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FreeCell -- Frequently Asked Questions (FAQ)
written by Michael Keller http://home.earthlink.net/~fomalhaut/fcfaq.html

Table of Contents
1. History of the Game
     * Who invented FreeCell? How did it get started?
     * Why is FreeCell so popular?
     * What has been written (off-line) about FreeCell?
     * What are the rules of FreeCell?
     * Why doesn't Microsoft FreeCell always tell me when I have lost?
2. The Microsoft 32,000
    * Can they all be solved?
    * Which deal is the hardest to solve?
    * How are the games (deals) numbered? Are those deals random or were they selected in some way?
    * Does the game automatically turn up games which have not been won?
    * How can I get the solution to a hard game I can't solve?
    * Why am I finding deal number xxxxx difficult when it isn't on any of the lists?
    * Has anyone found a solution for Freecell xxxxx? It seems awfully difficult because of the remote positions of the aces.
    * I have a streak of xxxx wins in a row and have won xx% of the games I have played. How does that compare to other players?
    * Are all of the solutions in the catalog correct?
    * Why won't you post every new solution submitted?
    * Why won't you post improved (shorter) solutions in the catalog?
    * Which deal is the easiest? Are there any deals in which all of the cards go automatically home at the start?
3. Variations and Related Games
    * I'm getting awfully good at FreeCell. How can I make the game more challenging?
    * Is it possible to win without using the freecells?
    * Is it possible to get all 52 cards to the homecells at once?
    * Can a card be played once it has been placed on a homecell?
    * What are some other solitaires closely related to FreeCell?
4. Computer Versions and Features
    * What is FCPro? What can it do that most other programs cannot?
    * Is it cheating to use computers?
    * Is there a version of FreeCell for Macintosh?
    * Are there any handheld versions of FreeCell?
    * What other computerized solvers exist?
5. More Statistical Facts and Curiosities
    * How often can I win?
    * How many freecells are needed to solve any possible deal?
    * What is a supermove? How does it help in playing?
    * How many possible FreeCell deals are there?
    * What is the fewest number of cards one can have left remaining and still lose the game?
    * Is it possible to play an entire suit to the homecells ahead of all of the other suits?

Note: I have looked at every Windows and Java version I am aware of. There are versions for Macintosh, OS/2, and other platforms which I cannot run on my system. If anyone has access to any such machines and would like to try out one of the other versions and make a brief report, check the URLs given in this FAQ.

1. History of the Game

* Who invented FreeCell? How did it get started?

The idea of a game with temporary storage locations to hold single cards is not new. One of the oldest games of this type is Eight Off, which provides eight depots (or freecells) which can each hold one card at a time. The tableau consists of eight columns of six cards each, with the four remaining cards being dealt initially to four of the eight depots. Cards may be packed (built on the tableau columns during play) downward in suit, not in alternate colors as in FreeCell. The foundations (homecells in FreeCell terminology) are built up in suit just as in FreeCell, but empty columns can be filled only with kings. In Martin Gardner's June 1968 Mathematical Games column in Scientific American (reprinted in his 1977 book Mathematical Magic Show), he describes a game by C.L. Baker which is a variant of Eight Off. Baker's Game, as it is now called, differs from Eight Off in having only four depots instead of eight -- the four extra cards are dealt to the first four columns. An empty column may be filled with any card, not just a king -- this allows them to be used as temporary storage areas too, and allows large sequences of cards to be moved from one column to another. This makes a better, more interesting game in my view, though it is harder because it has only four depots instead of eight. (An excellent freeware version of Baker's Game is available under the trademark Brain Jam from Brain Jam Publications' home page). An important feature of most of the games of this family is that unlike Klondike, only one card at a time can be moved, although computer versions allow a sequence of cards to be moved as a unit if they could be moved one by one using empty freecells (and/or columns).

Paul Alfille had the brilliant idea of changing Baker's Game in one respect, allowing cards to be packed on the tableau downward in alternate colors, as in familiar games like Klondike and Canfield, thus producing the game we know as FreeCell. This has the happy effect of making nearly every deal winnable, though many are still quite difficult. Alfille wrote the first version of FreeCell for the PLATO educational computer system in 1978. The popularization of the game is also due to Jim Horne, who wrote a character-based version for DOS and later a full graphical version for Windows. The latter first appeared in 1992 on Microsoft Entertainment Pack 2 (and later in the Best of Microsoft Entertainment Packs). Later versions were bundled with Windows For Workgroups and Win32s (the 32-bit extension to Windows 3), and eventually with Windows 95 (and 98). Dennis Cronin also wrote a freeware version for UNIX in the mid-80's, and undoubtedly there were other character-based versions floating around too. Both Horne and Cronin learned the game from the PLATO system.

Two correspondents in Sweden, Dan Glimne and Ingemar Ragnemalm, uncovered a closer predecessor to FreeCell, which dates back at least to 1945. In his book Världens bästa patienser och patiensspel (The World's Best Patiences and Patience Games) Einar Werner (European bridge champion in his day) describes a solitaire called Napoleon på S:t Helena (Napoleon in St. Helena), which bears an extremely close resemblance to FreeCell. The differences are that the last four cards of the stock are dealt to the four freecells rather than the first four columns, and only kings may be placed in empty columns. These two differences make the game much harder than FreeCell, but it can be definitely stated that a relative of Eight Off with alternate-color packing existed more than 50 years ago. Thomas Warfield has suggested calling the game ForeCell, since it is a forerunner of FreeCell, and he has implemented ForeCell in the edition of Pretty Good Solitaire released in March 1999. One of the books which describes ForeCell is Lägga patiens by Svend Carstensen, a 1971 translation of a Danish book. The book estimates the chance of success for ForeCell at 1 in 10, which is well short of the mark. I have played a block of 100 consecutive ForeCell deals using Pretty Good Solitaire, and I was able to win 36 out of 100 on the first try, and a total (so far) of 71 games including multiple tries. Some of the games can be clearly seen to be hopeless, but I suspect that the overall win rate for ForeCell with perfect play is probably in the range of 65-75 percent.

* Why is FreeCell so popular?

I believe it is primarily because of the puzzle-like nature of the game, and the fact that nearly every game can be won. Most solitaires (including the most popular ones like Klondike, Spider, Pyramid, Forty Thieves, and Miss Milligan) can be won less than half of the time even with perfect play. Almost every FreeCell deal can be won if played correctly; it has one of the highest win rates of any solitaire (Fortune's Favor and Westcliff, among others, may possibly be easier to win), yet individual deals run the gamut from trivially easy to excruciatingly hard. FreeCell is an open solitaire, meaning that all of the cards are dealt out face-up at the start of the game, and the effect of any series of moves can be worked out, without having to rely on judgement and probability as in games like Klondike. FreeCell also differs from most of its relatives in using alternate-color packing on the tableau, a feature which has proved its popularity in Klondike, Canfield, and many other solitaires. Alternate-color packing gives the player a much wider range of plays than in-suit games like Baker's Game and Seahaven Towers, and also makes the win rate somewhat higher.

