## An Illustrative Klondike Solitaire Game

Jupiter Scientific’s “expert” solitaire player provided some screen shots of a game illustrating the principles in a strategy for winning Klondike Solitaire. The ace-of-hearts was face up in the tableau at the start and was placed in the foundation. Our player went through the deck to discover all the cards in it. The remaining three aces turned out to be in the deck, but they were not played to the tableau until necessary. Indeed, the 6th card in the deck was the ace-of-diamonds

but our solitaire player did not put it in the foundation.
Near the beginning, the following situation was reached:

Cards from the deck should only generally be used to support the uncovering of face-down cards in the tableau. Here, the five-of-hearts can be placed on the six-of-spades and then the four-of-clubs can be put on the five-of-hearts. This creates a space to move the king-of-hearts in the tableau thereby revealing the card beneath it. It is better to move the king-of-hearts than the king-of-diamonds because more face-down cards are under the former. The six-of-spaces was not previously put on the seven-of-hearts just in case the six-of-clubs turned up under the king-of-hearts. When this did not happen, our solitaire player did move the six-of-spades-to-three-of-hearts streak onto the seven-of-hearts.
It turned out that the card beneath the king-of-hearts was the two-of-diamonds. Our player then considered playing the ace-of-diamonds from the deck to the foundation to remove the two-of-diamonds from the tableau.

However, he did not immediately play it at this point. He went through the remaining part of the deck looking for cards that could help flip over tableau cards. When those were exhausted, he returned to the 6th card of the deck, that is, the ace-of-diamonds, put it on the foundation and flipped over the two-of-diamonds. The following situation was reached soon after that point

and a decision had to be made as to whether to place the eight-of-spades on the nine-of-diamonds or on the nine-of-hearts. Because alternation of suits occurs better for the latter, the eight-of-spades was placed on it. [It is useful to return to this position after reading this entire webpage because if the eight-of-spades had been put on the nine-of-diamonds, our solitaire player would have failed to win.] The seven-of-hearts was then moved on top of the eight-of-spades to flip over a tableau card.
Our player noted a potentially problematic situation might be occurring in the 7th column:

The jack-of-diamonds might be beneath the nine-of-diamonds and the ten-of-clubs is in the deck. Hence, the ten-of-clubs might not be playable to the tableau to remove the nine-of-diamonds. This turned out to be the case (discovered after playing the game). Had our player known this, he would have moved the nine-of-diamonds to the ten-of-spades instead of the nine-of-hearts (which was in the 6th column of the tableau). Then, as the cards in the 7th column were flipped over, the jack-of-diamonds would have been exposed and it would have been possible to place the ten-of-clubs in the deck on this diamond jack to allow the nine-of-hearts to be moved. The reason our solitaire player did not do this is that the nine-of-hearts “revealed” itself before it was known that the nine-of-diamonds was in the 7th column. Even if both red nines had been “exposed” at the same time, our solitaire player would not have known in which column lay the jack-of-diamonds. The best play is to remove the red nine with the most cards under it because that column has the higher chance of having a potentially problematic situation.
When the following position was reached

the Jupiter Scientific staff member followed the guiding principle in trying to flip over face-down cards in the tableau. He moved (the three-of-hearts)/(two-of-spades) streak to the four-of-spades, placed the three-of-clubs and four-of-clubs on the two-of-clubs in the foundation so as to be able to move the (four-of-spades)/(three-of-hearts)/(two-of-spades) streak to the five-of-hearts thereby flipping over the card beneath it. At this point, our player was hoping that the jack-of-diamonds was in columns 4 or 6 beneath the four-of-spades or the five-of-clubs. A little later, he discovered this was not the case:

The only way to solve the game is to remove the nine-of-diamonds by building a diamond column in the foundation up to the eight-of-diamonds. Since the three-of-spades is not in the deck, further building of the spade column in the foundation is not possible. If the five-of-spaces could be removed from column 2, then diamond and club foundation builds could be performed all the way to the diamond 9. Note the importance of suit alternation here: If the streaks in the deck in columns 2 and 7 were mixed with spades, it would not be possible to solve this game at this point.
An example of idea 4 arose:

The four-of-diamonds in the tableau has no use in moving a card from the deck or in moving streaks or cards in the tableau because the three-of-clubs is in the tableau, and should the three-of-spades become available, it can be placed on the two-of-spades. Hence, no harm can come from putting the four-of-diamonds onto the foundation.
The following three screen shots show the first nine cards in the deck a little later:

The ten-of-diamonds from the deck was placed onto the jack-of-clubs in the tableau. When the Jupiter Scientific staff member subsequently went through the deck, the seven-of-spades occurred (as the 6th card). It was placed on the eight-of-hearts and the six-of-hearts was also moved from the deck to the tableau. One then arrived at the following:

The five-of-spades was moved onto the six-of-hearts. The cards in the suits of diamonds and clubs from five to eight were then placed on the foundation files to arrive at

After the nine-of-diamonds was moved to the foundation, the ten-of-hearts appeared. The ten-of-diamonds was placed on the foundation so that the ten-of-hearts could be moved to the jack-of-clubs in the 3rd column. The jack-of-diamonds appeared in the 7th column and was placed on the queen-of-clubs and the last card in the 7th column, which had to be the three-of-spades, appeared.

With all the tableau cards turned over and no problem in “playing out” the rest of the cards in the deck, our solitaire player succeeded in winning the game.
This game was atypical in that suit alternation played such an important role. Normally, it does not. The important principle is to use the cards in the deck (almost) exclusively for turning over cards in the tableau.

The game discussed in this webpage corresponds to the following:

Deck from top to bottom:
10c, Qc, 6d, Qs, Kc, Ad, 2h, Js, 6h, 3c, 10d, 10s, 7s, 9s, Ac, 2c, As, Qh, 4h, 3d, 5h, 7c, 8h, 8s

Tableau:
 4c 8d 6c 9c 8c 5d 3s
 7h Jh 4s 2s 5c Jd
 6s Ks 4d 7d 10h
 Kd 5s Qd 9d
 Ah 9h Jc
 3h 2d
 Kh

This report was prepared by the staff of Jupiter Scientific, an organization devoted to the promotion of science through books, the internet and other means of communication.

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