13 Random Cards

level 0, bfs queue size 0
D H D S C D H S D D C S C
J 5 5 Q J 8 2 J K A Q 8 3
level 1, bfs queue size 1
D H D SS D D CC D H S C
J 5 5 QJ K A QJ 8 2 8 3
level 2, bfs queue size 23
SS DD H D D CC D H S C
QJ KJ 5 5 A QJ 8 2 8 3
level 3, bfs queue size 181
DD H D D CC D H SSS C
KJ 5 5 A QJ 8 2 QJ8 3
level 4, bfs queue size 336
DDD H D CC D H SSS C
AKJ 5 5 QJ 8 2 QJ8 3
level 5, bfs queue size 687
DDD D CC D HH SSS C
AKJ 5 QJ 8 52 QJ8 3
level 6, bfs queue size 632
DDDDD CC HH SSS C
AKJ85 QJ 52 QJ8 3

original hand
D H D S C D H S D D C S C
J 5 5 Q J 8 2 J K A Q 8 3
move groups 5 to 7 after group 11
D H D SS D D CC D H S C
J 5 5 QJ K A QJ 8 2 8 3
move groups 1 to 4 after group 5
DD H D SS D CC D H S C
KJ 5 5 QJ A QJ 8 2 8 3
move groups 1 to 4 after group 5
DDD H D SS CC D H S C
AKJ 5 5 QJ QJ 8 2 8 3
move groups 3 to 4 after group 6
DDD H CC DD SS H S C
AKJ 5 QJ 85 QJ 2 8 3
move groups 3 to 5 after group 6
DDD HH CC DD SSS C
AKJ 52 QJ 85 QJ8 3
move groups 2 to 3 after group 5
DDDDD SSS HH CCC
AKJ85 QJ8 52 QJ3
sorted in 6 moves
level 6, bfs queue size 595