FreeCell is leading the voting in two online popularity polls for solitaire. In David Bernazzani's poll on his Solitude site, FreeCell leads the voting with 824 out of over 4000 responses, well ahead of Klondike at 403, Pyramid at 269, Aces Up at 248, Spider at 176 (Microsoft added a version of this game to Windows ME/2000/XP), Golf at 159, and Canfield at 128. In Thomas Warfield's poll at the Pretty Good Solitaire site, out of more than 850 votes, FreeCell leads with 66 votes, ahead of Aces and Kings (one of Warfield's many inventions) at 47, Klondike at 41, Demons and Thieves (another Warfield original) at 33, Forty Thieves at 28, and Yukon at 24.

* What has been written (off-line) about FreeCell?

Despite its popularity in the online world, very little on FreeCell has appeared in print. I wrote an article for Games Magazine (Michael Keller, Big Deal, June 1995, pages 10-13) about FreeCell and Baker's Game. Dan Glimne's new book of card games, in Swedish, published in December 1998 by Frida Forlag AB (Stockholm), 100 Kortspel & Trick: som roar hela familien (100 Card Games and Tricks to Entertain the Whole Family, ISBN 91-973473-0-2), is to my knowledge the first book of solitaires or card games to describe FreeCell (pages 66 and 67). The first English-language book of games to include FreeCell appeared in December 2001: the third edition of Hoyle's Rules of Games by Philip Morehead (384 pp., $6.99, ISBN 0451204840, Signet). Martin De Muro published solutions to the first 1000 MS deals in book form (Free Cell Game Solutions #1, January 2000, 338 pp., $19.95, ISBN 096763881X, self-published), available from on-line bookstores such as Barnes & Noble or Amazon.

* What are the rules of FreeCell?

I guess it's easy to assume that everyone reading this FAQ or the mailing list knows how to play, but I have seen this question asked on newsgroups, and apparently not everyone finds the explanation in the Microsoft help file adequate. It is also not uncommon to see the rules wrong in computer versions (the most common mistake being to allow only kings to be placed in empty columns). I have also had questions from people who don't understand the rules well enough to know why they have (or haven't) lost. The rules are explained clearly, I hope, in the beginners' tutorial. One important point is that a sequence of cards can be moved only if it would be possible to transfer the whole sequence by moving one card at a time, using empty freecells and/or columns. This is very important in understanding supermoves as well as when playing with less than four freecells.

* Why doesn't Microsoft FreeCell always tell me when I have lost?

It only tells you when you are completely out of moves (this can only happen when all of the freecells are full, there are no empty columns, no cards can go to the homecells, and no card can be moved from a freecell or the bottom of a column to the bottom of another column). The same is true of FreeCell Pro and probably other versions of FC. It is possible to be hopelessly lost, but always able to make at least one move. A common situation is to have, for example, a red five on a black six at the bottom of one column, and the other black six available at the bottom of another column. The red five can be moved back and forth indefinitely, but if no other moves are available, the game is lost. It would be possible for a program to be written to detect this situation, but there would always be slightly more complex situations which would not be detected. Championship FreeCell is the only program I know which detects many lost situations while a game is in progress.

2. The Microsoft 32,000

* Can they all be solved?

All of the 32,000 Microsoft deals except for number 11982 are solvable.

Jim Horne's version for Windows 3.1 contained 32,000 numbered deals (games), so that selecting a specific number would always produce the same deal. (These are random deals, generated by integer seeds using the random number generator in the Microsoft C compiler). He numbered the deals so that people could exchange the numbers of difficult/interesting games with their friends, and also in the belief that some people would try to play sequentially through the games; many people have in fact done so. Happily, when the game was ported to Windows 95 and later operating systems, the set of 32,000 deals was the same, so any discussion of deal numbers applies to all Microsoft versions. The help file for Microsoft FreeCell contains the claim "It is believed (though not proven) that every game is winnable." When Horne wrote this, he already knew that unsolvable deals could be constructed (see Hans Bodlaender's example): as a joke, the Windows 95 version includes two unsolvable games, numbered -1 and -2. Horne purposely made his claim ambiguous in order to challenge people to find such impossible games, but intending it to mean that all of the 32,000 included deals were winnable. This comes as close as possible to being true...

Another factor in the popularity of the game, besides Microsoft providing the game free with Windows 95, is Dave Ring's Internet FreeCell Project. Ring solicited volunteers on rec.puzzles and elsewhere (eventually getting more than 100 people involved), and coordinated the volunteers in an effort to solve all 32,000 of the deals in the Microsoft versions. He assigned each volunteer a set of 100 consecutive deals, and the volunteers would report back after they had solved (or tried to solve) all 100, when they would be assigned another set if interested. Ring would reassign any hands reported as unsolved to his best solvers. I got involved in the project fairly late, but still managed to solve 1,970 deals. Eventually the project was completed, and all but one deal was reported solved! This is the famous game number 11982. I wrote the article on FreeCell and Baker's Game for Games while the project was still finishing up. Dave Ring wrote to Games shortly after the article appeared, reporting that the project was finished. Games printed Ring's letter, along with a layout of the unsolved number 11982, in the October 1995 issue (page 4). A report that 11982 had been solved turned out to be incorrect when it was discovered that the solver was playing Baker's Game (by hand) rather than FreeCell. I have since heard from over a dozen players (Doug Schmieskors, Laura Ross, Martin E. Martin, Adrian Ettlinger, Freya Wieneke, John Williams, Dick Belmont, Don Rop, Morrie Hoevel, Ginger Martin, Bob Rankin, Wolfhart Wünsche, Rich Hook, Sheridan Wilson, Roberta C. Hendrickson, and Emilien Fenez) who have played the entire set of 32,000; many have won all but deal number 11982. 11982 has now eluded solution by probably thousands of human solvers, and at least eight independent computer programs I am aware of (most of which are designed to search exhaustively for a solution), and I am confident in calling it impossible:

A large catalog of solutions to (mostly difficult) deals, including all of those reported as hard during the Ring project, can be accessed from the main FreeCell page, along with other FreeCell information and links. The solution catalog was begun by Dave Ring, and was later maintained by Wilson Callan; I am now doing so. You can look in the index to find out whether a particular solution is included, and you only need to access the appropriate section of the full catalog if the solution you want is there. A large-scale computerized statistical study, conducted by Don Woods, analyzed a million random hands. Woods reported to the Usenet group rec.games.playing-cards that the program had solved all but 14 of them, making the win rate for FreeCell almost 99.999% (compared to win rates of 75% for Baker's Game and 89% for Seahaven Towers).

