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Impossible FreeCell deal?

The solitaire card game FreeCell distinguishes itself by having all the cards dealt face-up and having nearly all deals result in solvable games.  If you don't know how to play, you should learn.

Each deal (of which there are 52! or about 10^68) gives you a new game, though some deals are essentially equivalent by swapping suits or the swapping columns.  In all, there are around 10^64 possible games.  That's enough: if all of us humans chipped in and each somehow solved a million games per day, we'd cover them all in a hundred billion trillion trillion trillion years (or something).

About 99.999% of games are solvable according Wikipedia, but I wondered if it would be very hard to construct an impossible one.  If, for example, all the red cards are buried under black cards like this:
But after a few moves, it was looking more like a normal game:

So what if the cards are sorted so that you have all the high value cards of one color on top?  Wouldn't you fill up your fo…

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