Does anybody know if there is some software or a web page that let’s me play solitaire and at any given play it will tell me what the optimal play is?
I prefer to play Windows Klondike solitaire “vegas-style”–meaning, you turn over one card at a time and can go through the deck as many times as you want, however, dollar values are assigned to certain plays (I think you pay $1 per card for a new deck but get $5 every time you put a card up on the aces piles).
I have searched the intertubes for such a thing but I’m coming up empty. I think I’m just having trouble thinking of the correct search phrase. So, If anyone knows of any strategy software like this that is NOT for Windows-style Vegas Klondike, it still would help because it could help me search for the exact thing I’m looking for.
Thanks in advance!
ETA: maybe this should be in The Game Room. I wasn’t sure so I put it here.
Correction: I wrote that in Windows Vegas-scoring Klondike, (draw one card option) you can go through the deck as many times as you want. I meant to say you can only go through the deck once.
Yeah… after reading about it more online I’ve gathered that no one has figured out how to calculate the precise, perfect play for any given solitaire hand.
But I’ve also seen that some people have written so-called “guides” to solitaire strategy. So I guess what I’m wondering is: Is there any software that suggests the “best possibly play” (as far as can be calculated) for any given position?
It seems to me that (1) there a precious few points in most games when you have any choice at all, and that (2) when yo do have a choice, that the right strategy is almost to do whatever will leave the most cards face up, or spaces cleared. This may not be the objectively best strategy, the one that you should follow if you actually knew the order and position of all the face down cards, but, given that you do not know that, it clearly seems to be the optimal strategy.
I must say that I find what that **Cracked **article (linked in post 3) says, that the best available mathematical treatment of the game suggests that 80-90% of hands ought to be winnable, absolutely astounding. Given the dearth of choice points, and the frequency of losses, it is clear that a large majority of possible deals are not winnable. What astounds me, though, is that there is no better mathematical analysis. Why should this be? The game follows strict, simple,well defined rules and involves a finite number of cards (of fixed types.) It looks to me to be an ideal candidate for mathematical analysis, and just the sort of thing many mathematicians like to get their teeth into. Why has it not been more accurately described (let alone solved)? What is the problem?
It’s the fact that many of the cards (21, or 45 in the once-only game IIRC) are unseen that poses a special challenge to rigorous analysis. (21! is more than 50 quintillion.) This is compounded by the fact that, to find an optimal strategy by brute force, you might need to try every possible strategy: even with trivial decisions, number of strategies grows exponentially.
This is not to say the game is necessarily difficult, but to be almost certain what a correct move is, any straightforward solver might need a huge simulation. It would be better to develop general principles, but to do that manually would require more intuition than rigor, while to do that automatically would require fairly sophisticated AI.
Freecell solitaire is simpler in one important way: it’s a game of perfect information. I think there is perfect-playing freecell software; I don’t know how quickly it can find winning moves in very difficult positions.
Sure there are unseen cards, but it is not like each one could be anything. The possibilities are quite limited. I realize that with all the possible arrangements the numbers get pretty big, but they are still finite. At the beginning of a game there are 45 hidden cards, each one unique, so that is 45! possible arrangements, right? That is a big number but its not incomprehensibly big. Isn’t that sort of thing just what computes are for?
I don’t think you understand just how big that number is. 45! = 1.196222208654802e+56
If you set one billion computers working on the solution, and each one of them was able to process 10 million combinations per second, it would take 3.791e+33 years to complete the analysis.
There is no proven optimal strategy, but I did read an article with a “good strategy” and when I tried it, my percentages went up (seemingly significantly, though I didn’t even try to do the math). IIRC, I went from 10% success rate to 14%, or something like that, after hundreds of games, maybe as many as a thousand. Then I quit playing Klondike and went back to Freecell, because I like winning most of the time!
If you want, I can probably find the strategy I tried. It was based on intuition plus trial-and-error, as I recall, and made sense to me. It was different than what I had been doing without thinking too deeply, and those differences seemed to make sense to me at the time.
For example, I used to create blank spaces early as possible, to allow kings to come down. Nope: the strategy said to always reduce the biggest pile, whenever you have a choice. It also said never to move a king from the deck to a blank, until it helps to pull another card from a pile (or something like that). The principle of delaying something that can’t be undone until there’s a specific reason to do it seemed like a good one.
But I don’t know of any game software that has a built-in strategy for its suggestions. All that I have seen always show you all legal moves.
Why would you need to calculate all the possible combinations of hidden cards? Wouldn’t the analysis just have to know that if you have 2 kings visible, there’s a [del]1/26[/del]certain percentage chance of a card flip revealing a king and so on?
I play the iTunes version of Vegas solitaire. I like it because you can “undo” as many times as you wish. So, if you have a choice of moving one of two stacks to another row, you can do both and determine which is the “better” move. Even with this advantage, wins are still very rare.
As I tried to imply earlier, the game isn’t “insoluble,” just difficult. Brute force methods are the simplest to program but they wouldn’t work, so major programming effort would be needed. Why has no one done that? Not because the game is difficult, but because it is too simple to be interesting.
There are excellent backgammon programs; that’s a much harder but much more interesting game. Recently an exact solution for a simplified 2-person Goofspiel (a trivial-seeming game) was published. There are 12 unseen cards in that game; the paper doesn’t seem to indicate how much computer power was needed for solution, but I think it was hundreds or thousands of hours.
My father, Septimus VI, and I used to play this solitaire back during the Eisenhower Administration. He showed me that strategy. Another winning idea – although it makes the game more tedious – is to pass through the stock without playing to study options, finally making only the latest play – preserving earlier plays – unless you can see this reduces options.
One of my distinct recollections of Septimus VI, who passed away while Gerald Ford was President, was him looking over my shoulder and giving advice when I was playing Klondike. I think I then threw the cards in his face. :smack:
I do a variant of this, preserving only the first two plays, and playing any after that. Two, because that ensures I have access to any card following the second play, if I need it.