In 2001, Microsoft released a new version of FreeCell for its Windows XP operating system. This version extends the number of available deals up to 1 million. The additional deals are the same as those in FreeCell Pro and Pretty Good Solitaire. Eight of those one million are impossible.

* Which deal is the hardest to solve?

Difficulty is a rather subjective question, so it is not possible to give a definitive answer. The difficult deals page contains a number of lists of deals which have been found difficult. From my own experience and reports from other solvers, I would nominate 1941 as the hardest solvable deal. Another possible candidate is 10692 (in Windows XP or FreeCell Pro, try 80388). Besides the impossible deal number 11982, the most frequently asked-about deal is number 617. Although there are many harder deals, I suspect that 617 is the first really difficult deal that many players encounter when playing the deals in sequence. For some reason, about half the people who write asking for a solution without checking the catalog index (and please don't be one of them) are asking for a solution to 617. Worse yet, seven different people have written me to tell me that Brian Kraft's posted solution is wrong, and all of them were having trouble at the exact same spot, move 20 (51). The solution is correct; I wish I knew why it was causing so many problems (possibly because the trouble spot is a supermove?).

* How are the games (deals) numbered? Are those deals random or were they selected in some way?

The way computers create "random" deals is by using a number as a seed for a random number generator. The Microsoft version of FreeCell uses a number with a range of 1-32000 as its seed; the New Game (F2) function selects one of these using, I believe, the "seconds of day" system function. You can also type in any number you choose yourself. The deals are not "preset" in the sense of being deliberately chosen; they are the result of the algorithm Jim Horne used, and are as random as a computer can make them. The only way I know to get more random deals is to shuffle and deal an actual deck of cards. The actual C code used by Jim Horne is available, with Jim's kind permission. FreeCell Pro and a number of other programs for various platforms can produce the same set of 32,000 deals as in Microsoft FreeCell.

* I have played hundreds of the games randomly and started keeping a log by game number. But I notice that I never seem to win one twice. Does the game automatically turn up games which have not been won?

No. The Microsoft program does not keep track of games which have been played (whether won or lost). The New Game (F2) function picks games entirely at random. If you have kept track over 200 games, there is still a 53.2% chance of seeing no repeated game numbers. For 400 games, the chance drops to 8.2%; for 600 games, to 0.35%; for 800 games, to 0.004%. So if you continue to keep track, you should eventually see a repeat if you play enough games.

* How can I get the solution to a hard game I can't solve?

Check the index of the catalog of over 425 solutions (both the index and the catalog are in numerical order) to see if the solution you are looking for is there. It contains nearly all of the hardest deals. I acted as a volunteer solver until July 2, 2003. I am no longer doing so, but I will provide a solution to any solvable FC deal for a nominal fee of $5. E-mail me to ask for a solution to the game you want.

* Why am I finding deal number xxxxx difficult when it isn't on any of the lists?

Since a large number of people start at deal number 1 and work their way up in sequence, most of the lists of "difficult-to-solve" deals are bottom-heavy, with lots of low-numbered deals. One of the few lists which covers the whole range of 32000 is from Dave Ring's Internet FreeCell Project, but blocks of 100 were assigned randomly, and a deal may not have been reported as difficult there because the solver who got that block was an expert solver, or just didn't bother to report which hands he/she found difficult. So a deal may be very difficult even if it doesn't appear on any of the usual lists. Another point is that difficulty is somewhat subjective -- two solvers will not necessarily find the same deals hard. Most lists are compiled by one person or group, and most of those people/groups haven't tried every deal. There are some obvious things (depth of aces) to look for, but the best way I've found so far to objectively measure difficulty is to determine how many freecells are needed to solve a particular deal (FreeCell Pro is equipped to do this). FC 11982 requires five freecells to solve (i.e. it is impossible with the standard four freecells); only about one deal in 150 is difficult enough to require the standard four (most of these appear quite difficult to human solvers, so it seems like a reasonable measure). Surprisingly, it's only a little harder to solve many deals with three freecells rather than four, and FCPro lets you do this. Most hands (about 79%) require two freecells or fewer; any deal requiring at least three freecells is well above average in difficulty:

* Has anyone found a solution for Freecell xxxxx? It seems awfully difficult because of the remote positions of the aces.

The depth of aces is a relatively weak measure of difficulty. 14652 (one of the deals this question was asked about), despite 16 cards covering the aces, is only a little above average in difficulty, though it's pretty hard to solve with two freecells. The average deal has slightly more than 11 cards (576/52 = 11.077) covering the aces (possibly including other aces). Although the impossible 11982 has 22 cards covering the aces (close to the maximum 24), the hardest of the 31,999 solvable deals, 1941, has only 14, less than some of the zero-freecell deals. 617, which is nowhere near as hard as its reputation (and much easier than 1941), has 20, the same number as 164, which is a zero-freecell deal. The 69 zero-freecell deals average 8.41 cards covering the aces, only a few positions shallower than average.

* I have a streak of xxxx wins in a row and have won xx% of the games I have played. How does that compare to other players?

Since the statistics in Microsoft FreeCell can be easily altered, and you can escape from lost deals without recording them, there seems little point in collecting records on the honor system. (Unless you erase statistics and start over, your overall winning percentage may be a better indication of how quickly you became good at FreeCell rather than how good you are now. The more deals you play, the more slowly your overall win rate will change. Once you have played thousands of hands, it takes much longer to push your average up very much.) If you're really interested in comparing yourself to other players, try NetCELL, an on-line (Java) version of FC with has lots of features in addition to keeping records of streaks, win percentage, and average time. NetCELL has recently moved to a new server, and now holds free on-line tournaments daily (with a prize tournament each weekend). Using NetCELL for comparison, I would say that you need to be winning 95% of FC deals on the first try to be considered a top-notch player. 85% is a reasonable level for a good player. A number of streaks of over 1000 have been recorded on NetCELL, but I would consider anything over 100 excellent in any standard version of FreeCell.

* Are all of the solutions in the catalog correct?

Adrian Ettlinger has run the entire catalog through FCPro's replay function, and all of the errors it found have been corrected. There should be no incorrect solutions. We frequently get claims of errors, but none of these has turned out to be correct except for one report of a solution which was missing a couple of moves at the end.

* Why won't you post every new solution submitted?

