How a shuffled solitaire deal can have no winning path
In a game such as Klondike, the cards are not all available at once. Some begin face down beneath other cards; a player can use them only after uncovering them. Meanwhile, moves are restricted by the rules: tableau cards must follow a particular order, and foundation piles must be built in suit from ace upward. A card can therefore be present in the deal but unreachable when it is needed.
That creates a chain of dependencies. To uncover a buried card, you may need to move the card on top of it—but that move might require an empty column or a different sequence of cards. If no legal sequence opens the blocked cards and completes the foundations, the deal is unwinnable, even if every move is played correctly.
The rules change what “winnable” means
A deal’s prospects depend on the exact version being played. In Klondike, for example, drawing one card from the stock gives different opportunities than drawing three; rules about recycling the stock or moving groups of cards can also change which paths are available. A layout that cannot be won under one set of rules may be winnable under another.
A player getting stuck does not, by itself, prove the deal was impossible: an earlier choice may have closed off the route. To establish that a deal truly has no solution, its legal move sequences must be exhausted—or checked by software that searches them. That distinction is why a losing game can be either a tough puzzle or a dead end built into the deal.**
