TITLE: average number of moves needed to complete a game of FreeCell
QUESTION [8 upvotes]: Sometimes finishing a game of FreeCell takes me 10 minutes, other times just one minute.
I know that all but one of the FreeCell deals in windows can be won, but I'm not sure if they are random or not [yet that is irreverent].
Assume: ALL GAMES POSSIBLE. Random deal. NO Automation.
IE.  The minimum number of clicks is 52, not 0.
What is the average minimum number of moves necessary to complete a game of Freecell?

REPLY [2 votes]: It is interesting to see this discussion here which I discovered after the solutions' length has been discussed in recent (as of 6-December-2012) threads in the fc-solve-discuss mailing list (which I administrate), as well as some configurations that improved the solution length performance of Freecell Solver, a solver for Freecell and other solitaire deals (which I maintain).
Like other people note here, Generalised Freecell (where the number of ranks increase beyond the 13th rank (King)) is NP-complete, but regular Ace-to-King-based Freecell is not (although 13 is still a significant value for NP-complexity to handle) .
One issue that we found hard to resolve is how to measure the number of moves, because there are some variations for the "automatic-moves-of-cards-to-foundations" prune (also see Danny A. Jones' message about it with some pseudocode). This prompted me to phrase a specification of sorts for commonly agreed upon representation of a solution. 
Well, back to the issue at hand, here are some results from the solvers:

Danny A. Jones solvers (one of them fast and somewhat sub-optimal, and one of them slow being run on the first 1,500 deals).
Results from my sub-optimal (but open-source) solver
Close to optimal solutions for the first 1,000,000 deals on freecellgamesolutions.com - but with a very user-unfriendly interface that requires enabling JavaScript, filling in Captchas and other sorts of nastiness.

If you want a mathematical analysis of the average solution length upon all the set of possible deals, then I'm not aware of any, and I'm not sure I have the mathematical skills to do that.
Best regards,
— Shlomi Fish