Because there isn't room for solutions to all 32,000 deals. Most of them aren't interesting anyway: with reasonable experience almost anyone can solve about half of the deals on the first try. Actually we aren't currently soliciting any submissions of new solutions, and have removed some of the easier deals (like most of those from 11 to 52, leaving 1-10 for beginners). Mainly the catalog is intended to contain solutions to very hard deals, although solutions to a few deals using zero and one freecells are included, as well as curiosities like 52-card flourishes. For quite a while we didn't add any new solutions, but have just started adding solutions to deals requested more than once.

* Why won't you post improved (shorter) solutions in the catalog?

There are several reasons. First of all, it would mean extra work for me, and wouldn't do much for anyone except the person sending in the improved solution, who would get to see his/her name there. (For some reason, 617 is the champion here too -- I have received quite a few submissions shorter than the catalog solution, but I have even shorter ones in my files which I have not bothered to publish). But the catalog was never supposed to be a competition; the main purpose is to give solutions to hard deals so that people who are stumped by a particular deal can look up a solution. For that purpose, any decent solution will do. Another point is that minimum-length solutions are likely to be tricky rather than elegant -- solid technique will usually not help you find shorter solutions; playing around and cutting corners may. One of the reasons I stopped playing Championship FreeCell is that if someone is the first to post a 2-freecell solution to a particular deal, and someone else posts a shorter solution, the original poster loses all credit whatsoever for having posted it -- so there is little incentive (from a competitive point of view) to investigate and find the minimum number of freecells needed to solve a particular deal for which no solution has been posted -- it's better to steal deals from someone else, especially if they are ahead of you in the rankings. Championship FreeCell also counts every individual card move in determining shortest solutions, which discourages long sequence moves and further encourages loose play such as moving every possible card to the foundations.

* Which deal is the easiest? Are there any deals in which all of the cards go automatically home at the start?

A deal where all of the cards go home at the start is easy to construct, but it is fantastically unlikely for such a deal to occur at random, since Microsoft FreeCell or FreeCell Pro only plays an available card to its homecell automatically when all of the lower-ranked cards of the opposite color are already on the homecells (except that a two is played if the corresponding ace is on its homecell); aces are always played when available. This is one version of what can be called safe autoplay. NetCELL uses a more aggressive rule, making all of the plays that MS FreeCell makes, but also playing an available card if both homecells of the opposite color are within two ranks of that card and the homecell of the same color and opposite suit is within three ranks. For example, in NetCELL 28865-5, the four of diamonds is played as soon as the three of diamonds, both black twos, and the ace of hearts are on the homecells. The reason for this is that the four of diamonds is not needed on the tableau to hold either black three, since both can go to their homecells as soon as they are available, and the black threes are not needed to hold the two of hearts, since it can also go to its homecell as soon as it is available. (NetCELL plays as many cards as possible under this rule as soon as the cards are dealt; in 28865-5 ten cards go to the homecells at once. MS FC and FCPro don't do anything until the player moves the first card).

In order for a deal to have all 52 cards go to the homecells at the start (or even after one play), every column would need to be in (nearly) descending order of rank. There are no automatic deals even in the 8-billion-plus FCPro deals. The 32,000 Microsoft deals include 69 deals which can be won using no freecells at all. The largest number of cards which go to the homecells at the start of any of these zero-freecell deals is six (including all four aces), in deals 9998 and 11987 (a zero-freecell solution to 11987, which is in the catalog, is unusually short, at 36 moves). It's possible to get quite a few more cards to the homecells with a minimal amount of moves in both games, and these seem the two most likely candidates for the title of "easiest deal". Mike Dykstra found a one-freecell deal, number 8695, where seven cards go to the homecells at the start. Bill Raymond found another one-freecell deal, 27245, where eight cards go at the start -- ten cards would go if it used the NetCELL rule. 27245 is slightly more remarkable than NetCELL 28865-5, since NetCELL uses a special algorithm to make deals harder or easier (see next question); a level five deal is more likely to have aces and other low-ranking cards at the bottoms of columns than a completely random (level 10) deal.

Bill Raymond wrote a program to search for FreeCell deals in which large numbers of cards go to the homecells on the first play (using Microsoft's autoplay rule). His search of the 32,000 Microsoft deals turned up no other eight-card deals, and only one other seven-card deal (22265) in addition to the deal (8695) previously found by Mike Dykstra. All three of these are one-freecell deals. Bill extended the search through some of the FreeCell Pro deals: The first nine-card deal is 270618; this requires two freecells to solve, but is fairly easy. The first 10-card deal is 2710330, a hard one-freecell deal. The first 11-card deal is 3060287, a very hard zero-freecell deal. If you're looking for an extremely easy deal, try 22350203, an 11-card deal which is very easy even with zero freecells (my solution is only 35 moves).

The first 12-card deal is 12172106, a medium-hard one-freecell deal. The first 13-card deal is 17332733, another hard zero-freecell deal.
The first 14-card deal is 181627041, an easy one-freecell deal. The first 15-card deal is 143973501, a hard zero-freecell deal.

The autoplay rules used by NetCELL sometimes allow many more cards to be played initially. There are no large increases in the 32,000 Microsoft deals (deal 27245 plays 10 cards, and 2217 and 22265 play 8 each). The most extreme case Bill found is 1195233675, in which the simple Microsoft rule plays six cards to the homecells, but the NetCELL rule plays twenty-three! This is a zero-freecell deal, and might be the easiest in the entire 8-billion-plus FCPro deals. Another interesting deal found by Bill is 446806382, another zero-freecell deal, which plays only four cards using the MS rule but 16 using the NetCELL rule.

Joe McCauley independently wrote a program to count how many cards were autoplayed, and extended the search through the entire 8 billion-plus FreeCell Pro deals. He also checked to see how many cards could be played to the homecells if *every* possible homecell play was made (Joe calls this AllPlay): three of the 32,000 Microsoft deals (4196, 5319, and 27245) play 10 cards using AllPlay, with one other (27403) playing 9. Interestingly, 4196, 5319, and 27245 are all one-freecell deals, but 5319 *cannot* be won with one freecell if you play all ten cards immediately to the foundations! (Playing nine works, but the four of hearts is needed for packing.)

Using the Microsoft rule, there are five deals in which 16 cards play to the homecells (2016704153, 3453036771, 4418013924, 5856288588, and 8110636965). The first deal to break 16 using NetCELL rules is 1000572852, which plays 17 cards (only 5 in MS) -- despite 17 cards played and a whole column emptied, it cannot be solved with zero freecells, though it's not hard with one. 4418013924 plays 19 using the NetCELL or AllPlay rules. Using the NetCELL rules, two other deals play 19 cards (2178166022 and 2587385892), well short of the deal mentioned above which plays 23. Using AllPlay, three other deals play 23 cards (2587385892, 4931624547, and 7372172513) -- the last two play only four and six respectively under both MS and NetCELL rules. But two deals play more than 23 using AllPlay: 8305804964 plays 25 (only 5 under MS and NC), including all of the diamonds; 7841153263 plays 28, the only FCPro deal in which half the deck can be played at the start. Except for 1000572852, all of the hands mentioned in the last two paragraphs can be solved with zero freecells.

