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I play a lot of Solitaire games on my Android phone and love to keep an eye out for the statistics.

Given that the Solitaire version lets you restart the game endlessly, I usually play until I solve it. But I never managed to solve more than 80% of the games played (1000+).

So now I wonder, is every Solitaire game solvable?

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I presume you mean Klondike solitaire? – McKay Jul 7 '10 at 20:56
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I have played thousands of solitaire games both on pc and the old fashioned way (yes with real cards) and have deduced that in order to find a solution to every game you play is to cheat. – TheX Dec 1 '11 at 3:37
What a solitaire addict! Forever alone :) – kokbira Jun 25 '12 at 18:36

migrated from gaming.stackexchange.com Dec 1 '11 at 4:13

6 Answers

up vote 40 down vote accepted

No. Example: If all of your cards face up on the board are red, and the cards that come up every third card are also red, and none of them are aces. You lose. Do not pass go, do not collect $200.

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As a fact, I have come up with almost this exact setup on the computer version of Solitaire (but one card was black, just completely impossible to place anywhere). – Grace Note♦ Jul 7 '10 at 21:02
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Another example that just happened to me: All cards shown are even. – McKay Jul 14 '10 at 15:48
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Even simplier: all aces are on the same column and 2 is above them. – Oltarus Dec 1 '11 at 10:50
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@Oltarus Aces in same column and 2 above them is still winnable. Its annoying and probably a loss but doable. – MaskedPlant Dec 1 '11 at 14:33
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up vote 5 down vote

Solitaire is a game that precedes its computer version, and that means that all the cards are truly shuffled, without the computer peeking in to verify the game is solvable.

And like McKay mentioned, with a random shuffle you can definitely end up with an unsolvable game.

I'm sure it is possible to design a Solitaire variant in which each game is solvable, though.

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Would need a LOT of calculation, basically the computer would have to play through an entire game to make sure there's a solution, unless there's some kind of algorithm I'm missing. – Arda Xi Jul 21 '10 at 15:42
@Arda, there are some conditions that could be easily tested - for example, a card other than a King can be played on only three other cards in the deck (the next-lowest card in its suit, or the foundation for an Ace, and the next-higher cards of the opposite color). If all three of those cards are face down below that card on a pile, the game isn't winnable. Unfortunately I think that's a small percentage, and testing for other conditions might require a ton of recursion. – Dave DuPlantis May 25 '11 at 21:05
@DaveDuPlantis True, but you will have to test for all of those conditions that exist. I'm not sure whether we even know all of them. – Arda Xi May 26 '11 at 5:12
@Arda - that's true, that's what I was thinking with respect to recursion. Without some way to demonstrate that any given position is unwinnable, you'd essentially have to play a certain series of cards until you were blocked, back up to the last decision point, and repeat ... it's an intriguing concept, but I've never seen a solitaire program do that. – Dave DuPlantis May 26 '11 at 12:31
That shouldn't be too difficult. – AndSoYouCode Dec 1 '11 at 11:06
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up vote 17 down vote

There is very interesting reading at wikipedia about this topic.

For a "standard" game of Klondike (of the form: Draw 3, Re-Deal Infinite, Win 52) the number of solvable games (assuming all cards are known) is between 82-91.5%.

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Then I was actually doing a great job nearing it to 80% – Ivo Flipse Jul 21 '10 at 20:44
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However, if you started a list and enumerated the initial conditions -- I feel like I've seen this on a linux version of Solitare: the numbering of deck order, that is -- and you definitively decide a certain one is un-winnable, you then could compare notes across nodes (share with friends) and VOILA: a list of un-winnable starting deck stacks.

I've been starting to think the Windows 7 version has the un-winnable decks removed, ... I don't know, it's a little heavy-handed and smug about the statistics.

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With 52! starting shuffles, you'll need an... inconveniently long... time before you have a good list. Even after you solve the problem of determining unwinnable definitively. – Tynam May 24 '12 at 7:59
up vote 2 down vote

No. Eric Sink decided that he would start a micro-ISV to create a version of solitaire that is always winnable. This was mostly just an experiment to see what it would be like running a software company with one person, but he eventually sold the product which is still available for purchase.

There have been some estimates about the number of Klondike Solitaire games that are unplayable (no moves possible, about 1 in 400), and several guesses about how many games are unwinnable, although this percentage varies wildly from 30%-10%.

The difficulty of this problem stems from the sheer number of initial deals 54! that would need to be evaluated to determine which were winnable and which were not.

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up vote 3 down vote

Literally just played a game in which one of the stacks (the one containing 4 cards) was lead by the 9 of diamonds, and the cards inside of it were the King of Spades, the 5 of diamonds, the 10 of spades, and the 10 of clubs (I know this because I had the entire field solved except for this stack and used process of elimination). As far as I can see this makes the game impossible. I have a 9 of diamonds in which can never be moved, as the two 10s that it's eligible to rest upon are trapped underneath it in the stack face down. Attempting to get rid of the 9 by moving it to the diamond stack would also be fruitless, as the 5 of diamonds is stuck underneath it too. Unless someone can tell me some way that this could be solved, I'm pretty darned certain that if a card that is leading a stack is covering a stack that contains the two cards it is capable of resting on, and a lower number of it's own suit, then the game is made impossible right from the get-go.

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