I play a lot of Solitaire games on my Android phone and love to keep an eye out for the statistics.
Given that the Solitaire version let's you restart the game endlessly, I usually play until I solve it. But I never managed to solve more than 80% of the games played (1000+).
So now I wonder, is every Solitaire game solvable?
No. Example: If all of your cards face up on the board are red, and the cards that come up every third card are also red, and none of them are aces. You lose. Do not pass go, do not collect $200.
There is very interesting reading at wikipedia [1] about this topic.
[1] http://en.wikipedia.org/wiki/Klondike_solitaire#Odds_of_winningFor a "standard" game of Klondike (of the form: Draw 3, Re-Deal Infinite, Win 52) the number of solvable games (assuming all cards are known) is between 82-91.5%.
Solitaire 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.