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Strategy

Solitaire Strategy — Tips to Win More Klondike Games

No method wins every deal of Klondike, but the choices you make decide a large share of the ones that can be won. These tips follow from the rules, and several of them are the same ideas that researchers built into programs that play the game.

Does strategy matter in solitaire?

Klondike has a lot of luck in it: 21 cards start face down, and the stock is shuffled. Still, studies of the game show how much the decisions matter. Ronald Bjarnason, Alan Fern and Prasad Tadepalli tested programs on draw-three Klondike with no limit on passes and with the face-down cards hidden, as a person plays it. Over a million random deals, a program that picked its moves at random won 7.1% of them, and a simple program that followed a fixed order of preferences won 13.0%. Their best planning programs, which looked ahead by trying out possible futures, won over 35%.

The same holds when every card is known. In the study by Xiang Yan, Persi Diaconis and their co-authors, an expert player won 36.6% of 2,000 “thoughtful” games, and their best program won about 70% of the 200 games it played. Same rules, very different results: the way the cards are played counts.

The opening: before you touch the stock

  1. Scan all seven piles first. Look for every ace and 2 on show, and for every card that can go onto another pile. The stock can wait until the table has nothing more to give.
  2. Play aces and 2s up at once. This is always safe. No card can ever be placed on an ace in the tableau, and the only card that could go on a 2 is an ace, which belongs on a foundation anyway.
  3. Prefer the move that reveals a card. A move that turns over a face-down card gives you new information and a new card to play. A move that only shuffles face-up cards from one pile to another gives you neither.
  4. Dig where the most cards are hidden. When two moves both reveal a card, take the one on the pile with more face-down cards under it. Yan’s team gave their program exactly this preference, and report that it improved its success rate significantly. The long piles on the right are where most of the deck starts.

The tableau: building with a plan

Choose between twins

Often two cards could take the same place: both red 9s fit on a black 10. Pick the one whose move does more, usually the one that uncovers a face-down card or empties the waste of a card you need. The other twin may find a home later on the other black 10.

Treat an empty pile as a king’s seat

An empty pile is only useful for a king, or for a run that starts with one. Clearing a pile pays off when a king is waiting to move in, especially one with face-down cards under it. With no king available, the space sits idle, and the cards you moved to clear it might have been better left where they were.

Pick the king that a queen is waiting for

When you have a choice of kings for an empty pile, look at the queens. If a red queen is face up somewhere with nothing to land on, a black king gives it a place; a red king does not. Yan’s team taught their program the same idea, with this very example: offered the king of hearts and the king of spades while the queen of diamonds lies face up, it should choose the king of spades.

Move a run only for a reason

Moving a run from one pile to another when nothing is revealed is the move the programs below rank last. It is worth making when it frees a card you need or opens a place for one. Otherwise it changes nothing that matters.

The foundations: fast, but not too fast

Moving cards to the foundations is the goal, but a card sent up too early can leave another card with nowhere to go. A useful rule of thumb tells you when a card is safe to send up: when both cards of the other color, one rank lower, are already on their foundations. A red 5 is safe once both black 4s are up, because no card will ever need the red 5 as a place to land, unless you bring a black 4 back down.

If your rules allow cards to come back from the foundations, an early card is not lost: you can bring it down again to give a lower card a place. Blake and Gent found that this rarely decides a game: in draw three with every card known, only about one winnable deal in two hundred needs it. But in the deals that do need it, nothing else works.

The stock and the waste

  • Play out the tableau before you draw. When passes are limited, every turn of the stock uses up part of one, and a card that turns up before you can use it may be gone.
  • Remember what passed. On your first pass through the stock, note where the cards you need are. On the next pass you will know whether to stop for them.
  • With unlimited passes, there is no hurry. A card you skip will come round again, so you can wait until it fits.
  • With limited passes, take what you can. If you may go through the stock only once or three times, a card you could use now is worth more than a perfect position later.
  • In draw three, every card from the waste reshuffles the next pass. Taking one card changes which cards come up on top afterward. The details are in Turn 1 vs Turn 3.

What the programs prefer

The simple program of Bjarnason, Fern and Tadepalli chose its moves by a fixed order of preference. It is a reasonable checklist for a person, too:

  1. a move from the tableau to a foundation that reveals a card;
  2. any other move to a foundation;
  3. a move between tableau piles that reveals a card;
  4. a move from the stock or waste to the tableau;
  5. a move from a foundation back to the tableau;
  6. a move between tableau piles that reveals nothing.

On its own this order won only about 13% of deals. What lifted the programs to over 35% was looking ahead: trying a line of play, seeing where it leads, and choosing the best. For a person, that means asking before each move what it opens up two or three moves later, and not just what it does now.

Know when a deal is lost

Some deals cannot be won however well you play. Even with every card known, about 18% of draw-three deals have no solution, by Blake and Gent’s count, and the rest of the research is in Is every solitaire game winnable? A loss is not always a mistake, and a good win rate is one measured over many games.

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