Odds of Winning
For a "standard" game of Klondike of the forms Draw 3, Re-Deal Infinite, and Win 52, the number of possible hands is over 7,000 trillion. Between 82-91.5% are winnable, but people do not win 80% of the games they start, because they make a wrong move somewhere and lose the game prematurely. The number of "unwinnable" games is therefore between 8.5-18%, but there are also "unplayable" games in which no cards can be moved to the foundations even at the start of the game, which occur in only 0.25% of hands dealt.
So there are won games, winnable lost games, unwinnable games, and unplayable games.
A modified version of the game called "Thoughtful Solitaire", in which the identity of all 52 cards is known, has a known solution strategy that works 82% of the time but requires significant computing power. Because the only difference between the two games (Klondike and Thoughtful) is the knowledge of card location, all Thoughtful games with solutions will also have solutions in Klondike. Similarly, all dead-ends in Thoughtful will be dead ends in Klondike. However, the theoretical odds of winning a standard game of non-Thoughtful Klondike are currently unknown. It has been said that the inability for theoreticians to calculate these odds is "one of the embarrassments of applied probability".
Read more about this topic: Klondike (solitaire)
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