Sunday, September 30, 2012

Dave Computes Solitaire Strategy

Having invested countless hours in playing Klondike Solitaire, I have decided to share my current wisdom on Solitaire strategy.  Note that I'm talking here about the version where 3 cards are dealt from the stock at once, which necessarily complicates the strategy.  I should also say that my goal in solitaire is to attain the highest winning percentage.  Many people will prefer winning the most games per unit time, or scoring the most points per win.  Any of these goals will lead to different strategies.  Anyway, here are the rules that guide my play.


Rule #1:  Prefer to expose face-down cards.

At the beginning of the game, there are 24 cards in the stock, 7 face-up cards on the table, and 21 face-down cards underneath them.  To win the game, I must eventually gain access to all cards.  Clearly, I already have access to the 7 face-up cards.  Of the 24 stock cards, one cycle through the deck immediately grants me access to 8 of them, and the remaining 16 are just a play or two away.  On the other hand, most of the 21 face-down cards are buried under 2 or more cards, and the deepest is buried under 6 cards.  So, not only should I make plays that reveal face-down cards, but I should strive to reveal cards from the piles with the most face-down cards.  At the start of the game, revealing just one face-down card from the rightmost pile gets me one play closer to revealing each of the 5 cards below it.

Therefore, I will generally make all the plays I can with the table cards (first moving the cards from piles with the most face-down cards) before dealing further from the stock.


Rule #2:  Never empty a pile unless there is a king immediately available.

This rule is fairly straightforward.  There is absolutely no advantage to emptying out a pile unless you have a king handy.  Any move that would have left a pile empty has the potential to block a future play that may arise before a king comes up.


Rule #3:  Usually play the last playable card in the stock.

Let's number the cards in the stock from 1 to 24.  As I cycle through the stock, I first see card #3, then #6, #9, #12, #15, #18, #21, and #24.  Suppose I can play card #6 and #12.  Which should I play first?  Most people would play card #6 before they even discover card #12.  I'm convinced that's not a winning strategy.  Here's why.  If I play #6 and then #12, then on the next deal I'll have access to 6 new cards (#7, #10, #14, #17, #20, and #23).  If I instead play only #12, the next deal will give me access to #13, #16, #19, and #22, and if I now play #6 (which is still available to me), the deal after that will expose #7, #10, #14, #17, #20, and #23--a total of 10 new cards!

Therefore, I will always cycle through the entire stock once before choosing which card to play--usually the last playable card.  Yes, it takes longer to play this way.  No, it doesn't bother me.

Exception To Rule #3:
The exception to this rule is when playing a later card in the stock will prevent me from being able to play an earlier card.  For example, if both the 4-of-diamonds and the 4-of-hearts are accessible to me, but I can only play one red 4, then I should play the earlier four so as to expose more new cards on the next deal.  Here's another example where this comes up.  I have a 4-of-hearts exposed, and a 3-of-spades sitting on the table.  I can move the 3 onto the 4, in order to play a king from the stock, or I can put a 3-of-clubs from the stock onto the 4.  I can't make both plays, so I should play whichever appears earlier in the stock.  This kind of situation arises quite frequently, and if misplayed, can easily turn a winning game into a losing one.  Also, bear in mind that the two playable (but mutually exclusive) cards may be separated and/or followed by other playable cards which should be played first.  And sometimes playing a stock card may reveal a new playable card that should be ignored if it would prevent me from playing a card I saw earlier in the stock.


Rule #4:  Never play more than 3 cards from the stock on a single deal.

On a particular deal, once I've played a third card from the stock, all remaining accessible cards will continue to be accessible on the next deal.  By ignoring these remaining cards until the next deal, I may discover newly accessible cards that should be played first.


Rule #5:  Don't move any card to the foundations if it could still prove useful on the table.

For example, I shouldn't move the 3-of-spades onto the spades foundation if there's still a chance that I'll need it to support a red 2.  Of course, if both red aces have already come up, or if the ace-of-hearts has come up and the 2-of-diamonds is already supported by the 3-of-clubs, then it's safe to move the 3-of-spades to the foundation.  But I shouldn't be in a rush to move cards to the foundations.  I am certain that people who always move cards onto foundations are not playing optimally.  And yes, this means I always disable any auto-move feature on my Solitaire software.


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