Klondike solitaire turn one is a game that precedes its computer version, and that means that all the cards are truly shuffled, without the computer peeking in to verify the game is solvable.
And like McKay mentioned, with a random shuffle you can definitely end up with an unsolvable game.
I'm sure it is possible to design a Solitaire variant in which each game is solvable, though.
Literally just played a game in which one of the stacks (the one containing 4 cards) was lead by the 9 of diamonds, and the cards inside of it were the King of Spades, the 5 of diamonds, the 10 of spades, and the 10 of clubs (I know this because I had the entire field solved except for this stack and used process of elimination). As far as I can see this makes the game impossible. I have a 9 of diamonds in which can never be moved, as the two 10s that it's eligible to rest upon are trapped underneath it in the stack face down. Attempting to get rid of the 9 by moving it to the diamond stack would also be fruitless, as the 5 of diamonds is stuck underneath it too. Unless someone can tell me some way that this could be solved, I'm pretty darned certain that if a card that is leading a stack is covering a stack that contains the two cards it is capable of resting on, and a lower number of it's own suit, then the game is made impossible right from the get-go.
However, if you started a list and enumerated the initial conditions -- I feel like I've seen this on a linux version of Solitare: the numbering of deck order, that is -- and you definitively decide a certain one is un-winnable, you then could compare notes across nodes (share with friends) and VOILA: a list of un-winnable starting deck stacks.
I've been starting to think the Windows 7 version has the un-winnable decks removed, ... I don't know, it's a little heavy-handed and smug about the statistics.
