2^20 random scrambles solved optimally:

Depth	Frequency
10  	1
11  	0
12  	5
13  	13
14  	66
15  	273
16  	995
17  	3940
18  	14949
19  	54581
20  	173415
21  	385091
22  	358877
23  	56148
24  	222


3^7 pure corner twists: Depth Frequency 0 1 16 198 17 330 18 98 19 424 20 174 21 320 22 274 23 242 24 110 25 0 26 16 Depth 26 positions: U R U' R2' U R U2' R2' U2' R' U' R U' R2 U R' U2' R' U2' R' U R2' U R2 U2 R' U R U2 R U' R' U2 R2 U2 R' U2 R2' U R2 U' R' U R2' U R' U' R2 U R2 U' R2 U R2 U2' R2 U' R2 U' R' U' R2' U R2' U2' R U' R2 U2' R2' U R2' U' R2' U R U2' R2 U R2 U R U2 R' U2 R U2 R' U' R U2' R U' R2 U' R2 U2' R U2 R' U2 R2 U' R' U R U2 R2' U' R' U R' U' R' U' R2 U2' R' U2 R2 U2 R2 U R2' U' R' U2 R2 U' R2' U R U2' R2 U R2 U2' R2 U' R2 U' R' U' R2' U R2' U2' R U' R2 U2' R2' U R2' U' R2' U R U' R2 U2 R U2' R U' R2' U' R2' U' R U2 R' U R' U' R2' U2' R2' U R U2' R' U R U R U2' R2 U R2' U2' R2' U2' R' U2 R U R2' U2' R U2 R' U' R2' U2 R U R' U R U2 R' U2 R U2 R' U' R U2' R U' R2 U' R2 U2' R U2 R' U2 R2 U' R' U R2 U R U2 R U2' R U R' U R2 U' R2' U R2' U2 R U' R2 U2 R' U R2 U' R2 U R' U R U R2 U' R2 U2 R' U R2' U2 R2 U' R2 U R2 U' R' U2 R2' U' R2' U2 R2' U R2' U R U2' R2' U R2' U' R2 U2' R U2' R U' R2 U' R U R2' U' R2' U R2' U' R' U2' R' U R U2 R' U2 R2 U' R U2' R2 U2 R' U2 R U2 R' U' R2 U2' R' U2' R2 U2' R U2' R U R U R2' U R2' U2 R2' U' R2' U2 R' U' R2 U R2 U' R2 U2 R2' U R' U2 R2 U' R2 U R U R2' U2 R U2' R2' U2' R2' U' R2 U R U2' R2' U R2 U' R' U2' R2 U R U' R U R U R U' R U R2 U2' R' U' R2 U R2' U2' R U R2 U' R2' U2' R2' U2' R U2 R2'