The title is pretty self-explanatory. I’m wondering what percent of solitare games are unbeatable, no matter how well you play. The software I’m using is made by Solebon and the version I play is Klondike Deal 1. Assume that the game is played straight, no cheats or anything.
I can’t cite anything but I recall once hearing that only 25% of Klondike games are winnable if played by the official rules.
Clarification on “no matter how well you play”: Are we assuming a player who always makes the best choice availble, given the information he has at the time, or are we assuming the player is omniscient or equivalently always makes perfectly lucky guesses?
Does the player get unlimited reshuffles? If so, they know the exact contents of the draw pile. Does the player get 1 undo (like on Windows)? If so, they may see certain things to gather more information and then hit undo.
I play a game called Seven Devils, with two decks. The goal it to get all cards built in suits from A to K. It begins with seven cards on the left - these cards can only be built on the Aces etc. You can prove that if this contains three cards in a suit in reverse order the game is unwinnable. Saves lots of time. You also can’t win if you get a card above two cards of the same, lower value in the same suit.
I haven’t computed the percentage of hands like this, but it wouldn’t be that hard to do.
The number I saw was more like 1 in 30. Single-card drawing brings that up quite a bit, as does unlimited draws.
The version that I play allows for unlimited cycling through the deck and unlimited undo’s. i.e. you can undo back to the start of the game if you wish. What I’m looking for is given these constraints (or lack thereof), how often will the game be unbeatable.
Color me confused… but why would anyone create a game that is unwinnable? If they did so, who would play it?
And even if someone did create an “unwinnable” game and people did play it, people would still win… you’d just have to redefine winning.
For example, if the object of the game is to get all 52 cards into four piles in ascending order by suits (as in Klondike) and it is mathematically impossible to do so according to the rules of the game, then the winning condition would simply be the maximum number that can be placed. If, for example, the maximum number that could be placed is 48, wouldn’t placing 48 cards then be a win?
Zev Steinhardt
I think we have two conflicting meanings for the word ‘game’ here, confusing the issue.
The OP is, I think asking for situations in which the game in general, a set of rules to play by, is certainly winnable, however, immediately after beginning a particular session, a particular deal, a particular attempt to win the game, it can be demonstrated that no matter what choices are made, the conditions in this session are unwinnable. You can still win the general game, by dealing all over, but you cannot win this particular game.
Did that make any sense??
You can easily construct a Klondike deal that’s unwinnable. For instance, bury all the aces deep in the tableau, cover them by kings, and make sure there won’t be any open spaces into which to move the kings.
What you’re confounding is the game Klondike and the instances of the game that result from various shuffles. Some shuffles are winnable, some aren’t.
OK, I see. It was confusion over the word game meaning a specific instance of a game, rather than the game itself.
Sorry about the interruption… carry on.
Zev Steinhardt
And to answer the question “why would a computer game display a shuffle that cannot be won?”: because for many games it is not simple to term if a given shuffle is winnable or not. There will be shuffles that are obviously winnable, and some that are obviously unwinnable. But there are some shuffles that are not easy to classify.
Exactly. It’s the last group that I’m wondering about. As Mathochist described earlier that is obviously unwinnable. Surely someone has come up with a way to classify the other ones. If not, does someone want to give it a go?