Some other curious statistics: slightly over half (50.15%) of all deals play no cards initially to the homecells (remarkably close to the theoretical value 19393/38675 = 0.50144). Another 30 percent (30.38%) play one card; another 14 percent (13.57%) play two (slightly less, 12.6%, with AllPlay); another four percent (4.38%) play three. Slightly over one percent play four or more; slightly over one in a million play ten or more using the MS rule (about four in a million in NetCELL and thirty-six in a million using AllPlay). It seems likely that the odds against all 52 cards playing automatically in a random deal are astronomically high; even if five percent of random columns are sufficently well-ordered, the odds are more than 25 billion to one against a complete deal playing automatically. Even with AllPlay rules, only 38 FCPro deals play 20 or more cards to the homecells.

3. Variations and Related Games

* I'm getting awfully good at FreeCell. How can I make the game more challenging?

The only drawback to FreeCell is that about half the deals are pretty easy once you're experienced. Naturally you can try the lists of difficult deals. Dennis Cronin's NetCELL, an online Java version of FreeCell, has an ingenious algorithm to make hands harder or easier (on a scale of 1-20), by dealing more high cards at the tops of columns and low cards at the bottoms of columns (and vice versa). There is a very competitive list (with hundreds of players), ranked by consecutive wins. The server also keeps track of winning percentage and average solving time for each player. NetCELL also now has a number of variant games, ranging from 6 to 10 columns wide, and from 2 to 6 freecells available. Almost certainly some of these are too hard or too easy, but the 10x2 (10 columns of 5 or 6, two freecells) and 6x6 (6 columns of 8 or 9, six freecells) are interesting. In each game, you start at level 5 (pretty easy), and go up one level after every 10 consecutive wins, until you reach level 10 (random deals) after 50 deals. I've managed 50 in a row in the standard 8x4 game; the all-time best streak (still current) is over 5000 (in order to break into the current top 100, you need to win over 90 in a row)!

If solving with four freecells is too easy, why not try two or three? This option is available in NetCELL, as well as several Windows 95 versions of the game, including FCPro and Championship FreeCell. The people at Championship FreeCell estimated that nearly all games (about 99% judging from their first sample of 500 games) can be solved with only three freecells, about 80 percent with two freecells, and perhaps 15 percent with one freecell (see section 5 for more precise statistics). Thomas Warfield's solitaire compendium package Pretty Good Solitaire, an excellent Windows shareware program with over 200 solitaire games (including FreeCell), includes the Solitaire Wizard, a system which lets you define your own games by setting a handful of parameters. It is simple to use this to set up FreeCell or Baker's Game with any number of freecells up to 8, and with variable column widths. I first saw these options in a shareware version of FreeCell for Windows 3.1, written in 1992 by Marc L. Allen. I expect it must still be available somewhere on the Internet, but I can't give you a current URL. Pretty Good Solitaire also lets you change the rules so that only kings may be placed in empty columns; I think this loses some of the flavor of FreeCell, but it certainly makes the game more challenging (I don't know yet how it affects the win rate). Pretty Good Solitaire also has a game called Challenge FreeCell, in which all of the twos and aces are automatically dealt to the tops of the columns. This makes the deals harder to solve, but almost all of them are still solvable.

* Is it possible to win without using the freecells?

Yes, but very rarely. Remember that cards can only be moved one at a time unless you have enough freecells or empty columns to move sequences, so a zero-freecell deal means, among other things, that you can never move more than one card at a time unless you can clear out an entire column, which will allow you to move two-card sequences, etc. (see the discussion of supermoves below). Wilson Callan had received several claims of deals which could be won without using any freecells at all (even temporarily during sequence moves), but we were unable to verify any of these reports. When the Don Woods solver used in FreeCell Pro was modified to allow zero freecells, the solver contradicted every claim received of a win without using freecells. Under the strict conditions of zero-freecell play, it is surprising that any deals can be solved, but remarkably, it turns out to be possible to win roughly one out of 500 deals with zero freecells (my solution, found by hand, to 1150 is posted in the solution catalog). A complete analysis of the 32,000 standard deals using four different solvers shows that 69 are winnable with zero freecells:

164, 892, 1012, 1081, 1150, 1529, 2508, 2514, 3178, 3225, 3250, 4929, 5055, 5152, 5213, 5300, 5814, 5877, 5907, 6749, 6893, 7018, 7058, 7167, 7807, 8355, 8471, 8961, 9998, 10772, 11863, 11987, 12392, 12411, 12676, 13214, 13464, 13532, 14014, 14624, 14826, 15140, 15196, 17772, 17871, 18026, 18150, 18427, 19951, 20533, 21657, 21900, 22663, 23328, 24176, 24919, 25001, 25904, 26719, 27121, 27853, 28856, 30329, 30418, 30584, 30755, 30849, 31185, and 31316.

Playing with no freecells makes the game a much harder form of the standard solitaire Streets and Alleys, with alternate-color packing instead of packing regardless of suit. It's actually much more likely, when playing with zero freecells, to have no moves at all from the initial position. In about 3% or 4% of deals it is impossible to make any moves at all without any freecells (36 deals out of the first 1000 are blocked at the start -- see deal 2 for example). Dozens of people have written claiming to have solved other deals without using the freecells, but invariably they are playing with Microsoft FreeCell and are using the freecells temporarily for moving sequences. If you really want to play without freecells, you can do so with FreeCell Pro.

* Is it possible to get all 52 cards to the homecells at once?

Yes. While I was participating in Dave Ring's project, I noted that some deals ended with 40 or more cards going to the homecells at the end of the game (called a flourish, cascade, or sweep -- the latter term coming from peg solitaire). The best I managed was 47 cards. George W. Edman discovered a number of deals on which he could end with a 50-card flourish: 7329, 7851, 15824, 23600, 26963, 31126 (game found by Carol Philo), and 31637. Edman's solution to 7851, remarkably short at 35 moves, is found in the solution catalog. Since the standard version of FreeCell plays aces automatically to the homecells as soon as they are available, these games depend on having two aces buried at the bottom of the same column, and arranging the remaining cards into sequence before uncovering the last two aces. But in March of 1998, Andy Gefen found the ultimate: a 52-card flourish. After noticing that deal number 18492 had four aces at the bottom of column six, he realized that if he could get all of the other cards in order without moving the seven of diamonds which covers the aces, he could achieve the 52-card flourish! He was able to do so after considerable effort, and his solution is now available in the solution catalog. Dave Leonard later found a second 52-card flourish, 22574 (with a different arrangement of aces), and a 51-card flourish, 765. Brian Barnhorst found a third 52-card flourish, 7239, Dave found a fourth, 23190, and Kenneth Goldman found a fifth, 16508. All of the solutions to these 52-card flourishes are found in the catalog. Ben Johannesen found five more, 9993, 10331, 12387, 17502, and 27251. Jason A. Crupper found 18088, and then used Jim Horne's dealing code to write a program to search the 32,000 standard deals for more candidates. He found six more for which he was able to find solutions: 7321, 8536, 16371, 28692, 29268, and 29640. This brings the total to seventeen. Jason found two other possibilities, but writes: "14150 and 26852 have the right setup of aces, but also present extreme strategical difficulties, enough that I suspect that they are unsolvable, in the same way that 11982 is unsolvable".

