Can you always win at Solitaire?

Passing time recently in an airport playing Solitaire I wondered this.

In theory is any deal of Solitaire winnable with it just being a matter of you playing correctly?

Or is it possible to get deals that are unwinnable at the outset regardless of what you do?

FWIW I am thinking of the common Solitaire you can find on any Windows PC and using the three-card deal you can go round and round with rather than the one-card at a time, once through the deck style.

If each pile had either a Jack or a King on top and none of the queens are in the deck you will not be able to win the game I belive. There are others situations but that is the first I could think off.

Yeah…I was just thinking (without actually testing it) that I could manually put together an arrangement that would be unwinnable at the outset. Naturally that configuartion of cards would be a possibility after a real shuffle.

But to extend this…

Any way of knowing what percentage of possible arrangements would not be winnable from the outset? Calculating all possible deck configurations is straightforward enough but determining if at least one possible way exists to win is present for a given configuration is totally beyond my meager math skills.

Are you talking about Patience specifically or “solitaire” in general? There are definitely varieties of solitaire in which it is not possible to win if the cards aren’t falling right.

What exactly are the rules?

And given that there are 52! possible arrangements, I don’t think that calculating a percentage will be so easy.

If you want to guarantee that every game you play is winnable there is always Winnable Solitarire

The OP needs to clarify what solitare(s) he is thinking of. Klondike, the game that generally comes to mind at first when solitare is mentioned thanks to a couple decades of being labeled as Solitare as a computer game, is not winnable all that often. There are a ton of solitare games, all with different odds of winning. In any case, I know that Klondike has unwinnable games. Your odds of winning are better if you draw one instead of three, but there are still unwinnable games. FreeCell, on the other hand, is theoretically winnable every time.

Except for game number 11982 (in the older version of Free Cell, which gives you 32000 starting positions). AFAIK, no one has ever beaten that one.

Returning to Klondike, the odds of winning, when you turn over three cards, and can go through the hand as many times as you like, are often given as 1 out of 34. In fact, the odds are 1 out of 17.

How do I know? Back in the dark ages of computing, I programmed a solitaire game (in C - not C++, just plain C), as the infernal machine (an AT&T 3B5 minicomputer) had been delivered with no games (we’re talking old Unix, here, System V, Release 2). I quickly realized that I had, of necessity, built into the game a little subroutine to determine whether a move was legal or not. It was an easy matter to alter the program to play by itself, simply by trying every possible move, and making any move that was legal.

Obviously, I built in enough logic so that it wouldn’t move a king from one empty space to another, or otherwise end up in an endless loop. However, I didn’t go so far as to let it move partial columns, or to “retrieve” cards once they had been put on the “home” piles.

I turned the sucker loose overnight, and it played thousands upon thousands of games, keeping track of its winning percentage. To within a couple of decimal places, it won 1 game out of 17. Of course, a human player, making some informed choices, and able to move partial columns, would be able to beat those odds.

Why are the odds usually given as 1 in 34? I can only speculate, but I believe that someone once worked out the probabilities, and made a simple error somewhere along the line, leading to a result that was off by a factor of 2. Since then, no one has ever bothered to figure it out again, and the wrong figure has simply been repeated so often that it’s accepted as correct.

The probability of dealing out an unwinnable game of solitaire is well addressed, though not definitively answered, here.

The question, “What’s the probability of winning a game of solitaire?” was, according to mathematician Stanislav Ulam, the inspiration behind the invention of the Monte Carlo method of determining probability. Basically, rather than try to count up all the possibilities (which gets way too complicated in a case like this), you run a simulation where you perform the experiment a whole bunch of times and see what fraction of the time your desired outcome occurs.

Game -1 and -2 are suposed to be unbeatable as well.

They most certainly are. They are quite obvious, in that there are no possible moves. I cant remember off the top of my head, but i think its arranged by suit in reverse order starting at the bottom.

Which is pretty much exactly what Early Out described doing above to determine the 1-in-17 probability of winning, right?

Is this an urban legend or a specifically designed game that nobody was supposed to beat? :confused:

Here’s a FAQ that I believe answers both your questions. That there is one unsolvable game in the “Microsoft 32,000” is well-known, and it occurred simply by chance.

(emphasis mine)

Exactly, though my method contains some obvious (and fatal) flaws. My simulation didn’t make use of all the possibilities of the game (partial column moves, in particular), and it played very stupidly, making any legal move that was possible.

Also, what it did not do, because it would have taken more computing cycles than I’ve ever had at my disposal, was start with a specific game, and play that same game in every possible permutation, to see if it was winnable, then deal out another game, and repeat that process, ad infinitum.

So, if its pre-programmed approach to a given game failed to win (try moving column 1 to column 2, 1 to 3, 1 to 4…, 2 to 1, 2 to 3, 2 to 4, etc., etc.), it counted the game as a loss. That “lost” game might, of course, be winnable if played in a different way.

Game 11982 can be beaten.




No fair! Five demerits for cheating!

I want to second some things here.

First off, I thought Patience was the same concept as Solitaire, and not simply Klondike. I once checked out a book that had rules for 500 different Solitaire card games.

Also, on Klondike being always winable… I would think that it is more likely the case that it is losable, the further you win, the more important your original card layout has to be. Its one thing to move the cards (legaly) to place the aces in the foundation, but a little harder to un-do it all (if so arranged) to get the twos. Then the fives are harder still, and 10s etc.

I always like the “cleaning up” epiphany one gets the moment they KNOW that the game they are playing will be won.

Free Cell on the other hand is a different beast altogether. I knew about the games numbered “-1” and “-2”, but found that some people spent time writing reports on why exactly (in GREAT detail) they are not winnable. I could not beleive that people spent time on this, when it was implied to be an easter egg/joke.

A final note, other books I have on card rules indicate rather a particular Solitaire game (By its title, not by a deal of a particular game) is more skill or luck. Clock Soitaire/Travelers (Same game, Different names) is all luck… but I still play it. Obviously, the more luck enters the equation, the less likely you are to win. I think the general concensus is that “klondike” is more skill than luck, but luck is not entirely ruled out… nearing end game (as I mentioned above).

Thanks for the link on the “winnable solitaire” … Like I need a new addiction steming from an online encounter. :smack:

I just pulled up a game of MS Solitaire where there were absolutely no moves! The cards were delt, I flipped through the deck (3 at a time). After flipping through the deck once I got the No More Moves dialog box.

I couldn’t undo the last moves because no moves were made!

thanks to zombie Klondike solitaire i have some interesting links to now visit.

i have a number of times had no moves possible in the Windows game playing 3 at a time.

the per cent of winnable games in that is too low for me, though it takes no more than a minute to win when i do.

Spider in 1,2 or 3 decks is more fun. one deck Spider is more winnable than Klondike and worth the extra time. though the Windows version is less winnable than some others i’ve tried.