoiler

best avg5: 9.43 (σ = 0.34)
1. 9.12 R U2 R2 U' R U R U' R' U' R' U2 R U' R' U R' U' R2 U2 R2 U2 R' U R'
2. (6.38) U' R U' R2 U' R' U' R2 U R' U2 R U R2 U R2 U2 R' U2 R' U2 R U2 R2 U'
3. 9.26 R' U2 R' U R U2 R U R2 U R2 U' R2 U' R U R2 U' R2 U' R' U R2 U2 R'
4. 9.90 R U R' U R2 U2 R2 U R U' R U R' U' R' U R U2 R2 U' R2 U' R2 U R2
5. (10.04) R U R' U R U R' U R' U2 R2 U' R' U' R U' R2 U' R' U R2 U2 R U2 R'
Followed by 9.87 and 8.34, but bad times before and after, so no good Ao12.

best avg12: 10.78 (σ = 2.10)
1. 9.30 R U R2 U' R U R2 U' R' U' R' U' R U' R U2 R' U2 R2 U2 R2 U' R2 U' R U' R U' R U2
2. 12.86 U2 R U' R' U' R' U2 R' U2 R' U R' U R' U R2 U' R2 U R2 U2 R' U R2 U R' U2 R U2 R'
3. 12.91 U2 R2 U2 R2 U' R' U2 R2 U' R' U' R2 U R2 U R' U' R' U' R' U R' U R2 U R U R' U' R2
4. 11.19 R' U R2 U2 R' U R' U' R' U2 R' U' R U2 R' U' R' U R U R' U' R' U' R U2 R2 U R2 U'
5. (7.29) U R' U2 R U2 R2 U' R2 U' R' U R2 U' R2 U' R U' R' U R U' R2 U' R' U' R U' R U R'
6. 10.81 U' R' U2 R' U' R' U R' U R U' R2 U2 R U2 R' U' R' U' R' U R U2 R' U R U R2 U' R'
7. 14.43 U' R' U R' U2 R U' R U R2 U R U R' U2 R U R U' R2 U' R U2 R' U' R' U' R U R
8. 10.34 U' R2 U2 R U' R2 U' R2 U' R U' R' U2 R U2 R' U R U' R2 U2 R U2 R2 U R' U' R U' R2
9. 7.46 R2 U2 R' U R' U2 R2 U' R U R' U R2 U2 R2 U2 R U2 R U R' U2 R U R' U' R' U2 R2 U2
10. 10.60 R' U' R' U' R' U R' U R U R2 U' R2 U R U' R2 U' R2 U R' U2 R U' R U' R' U2 R2 U2
11. (14.71) U R' U R2 U' R2 U' R' U2 R2 U' R2 U' R2 U2 R' U' R U' R2 U2 R' U' R2 U2 R' U R2 U R2
12. 7.89 U' R U2 R2 U' R2 U R U' R2 U2 R2 U2 R' U R U2 R U R2 U2 R U2 R2 U' R' U' R U2 R

best avg100: 12.27 (σ = 3.10)
10.12, 14.49, 6.31, 13.69, 17.65, 7.91, 14.25, 22.18, 14.93, 13.78, 15.91, 11.15, 11.11, 8.44, 16.96, 14.83, 12.18, 10.39, 10.18, 11.70, 9.42, 12.97, 12.54, 13.44, 20.27, 11.62, 9.34, 12.76, 13.11, 10.22, 11.84, 17.89, 13.37, 7.19, 4.48, 15.97, 14.78, 10.25, 9.40, 10.02, 9.22, 11.78, 16.27, 12.00, 7.97, 9.56, 13.30, 13.91, 12.53, 14.60, 9.20, 13.32, 12.74, 11.30, 8.42, 12.61, 9.77, 20.05, 10.83, 16.84, 6.39, 11.61, 10.75, 8.53, 15.73, 11.37, 9.58, 9.19, 10.43, 17.29, 11.25, 17.74, 10.77, 14.18, 7.31, 10.25, 16.07, 8.79, 13.86, 12.72, 11.26, 8.46, 11.95, 23.16, 10.24, 11.39, 14.99, 9.71, 15.54, 11.74, 15.80, 15.09, 13.80, 14.19, 12.26, 9.11, 11.07, 12.71, 10.00, 8.83

 

[Deleted member 36445]

My method on this:

Solve DF and DB.
Make the right block.
Solve EPLL with normal algs.