Count the number of winnable Freecell games?

[benorin]

So you've played Freecell, right? I would like to prove or disprove that every possible Freecell game is winnable. If there exists a game that is not capable of being won (within the normal rules) I would then like to count the number of games which are possible to win. Ideas?

Here's a screenshot of the game to refresh your memory:

 

[NateTG]

So you've played Freecell, right? I would like to prove or disprove that every possible Freecell game is winnable. If there exists a game that is not capable of being won (within the normal rules) I would then like to count the number of games which are possible to win. Ideas?
Here's a screenshot of the game to refresh your memory:

Well, there's the option of playing games -1 and -2 on MS freecell, for one of those questions.

 

[Joffe]

I think I remember reading somewhere that it is presumed all are possible but has never been proven, after all the game is NP-complete.