What is the average winning percentage in spider 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. Out of these winnable Solitaire Klondike games, it is not clear what are the odds of winning.

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. As with Solitaire Klondike, the cards are also facing down and are unknown to the player in a game of Spider Solitaire. This is a preposterous and unsubstantiated claim. At the 1-suit level there are more that a googol unique possible games, and many times more at higher levels.

A googol is a one followed by a hundred zeros, an unimaginably huge number, much more than all the particles in the observable universe. Yes, I have done the math. As it turns out, practically all of these unique games are winnable, meaning that there exists a sequence of moves, no matter how unintuitive they might be to play, that would lead to a victory. So, in the first place, there's really no need to filter out games that cannot be won. From a programmer's perspective, finding games that could not be won would be impossible.

There are just too many possibilities to check out. Even if it could be done, it would take a very, very long time. This is not feasible.

One might keep a data base of games that have already been won, and therefore known to be winnable, but this would use up a lot of disk space and upset a lot of people.

I think it's very safe to say that no version of spider solitaire filters out games that are not winnable. In fact, the percentage of winnable games is so high at every level that a player could quite conceivable play millions of games and never encounter a single unwinnable game.

But, as some of the paths to victory would be very unintuitive, the player would not be expected to win every game. However, many of the games might require a lot of iterations and some ingenuity to win. Good point. I do think in any game the last deal can have ALL impossibles, e. Then no card would fit. There are of course different versions of the game - maybe in some collections the "impossibles" are shuffled out?

I would think that now the Microsoft Solitaire Collection would be the standard - all should talk about the same version otherwise we cant compare. I have a I use the undo but never restart a game. My best moves game is and the most moves game is I use random shuffle never winning deal. It a tedious, relentless and patient challenge. I don't play the top level much.

I play the two suit level. I have a high of I essentially play till I win. I always select the game I want to play. No more than 1 ace that has a 2. I want all but 3 or below cards to be moved or played on. The best series of movable cards are in the middle of the series as the odds of having a play is increased with those cards.

I have lost some games as a result of hitting the wrong button when I make a mistake in the pull down menu and accidentally end the game. On this computer I have played games and won I think all of the losses have been accidental or computer freeze.

I may have to play a long time and use unconventional methods such as doing a throw and not playing some of the possible plays on the throw. I believe, however, that if you pick the right games you can win them all. My lowest score was On my lap top I haven't lost a game yet.

On one of my computers I am going to reset and always take the first game delivered. It's interesting that, by your own admission, you don't use capital letters because you are lazy, yet you immediately continue to not use capital letters.

Is being lazy a good thing? Do you not understand that not using capital letters -- as well as other things -- makes it more difficult for the reader on the other end to comprehend your thoughts?

Or, do you simply just not care? But, I must give you some credit. At least you use periods and paragraphs. That's better than some. How a person writes a letter says a lot about them. And yes, not using capital letters says that you are lazy, but I obviously already knew that without you telling me.

It goes without saying that if the writer is not writing in their native language, then standards are much lower. However, to repeat myself, I believe that you could do a lot better.

How much better? What makes me think this? Read on. You never said whether you reject games. For example, if you begin a game where no moves are possible, do you play it? Rejecting games can raise a player's win ratio significantly. Do you reject games? If so, how do you determine which games to skip? By this, I assume that you reset your statistics keep by the spider software. Have you ever considered keeping your statistics in a spreadsheet? At the minimum you could keep the date, a game number, your score, and whether you won or lost.

Then, computing your win ratio would be extremely simply. But there are advantages to maintaining you own statistics. You can keep other information. For example, among other things, I keep the move count and the number of hidden cards at the end of every round. When I graph these and other statistics, I usually get rather smooth curves that sometimes reveal clues as to how I might improve my game.

Knowing these, and other things, influences my game play, more so as the game progresses. Of course, since you are not me, what you might learn from keeping statistics should not be expected to be the same. As well, you undo moves; I don't. These are two very different games. The strategies are somewhat different. I also keep a record of the initial 10 cards dealt. This allows me, with the help of a little code, to try out different scenarios to determine the best criterion to reject games by, even though I don't reject games -- ever.

In fact, if I did, I could not make these calculations. However, I admit that part of the percentage is a guess. I could explain how I arrived at this figure, but you're probably not interested. I speak from both experience AND statistics. I very much know what you mean when you say that you play fast. It's a hard habit to break. I know that I've lost many games in the same manner. However, I find that keeping my own statistics in a spreadsheet forces me to slow down a little.