A related variation, which does not depend on any special arrangements of the cards, is to play without moving any cards to the homecells (foundations), trying to arrange the cards in four ace-to king sequences on four of the empty columns. (This idea may have come from the solitaire Spider; it also can be used in Yukon and other games). This Spider variant is very difficult, and I do not know what percentage of games can be solved in this way. FreeCell Pro now allows you to play the Spider variant, but you cannot play the Spider variant in the Microsoft version, or any other version where autoplay is automatic and cannot be turned off. The Warfield and Allen programs mentioned above both allow it, as do some other programs. In a future section of the FAQ we'll look at the various versions of FreeCell and eventually there will be a table of comparative features.

* Can a card be played once it has been placed on a homecell?

No. In the standard form of the game, cards which are played to the homecells must remain there. Some variations of solitaire (e.g. Giant, a variant of Miss Milligan), specifically allow cards to be played from the foundations back to tableau columns (in English solitaire parlance, this is called worrying back). It doesn't make sense in games such as Baker's Game which pack in suit, but there's no reason why it couldn't be allowed as a variant in FreeCell. Pretty Good Solitaire is the only major FC program I'm aware of which allows worrying back. Worrying back has a very small influence on the win rate, at least in the standard four freecell game: Tom Holroyd has done some computer analysis and found that worrying back a card onto an occupied column allows 11 of the 126 impossible deals up to 20 million to be solved. 11982 is still impossible, though.

* What are some other solitaires closely related to FreeCell?

In the brief section on history, we mentioned Baker's Game, the in-suit relative of FreeCell, as well as much older predecessors like Eight Off. Baker's Game and FreeCell are the two most interesting games, in my view, since they allow any card to be moved to an empty column, so that the emphasis is on building sequences on the tableau, rather than moving cards to foundations as quickly as possible. But two other modern variants of Eight Off are also worth mentioning:

(1) Seahaven Towers, invented by Art Cabral, which resembles Eight Off, except that there are ten columns of five cards each, with the two remaining cards dealt into two of the four available depots (freecells). This first appeared as a Macintosh game, but versions for Windows (and probably other platforms) are easy to find. Don Woods' solver estimates the win rate to be slightly over 89%.

(2) Penguin, invented by David Parlett, and found in several of his books (Teach Yourself Card Games For One, published in 1994 is excellent and is in print). It also appears in a number of compendium programs, including Pretty Good Solitaire and Solitude. Penguin is an interesting variant of Eight Off, with seven columns of seven cards, and seven depots. The first card dealt to the first column is the foundation base, and the other cards of the same rank are played immediately to the foundations as they are dealt. Sequences in suit can be moved from pile to pile without requiring depots; this is an exception to the usual rule in games of the Eight Off family. Mark Masten modified the Woods solver and ran fifty million random deals, estimating the win rate at 99.94%, slightly harder than FreeCell but slightly easier than Eight Off (99.88%).

Thomas Warfield, author of Pretty Good Solitaire as well as other solitaire packages, has started a FC page which includes links to various sites, including ours, and a few of the computer versions of FC, including Warfield's packages FreeCell Plus (a Windows 3.1 package with FC and seven other related solitaires) and FreeCell Wizard (a Windows 95 package with 13 games and a modified version of the Solitaire Wizard, which allows players to set up games with a variety of rules variants). Both FreeCell Plus and FreeCell Wizard include Eight Off, Baker's Game, Penguin, and Seahaven Towers.

4. Computer Versions and Features

* What is FCPro? What can it do that most other programs cannot?

FreeCell Pro is a Windows 95 version of FreeCell written by Wilson Callan and Adrian Ettlinger (available free at our site). FCPro was originally written in 1997 for the purpose of automatically recording solutions to interesting deals as they are solved by the user. The first version was a "tracking" program which ran while the user was playing the standard Microsoft FreeCell. It read mouse clicks, interpreted them, and correctly recorded solutions according to the standard FC notation devised by Andrey Tsouladze. In correspondence with Jim Horne, I asked about his algorithm for generating random deals, and he sent me the full C code for the dealing routine. There's nothing particularly tricky about it; a clever programmer could probably work it out by trial and error. But Jim kindly allowed us to incorporate the code into FCPro, and this allowed us to recreate the entire set of 32,000 deals of the Microsoft version (e.g. 11982 is unsolvable in FCPro too). Adrian later realized he could create a larger range of deals using a different storage type for the deal number, and extended the range of deal numbers to over 4 billion. The first 32,000 are the same as those in Microsoft's standard version, and the first million are the same as in the Microsoft XP version released in 2001. Having Jim's dealing code and the FCPro solution-recording function allowed us to save (and later check) solutions to the standard deals. I used FCPro to record and send to Wilson dozens of my solutions to difficult or interesting deals.

The next big leap forward for FCPro occurred when Don Woods sent us the C code for his automatic solving program. He had used this to analyze one million random deals, and found that all but 14 were solvable. Adrian incorporated the code into FCPro, and added a function to allow a range of hands to be automatically processed. He also added some sorting routines to rearrange the eight starting columns according to various schemes; this frequently allowed the program to quickly solve a hand which otherwise proved difficult. Another feature in the program allows the user to select any number of freecells from 0 to 7 -- this works with both the manual play function and the automated solver. FCPro also includes a Next Game function (F5) which allows the deals to be easily played in sequence, a new Options menu which allows player preferences to be saved in the program registry, and a Custom Game function which allows any possible deal to be entered through a simple text file. FCPro also runs under Windows NT/2000 and Windows 98/ME.

If you play FC using FreeCell Pro or Windows XP FreeCell, let me offer the following deal as a challenge: 80388. It is solvable, but it is the most difficult deal I have yet found outside the first 32,000.

* Is it cheating to use computers?

