Is Every Game of Solitaire Winnable?
What makes a game of Solitaire winnable is the existence of at least one path that leads to victory. Winnability is not the same as the odds of winning. The game can have a solution and yet the player may fail to find it. What makes these games challenging and entertaining is precisely the relation between these two probabilities. When a game has a high winnability rate but low winning odds the explanation usually falls on the players’ skills and their ability to find the most suitable strategy to reach victory.
Is every game of Solitaire winnable?
The short answer is no. However, this issue is more complicated than it seems as it involves too many unknowns to be certain.
The term Solitaire encompasses a wide variety of card games, each with its own set of rules and winning probabilities. While the latter can be higher or lower depending on the game, it is never an absolute value, meaning that it is not possible to ensure that 100% of the games are winnable. That being said, this information should not be discouraging. Not all Solitaire games are winnable, but the great majority is.
On average, around 80% of every Solitaire game is winnable. FreeCell is the variant with the best odds, as around 99% of all games are winnable, for instance. Interestingly enough, the Pyramid, one of the simplest and most straightforward games of Solitaire has the lowest chance of winning, with the odds oscillating between 0.5 and 5.5%.
Unfortunately, even if an average of 80% of all Solitaire games is winnable, players do not win all of these games. A game is considered winnable when there is at least one path to victory. When games have several paths available, there is a higher chance that the player will find at least one of these. However, when there is only one single path to winning, it is easy for the players to make a mistake or follow a different route that will turn the game unsolvable.
What are the odds of winning at Solitaire Klondike?
Solitaire Klondike is the most popular and commonly played game of Solitaire. So much so, that the term Solitaire is often used to refer to this particular variety.
Due to its popularity, it is also the most studied Solitaire game and yet calculating its winnability is still a problem for mathematicians. The main issue is that there are too many unknowns. Mathematicians have to have into account the possible position for each card at each deal and all the possible paths to win. The trickiest unknown, however, is the fact that the players do not know the position of the cards, which means that they depend on a certain amount of luck to find and play the right cards to follow the winning path.
To be able to calculate the odds of winning at Solitaire Klondike, the mathematicians analyze a Thoughtful Klondike, a version of the game in which the players know the position of all the cards. All the rules are exactly the same as in the regular Klondike, but this knowledge removes the luck factor from the equation.
The most recent analyses of Thoughtful Klondike estimate that around 82% of all Klondike games are solvable, whenever the use of the Stock Pile is unlimited and the players can undo their movements without any limitations either. Out of these winnable Solitaire Klondike games, it is not clear what are the odds of winning. Some studies point to an average of 43%, taking into account unlimited Undo movements and playing the 3-draw variant. Nevertheless, there is some debate regarding this value as it is sometimes perceived as too low or too high depending on the focus of the analysis.
What are the odds of winning at Spider Solitaire?
As with Solitaire Klondike, the cards are also facing down and are unknown to the player in a game of Spider Solitaire. For this reason, a version of Thoughtful Spider is also used to calculate the winnability and odds of winning at Spider Solitaire.
Using this version, most studies agree that the winnability of this game stands between 98.8% and 99.9%. This means that, in theory, there is a very high probability of winning every game regardless of the number of suits employed.
Nevertheless, the odds of winning a game are actually much lower as some of the games only have one winnable path and become unsolvable whenever the player makes a mistake or follows a different route. Furthermore, in a regular game of Spider Solitaire, the players do not know the position of each card which increases the odds that they might follow the wrongful path. On average, the chances of winning are 1 in every 3 games, although these odds can vary significantly depending on the number of suits used and whether it is possible to undo the movements throughout the game.
In a study titled Solitaire: Man Versus Machine published in 2004, the researchers stated that “It is one of the embarrassments of applied mathematics that we cannot determine the odds of winning the common game of solitaire” as even simple questions such as what are the odds of winning at these games “remain beyond mathematical analysis”.
The Thoughtful versions of Solitaire, be it the Thoughtful Klondike or Thoughtful Spider, do not allow for an extensive and in-depth analysis of the game, but they are still useful to provide a general perspective over the various Solitaire games and what makes them challenging for the players.
According to these analyses, most games of Solitaire are indeed winnable. Therefore, if you are having a hard time finding your way to victory, you may need to step up your game and work on your skills by learning new strategies. And remember that practice makes perfect. If there is a path, you can find it! Good luck!