It seems to help, but maybe it's all in my head. I think that a lot of people lose games because they follow the usual advice online; such as: always turn the hidden card in the pile with the fewest hidden cards, never place a king into your only empty column, and my favorite, the secret to the game is emptying columns. None of these is true. It's really the state of the game at the particular moment of play that dictates the next move.

Maybe I wasn't clear in my last post. My idea WAS that each player would play the exact same games, but the games would be randomly generated beforehand. Your record of 11 consecutive wins is not bad. My record is 7, which I have only managed to do once, but I have managed 6 a few times and 5 quite a few times. Oh course, my streak is without undoing a move, without restarting a game, and without refusing to play a single game presented by the computer.

In my last several hundred games, I have also not lost more than 6 in a row. I also track my last consecutive games. My most wins in consecutive games, as presented by the computer no undo and no restart , is Of course, I've been called a liar because it's impossible without undoing moves. No, it's not! Furthermore, I know that my game is not perfect because I still catch myself making mistakes.

This mean that I could potentially do better. It's also quite probable that someone else already has. As you can see there is nothing wrong with my keyboard Do you think they're lying? I've done the math. I don't thing they are. However, you should be able to do much better. Another question is: Are you rejecting games that the computer presents to you?

Now, concerning your tournament idea: I've given this quite a bit of thought over the last few years. Lets suppose that we allow players to undo and restart.

Assuming that they have lots of time to play their games, we should expect that many of them would win all of their games. But, your idea was to limit their time. This might actually work, but it's not my idea of fun. Yes, I think that there should be a tournament -- similar to blitz chess -- where the player can undo, restart, and has a limited amount of time. But, what about the player who doesn't undo or restart games?

There should be a parallel tournament where the player can neither undo moves nor restart games. Special software would need to be written to ensure that nobody cheated. Anyway, I'll continue playing out, mixing suits as much as I need to in order to reveal as many cards from the original deal as I can without sullying my target. If I would have to sully the target, I just won't make the move, unless I spot a way to make a new, longer target with playable, visible cards.

So I guess I would say that at least early on in the game I aim to play all the "dealt" cards the ones on the board, not the deck in "my hand" the lower right-hand corner while preserving a target.

Once I've had to deal from my hand, it's a matter of cleaning things up, with the aim of making the sullied runs long, and sullying fewer runs. The goal, still, is to uncover the cards from the original deal. That's pretty much it. Hope that helps, and good luck! Once you get to the point where you have two stacks open, try to maintain that. When you have two stacks open, you can do a lot more rearranging. As an aside, I have to say that I find it odd to keep track of statistics if you reject games based on the hand you are dealt.

I've thought about asking this exact question many a time, so thank you! My question is, are the four suit games winnable at all? I've never even come close. Idiot's Delight allows the player the option of specifying a given seed number from 1 to For instance, if the seed were chosen the first ten cards would always be 2J56J9JQ59 of various suits. Note that if the player randomly generates a long sequence of seed numbers in advance to playing the game, then the program cannot adjust the difficulty level according to the player's win rate.

For this reason, I used Idiot's Delight to estimate my win percentage. I played games on Idiot's Delight , using the seed numbers between 1 and I played games of Spider on Free Spider Solitaire.

This was chosen since after some experimentation it "seems to be consistently bad": winning is possible but usually requires some effort even for an expert player. Unfortunately I won only 46 games, thirteen less than expected. This might suggest further testing is justified; however recall that the win rate is player-specific and it is quite possible I did not play optimally over the course of games.

I conclude there is not enough evidence to prove Free Spider Solitaire is biased. Forty-six wins is a bit disappointing however, methinks the program dodged a bullet. However other Spider programs may not be so lucky Trevor Tao has a PhD in applied mathematics. He is a research scientist currently working for the Department of Defence.

Trevor is a keen chess and scrabble player and his other hobbies include mathematics and music. Trevor is the brother of world-renowned mathematician Terence Tao. This is the term I use when arranging the columns. I thus obtain series of only one "color". Out of general interest I wrote a small program that will reveal all the cards in any deal in the Microsoft Windows version of Spider. Every game starts with a bit "seed" generated at random, and the cards are dealt progressively using a fixed algorithm based on that seed.

Every game can be reproduced if you know its seed, and the only way a game could be "fixed" would be if the program had a huge list of "difficult" seeds and was coded to select one in certain circumstances.