I have received several private E-mail messages indicating that
the algorithms used by speed cubists solve the cube in 50 or
60 moves. On the one hand, that seems astonishingly good to me,
being fairly close to the solutions from early Thistlethwaite
programs. On the other hand, it is roughly double (depending, I
suppose on whether H-turns are counted or not) what is probably
the true God's Algorithm. Hence, it doesn't tell us much about
God's Algorithm except that the speed cubists are very, very
good.

The best current algorithm has a proven upperbound of 37 turns (q
and h). God's Algorithm is probably much shorter. In fact the
program that implements Kociemba's algorithms has not yet found
a configuration (out of many thousands random configurations
tested) that could not be solved in 20 turns or less. If we look
at distributions for similar puzzles it is expected that more than
one in three configurations requires the maximum number of turns
minus 1 or 2. So I expect God's Algorithm to be at most 22 turns.
Still a long way to go.

dik