Reasons for Getting Stuck in Klondike Solitaire

Most of the time, a setup is not winnable in Klondike Solitaire because it is impossible to turn over all the cards in the tableau. The following is an example

Figure. A Setup that Is Not Winnable

The problem is in the 7th column of the tableau. To remove the cards in this column, the two black fives must be moved. The five-of-spades may be removed using the diamond six in the 3rd column but the five-of-clubs cannot be put on a red six (the six-of-hearts) because it is buried deeper in the 7th column. The only other way to remove the black fives is to establish a spade or club pile in the foundation up to a four. However, one cannot do this for spades because the ace-of-space is underneath the two black fives in the 7th column and one cannot do this for clubs because the two-of-clubs is also “buried” there. Hence, it is impossible to move both black fives off the 7th column of the tableau.
     Define a potentially problematic situation as one in which a card in a tableau has one or more cards below it that might be needed to move it off a column. In the Figure above, the five-of-spades is potentially problematic because the six-of-hearts is beneath it; ditto for the five-of-clubs. If the six-of-hearts were to be replaced by the seven-of-clubs, the two black fives would still be potentially problematic because the seven-of-clubs might be needed to place a red six on it to remove a black five: For example, if the six-of-hearts is replaced by the seven-of-clubs in the 7th column in the Figure and both red six’s are in the deck then the situation is still not winnable because the seven-of-spades can be used to place one red six on it to remove the five-of-spades but the other red six cannot be placed on the seven-of-clubs to remove the five-of-clubs because the seven-of-clubs is buried in the “stuck” 7th column of the tableau.
      Generally, having a #red below a (#-1)black (or a #black below a (#-1)red) is worse than having a #red below a (#-2)red (or a #black below a (#-2)black) and the latter is worse than having a #red below a (#-3)black (or a #black below a (#-3)red), et cetera. However, all of these are potentially problematic situations.
      The first few cards of the deck can also be potentially problematic. For example, suppose the first three cards where ten-of-diamonds, ten-of-hearts and nine-of-clubs. Then, the nine-of-clubs cannot be moved to the tableau because the red tens are “buried”. It is still possible (but not too likely) to be able to build a club foundation up to the eight-of-clubs to remove the nine-of-clubs.
      Potentially problematic situations are more likely to occur in the 7th column of the tableau than the 6th column, and more likely in the 6th column than the 5th, et cetera because the number of cards in the former is greater. This is why the deck is less likely to have a potentially problematic: if it happens then usually it involves just the first three cards.

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