Well, most of us are using a computer to deal and keep track of the hands, and FCPro can record solutions automatically. I think it is quite reasonable to use a computer to do things which would be impossible, tedious, or time-consuming to do otherwise. The Internet FreeCell Project took 110 people to finish; Adrian Ettlinger did more than 300 times as many deals alone using FCPro and his computer. The variable-freecell solver makes it possible to categorize random deals into six groups based on a rough difficulty rating, while leaving the more interesting task of actually solving individual deals to humans (all of the solutions in the catalog were found by humans without computer assistance).

* Is there a version of FreeCell for Macintosh or other systems?

While there are probably at least a dozen in Windows, I know of four versions for Macintosh: David Bolen's Super Mac Freecell, Rick Holzgrafe's Solitaire Till Dawn (which includes FreeCell among its 40 games), and Eric's Ultimate Solitaire (which includes FreeCell among its 23 -- also available for Windows 95), and Ingemar Ragnemalm's new Solitaire House (which includes FreeCell among its 32). I have no access to a Macintosh, and have only seen Solitaire House and Super Mac FreeCell, both of which run on experimental Macintosh emulation programs. I have also not seen the versions of FreeCell available for Amiga, OS/2 (both of these links have unfortunately disappeared), and Clipper. If anyone has played these and can comment further on their features, or knows of other versions of FreeCell, please let me know. We will be writing up versions found in various Windows packages when we have time, including the Windows 95 version Xcell, and two other Java versions from Hriyadesh and Jean-Francois Bustarret. There is also a version of FreeCell (and other solitaires) for Web TV, from Epsylon Games; this does not work well on an ordinary browser, and I have received conflicting reports on how well it works on Web TV. If you have Web TV and try it, please let us know. [Note: as of December 2001, the site is not working at all.] A package which runs on a wide variety of platforms is a new edition of the Solitaire Antics package by Masque Publishing. The new edition, on CD-ROM, has 50 games, including FreeCell, and runs under Windows 95/98/NT, Power Macintosh, Windows CE, and Palm OS (the latter two allow it to run on many handheld PCs).

* Are there any handheld versions of FreeCell?

MGA Entertainment has released a handheld FreeCell, selling for $15-16 retail. I wish I could say it was well done. The screen is tiny (about 49x42 mm), and is in color (but the suits are red and white and it is easy to mistake hearts for diamonds and clubs for spades). There are apparently only about 1000 different deals (the reason for this limitation is not clear), and they are not numbered. The interface is somewhat clumsy, requiring multiple buttons to be pushed for many simple operations such as moving sequences (the whole sequence must be selected with a roll up button) and moves from freecells other than the lefthand one (similar to keyboard notation). Only six cards per column can be displayed, and the roll up button must be pushed to view deeper cards. Another handheld version has appeared from Radica (about $20 retail), but this version is even worse than MGA's; it displays only four cards per column and uses a thumbwheel to scroll deeper in the columns.

There are also a number of FreeCell packages available for handheld and palmtop PC's including the HP, Psion and Palm Pilot. In fact there are now at least three versions of FreeCell for Palm Pilots: one from Electron Hut (this has the same deal numbers as Microsoft FC), another called Acid FreeCell from Red Mercury, and a new portable version of NetCELL. Microsoft makes a version of the Windows Entertainment Pack (including FreeCell) for the Windows CE operating system, for $34.95. This runs on various handheld PCs (H/PC) such as the Hewlett Packard HP360/620 LX and Sharp Mobilon (I don't have a current link -- MS keeps moving the page -- but it should not be hard to find in retail stores or online vendors).

I have also seen a countertop version of FreeCell (this is a touchscreen unit, similar to a video game, which can be found in restaurants and bars). The version I saw was called QuickCell, and is one of the games offered by Merit Industries' Megatouch XL unit (a bit pricey for home use, at $3195). Another touchscreen version of FC is found in the JVL Concorde 2 by J.V. Levitan Enterprises, Ltd.

ElectroSource International has published a version of the Microsoft Entertainment Pack (including FreeCell) for the Color GameBoy. Jeffery K. Hughes, the programmer for ESI's version, notes that the deal numbers in this version match those of the standard Microsoft Windows version exactly. Interplay published a package (written by Beam Software), Solitaire FunPak (about $20), for GameBoy and GameGear, with 12 solitaires, including FreeCell, but this now appears to be out of print. If anyone knows of other versions of FreeCell for video games (Nintendo N64, Sony Playstation, etc.), please let us know. It's been years since I played any video games (Intellivision and the original Nintendo), and I have no idea whether there are any other solitaire card games for them.

* What other computerized solvers exist?

Don Woods also wrote versions of his solver to analyze the related solitaires Seahaven Towers and Baker's Game; Mark Masten has modified these to analyze Eight Off and Penguin. Shlomi Fish has a solver available at his home page (it is written in C and runs on various platforms, including DOS). It has many features and can solve deals from FreeCell and a variety of solitaires related to FreeCell.

There are a number of other FreeCell solving programs; none of those I have seen appear to be as fast or powerful as the programs mentioned above. Lingyun Tuo wrote a solver as part of his Autofree program. Luc Barthelet wrote a solving application (notebook) for the analysis package Mathematica. XCell also has a built-in solver.

5. More Statistical Facts and Curiosities

* How often can I win?

Adrian Ettlinger, using Don Woods' solver with some extensions of his own, has analyzed 20 million deals, starting with the standard 32,000 of the Microsoft version, and continuing on through deals numbered up to 20,000,000 (using the same random number scheme as Microsoft FreeCell, thanks to Jim Horne). This analysis was primarily carried out with the program FCPro, written by Ettlinger and Wilson Callan. Of the first 10 million deals, 126 are unsolvable in the standard four-freecell game:

11982, 146692, 186216, 455889, 495505, 512118, 517776, 781948, 1155215, 1254900, 1387739, 1495908, 1573069, 1631319, 1633509, 1662054, 2022676, 2070322, 2166989, 2167029, 2501890, 2607073, 2681284, 2712622, 2843443, 2852003, 2855691, 2923820, 3163790, 3172889, 3194539, 3217820, 3225183, 3366617, 3376982, 3402716, 3576395, 3595299, 3878212, 3946538, 4055965, 4207758, 4266168, 4269635, 4324282, 4334954, 4440758, 4446355, 4765843, 4863685, 4910222, 5046726, 5050537, 5086829, 5225172, 5244797, 5260342, 5401675, 5478410, 5611185, 5672090, 5817697, 6020049, 6099064, 6100919, 6234527, 6314799, 6332629, 6416342, 6749792, 6761220, 6768658, 6844210, 6895558, 6898316, 7035805, 7261039, 7334559, 7360592, 7400819, 7484159, 7497878, 7530003, 7536454, 7801943, 7814345, 7825750, 7863486, 7887312, 7923001, 7965413, 8000527, 8046431, 8076134, 8104908, 8105324, 8114984, 8119415, 8121228, 8237732, 8267373, 8354257, 8381178, 8527378, 8608154, 8712426, 8719444, 8736337, 9093368, 9110337, 9190487, 9222830, 9262134, 9414989, 9415104, 9435589, 9452398, 9626317, 9647001, 9660366, 9747437, 9771903, 9830419, 9855268, 9861848, 9917279.

