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Klondike is the well-known 52-card Solitaire game available on almost every computer. The problem of determining whether an n-card Klondike initial configuration can lead to a win is shown NP-complete. The problem remains NP-complete when only three suits are allowed instead of the usual four. When only two suits of opposite color are available, the problem is shown NL-hard. When the only two suits have the same color, two restrictions are shown in AC^0 and in NL respectively. When a single suit is allowed, the problem drops in complexity down to AC^0[3], that is, the problem is solvable by a family of constant-depth unbounded-fan-in {and, or, mod"3 }-circuits. Other cases are studied: for example, ''no King'' variant with an arbitrary number of suits of the same color and with an empty ''pile'' is NL-complete.