Of the first 20 million, 263 are impossible, a win rate of nearly 99.999%, or about 1 loss in 76,000 deals. Most notably, we verified the result of the Ring project: all but one deal (11982) of the 32,000 standard deals is solvable! No more unsolvables turned up for more than 100,000 more deals. Eight of the one million deals in FreeCell for Windows XP are unsolvable.

A more difficult variant of FreeCell, as mentioned above, is to play with fewer than four freecells. Even with three freecells, approximately 99-1/3% of deals can be won (200 of the first 32,000 cannot be won with three freecells; Ettlinger also ran another segment of some 67,000 deals with a similar win rate). The deals below 1000 which require four freecells to win are: 169, 178, 285, 454, 575, 598, 617, 657, 775, 829, and 988. A full list is in the lists page.

Based on analysis of the first 32,000 deals, we can also give tentative results for smaller numbers of freecells. With two freecells, the win rate is about 78 or 79% (at least 25,100 of the first 32,000 deals are possible), and with one freecell, the win rate is about 19% (at least 6075 of the first 32,000). The win rate for zero freecells (discussed in section 3) is about 0.2%.

* How many freecells are needed to solve any possible deal?

At least seven, it appears. All of the 126 impossible deals in the first 10 million can be solved with five freecells, including of course 11982. I looked at a number of other constructed deals, including Hans Bodlaender's, the Microsoft joke deals -1 and -2, and others which have been posted at various websites and on Usenet newsgroups. All of them are solvable with five freecells. I was beginning to wonder if all deals were solvable with five freecells, when Adrian Ettlinger sent me a deal he constructed, which appears to be impossible with six freecells as well as five (confirmed with two different solvers). The arrangement of suits and colors is particularly fiendish. You can play this deal in FreeCell Pro by copying the lines below into a file and using the Custom Game option:

AE-Imp6
AC AD AS AH TD JD QD KD
6D 7D 8D 9D TH JH QH KH
6H 7H 8H 9H 2D 3D 4D 5D
2C 3C 4C 5C 2H 3H 4H 5H
2S 3S 4S 5S 6C 7C 8C 9C
TC JC QC KC 6S 7S 8S 9S
TS JS QS KS

Making extremely hard deals seems to require such effort that I suspected that every one of the 8,589,934,592 deals in FreeCell Pro could be solved with five freecells. This turned out to be wrong too: Tom Holroyd ran the 126 FCPro deals known to be impossible (with four freecells) through his solver, and number 14720822 turned out to be impossible with five freecells! This is the first known random deal to be impossible with five freecells (it is solvable with six).

David A. Miller has worked on making even harder deals than Adrian Ettlinger's, and has constructed some deals which may be impossible even with seven freecells. Here is one of his deals; Tom Holroyd's solver Patsolve says it is impossible, FreeCell Pro does not reach a conclusion:

Magic8
AS AD AC AH QS QD TS TD
5S 5D 3S 3D QC QH TC TH
5C 5H 3C 3H 8S 8D 6S 6D
9S 9D 7S 7D 8C 8H 6C 6H
9C 9H 7C 7H 4S 4D 2S 2D
KS KD JS JD 4C 4H 2C 2H
KC KH JC JH

* What is a supermove? How does it help in playing?

Every good computer version of FreeCell allows the player to move a sequence of cards all at once using vacant freecells as momentary storage locations. This can also be done in related games of the Eight Off family. But in FreeCell (and Baker's Game), where any card may be placed in an empty column, even longer sequences can be moved using a combination of empty columns and empty freecells. Normally a sequence one card longer than the number of empty freecells can be moved from one column to another, but this is doubled for every empty column (except for the destination column -- if you are moving *to* an empty column, that column does not count). For example, a four-card sequence can be moved with three empty freecells, but if there is also a vacant column, an eight-card sequence can be moved, putting the first four cards temporarily in the empty column (using the freecells), then moving the other four cards to the destination (using the freecells again), and finally moving the first four cards from the formerly-empty column to the destination (using the freecells a third time). Long sequence moves using empty columns as well as freecells have been called supermoves.

The most common and useful supermove situation is moving a four-card sequence from one column to another when there is an empty column but only one empty freecell. For example, if you want to move four cards from column 1 to column 2, with column 3 and freecell a empty, the sequence of moves one card at a time would be: 1a 13 a3 1a 12 a2 3a 32 a2. A move of this kind occurs at move 20 of the catalog solution to FC 617, and Richard Schiveley suggests that this is why so many people think the solution doesn't work -- if you are unfamiliar with supermoves, the move may look impossible, although Microsoft FreeCell carries it out with no difficulty.

FreeCell programs vary in their ability to use supermoves. Microsoft FreeCell uses it correctly when there is one empty column and at least one empty freecell, but fails to make the maximum use of more than one empty column. When there are no empty freecells, but multiple empty columns, it treats the empty columns as freecells (e.g. three empty columns can be used to move an eight-card sequence even without any freecells, but MS FC only allows four to be moved). FreeCell Pro now works correctly in all supermove situations.

* How many possible FreeCell deals are there?

Strictly speaking there are 52! different deals, about 8x10^67. However, deals can be transformed in several ways which make no mathematical difference, which cuts down the number a bit. The four left-hand (7 card) columns can be interchanged in 4! (24) ways, as can the four right-hand (6 card) columns. Also, suits can be interchanged in certain ways. If you swap suits so that all the black cards become red and vice versa (there are 4 ways to do this: SHCD can become HCDS, HSDC, DCHS, or DSHC respectively), the mathematical properties of the deal do not change; you can also maintain colors, but swap spades for clubs, diamonds for hearts, or both (3 more ways). So there are 576 permutations of columns (including no swaps) and 8 permutations of suits (including no swaps), which reduces the number of essentially different FreeCell deals to roughly 1.75x10^64 (a few rare hands will be identical under one of the 4608 transformations). The 32-bit integers used in FreeCell Pro and other programs can in theory generate 4294967296 deals (FCPro uses another trick to double this to 8589934592; it appears that these are all different).

* What is the fewest number of cards one can have left remaining and still lose the game?

Since there are 12 places to put cards (eight columns and four freecells), *any* position with 12 cards or fewer is winnable. With plausible but careless play, it's possible (though fantastically unlikely) to have 13 cards left and lose. Here is an example worked out by David A. Miller, which finishes with only spades left: