FreeCell -- Frequently Asked Questions (FAQ)

written by Michael Keller, Solitaire
Laboratory

This article is the result of more than 20 years of work by me
and
a small group of like-minded FreeCell enthusiasts. You may
freely link to it from your website, but please do not steal its
contents.

Thanks for questions and answers to:

Kate Ackley, Brian Barnhorst, David Bernazzani, Marion W. Berryman,
Bill Borland, Yuri Bortnik, Frank Bunton, Wilson Callan, Gary Campbell,
Vickie Caster, Mike Cochran, Dennis Cronin, Jason A. Crupper, Cheryl
Davis, Jason Dyer, Mike Dykstra, George W. Edman, Vince Egry, Adrian
Ettlinger, Karl Ewald, Shlomi Fish, Andy Gefen, Dan Glimne, Kenneth
Goldman, Micah Gorrell, John Hironimus, Tom Holroyd, Jim Horne, Brian Jaffe, Danny A.
Jones, Scott Kladke, Dave Leonard, Brenda Marriott, Martin E. Martin,
Mark Masten, Joe McCauley, Rick Mendosa, David A. Miller, Ryan L.
Miller, Mike Moak, Charlotte Morrison, Jonah Neff, Jo Ann Perry,
Madeleine Portwood,
Ingemar Ragnemalm, Bill Raymond, P.L. Richart, Dave Ring, John Ross,
Ronald P. Ross, Richard Schiveley, Greg Schmidt, Frankie Seidel, Laurie
Shapiro, Lowell Stewart, Judy Stratton, Terry Thomas, Thomas Warfield,
Brent Welling, George West, Don Woods, and Clinton Yelvington.

Please report any errors (even typos), broken links, omissions, or
suggestions for additional questions to me.

A catalog of selected solutions to the standard FreeCell deals, begun
by Dave
Ring and later maintained by Wilson Callan, is now located on this
site.
It is now a single file. It is retained for historical purposes,
as it contains a number of specialized solutions, including
zero-freecell and flourish solutions. There is at least one
complete catalog available elsewhere for the extended set of 1 million deals.

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 deals numbered? Are those deals random
or were they selected in some way?

* Does the program automatically turn up deals which
have not been won?

* How can I get the solution to a hard deal 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 deals 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?

* Can I play with a different number of columns?

* What is Ephemeral FreeCell?

* Is it possible to win without using the freecells?

* Why is it required to use freecells or empty
columns to move sequences?

* 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?

* What are some other programs which allow you to
play FreeCell?

* What are the minimum requirements for a good
computer version of FreeCell?

* 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?

* 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

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 Demon (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. Thanks to the people at Cyber1, a version of PLATO is available online (thanks to Mike Cochran for help), and I have been able to try out Alfille's original Free Cell (as it was spelled there). It does not have numbered deals (though users can save interesting deals and share them with the PLATO/Cyber1 community), but has options for 4-10 columns and 1-10 freecells, with a statistics page showing the overall win rates of the community of players. You need to register to get access, but registration is free.

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

*** 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 deal 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
(Accordion and Fortune's Favor, among others, are probably higher), 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, 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, Demon (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 led the voting in two online popularity polls for solitaire.
In David Bernazzani's poll on his Solitude site, FreeCell won 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 (i.e. Demon)
at 128. In Thomas Warfield's poll at the Pretty Good Solitaire site,
out of more than 850 votes, FreeCell won 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.

For some reason, FreeCell seems to have spawned an unusual number of urban legends (look up FreeCell on Yahoo! Answers, e.g.). We will try to dispel these legends here.

*** 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 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), was 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.
A new (2004) solitaire collection which includes FreeCell is *100
Best Solitaire Games* by Sloane Lee and Gabriel Packard (188 pp.,
$9.95, ISBN 1-58042-115-6, Cardoza).

*** 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?**

The Microsoft program flashes the blue title bar at the top when you
have exactly one available move. It puts up a text message only 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. But 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 player has 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 was the first
FreeCell program
I saw which detected many lost situations while a deal is in progress (Faslo FreeCell
Autoplayer, discussed later, can also do this passively; FreeCell
Pro can do so on demand).

**2. The Microsoft 32,000
* Can they all be solved?
**

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 deals with their friends, and also in the belief that some people would try to play sequentially through the deals; 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 deals, numbered -1 and -2. Horne purposely made his claim ambiguous in order to challenge people to find such impossible deals, 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, was Dave Ring's Internet FreeCell Project. In August 1994, Ring solicited volunteers on rec.puzzles, sci.math, 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 deals reported as unsolved to his best solvers. I didn't get involved in the project until November 1994, but still managed to solve 1,970 deals. The project was completed in April 1995, and all but one deal was reported solved! This is the famous number

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, and even later by me. I am no longer doing so, since there are complete catalogs of solutions available now; the catalog is still available as a kind of historical record. You can look in the index to find out whether a particular solution is included. Probably the first large-scale computerized statistical study, conducted by Don Woods in 1994, analyzed a million random deals. In 1995, 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 extended the number of available deals up to 1 million. The first 32,000 are the same as in earlier versions of MS FreeCell. The additional deals are the same as those in FreeCell Pro, Pretty Good Solitaire, and other programs. Eight of those one million are impossible.

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 among the first 32,000. 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

7D
AH AS TD 6C TC JH AC

2S
4H 2C 3C TH 5H 9C 7H

9H
KH 3H AD 9D 8S JD 7C

5C
4D 8C 6D QS 5D KS 7S

9S
8D JC 6H 4S 3S QH 2D

TS
QD 8H QC 2H 6S JS KC

3D
KD 4C 5S

Deal number 94717719

With solvers now having analyzed the first 100 million deals, a
new candidate for hardest has turned up. Shlomi Fish posted a
solution to deal number 94717719 which was over 200 moves long, in
which 7 spades are played to their homecell before any other aces are
freed, and the entire spade suit is run while only two clubs and no red
cards have been played to the homecells. He later got it to 139
moves. Gary Campbell cleaned it up a bit, down to 119
moves. Danny A. Jones used an older version of his solver
to get it down to 92 moves. Danny notes that it takes 40 moves
just to reach the ace of spades, while many deals are already solved by
that point:

#94717719 Danny A. Jones PRI solver 92 moves

13 6a 56 5b 52 51 57 5c 65 b6

78 7b 72 78 12 4d 74 a7 67 62

37 6a 64 c6 a6 1a 24 1c 12 17

14 a1 64 34 31 46 3a 32 36 36

a3 83 5a 5h 75 7h dh 7d 7h 42

87 d2 37 3d b3 83 8b d3 8d 8h

81 84 b8 38 78 18 4b 4h 1h b1

21 24 2b 2h 7h 27 2h 3h b3 43

47 42 48 4b a4 25 c8 2a 2c 2h

2d 28

*** How are the 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

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

No. The Microsoft program does not keep track of deals which have been played (whether won or lost). The New Game (F2) function picks deals entirely at random. If you have kept track over 200 deals, there is still a 53.62% chance of seeing no repeated numbers (if selecting from 32,000 deals). For 400, the chance drops to 8.2%; for 600, to 0.35%; for 800, to 0.004%. So if you continue to keep track, you should eventually see a repeat if you play enough.

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. Gary Campbell's solver, now built into the Faslo FreeCell Autoplayer, can often provide reasonable solutions to deals (more on this below). I acted as a volunteer solver until July 2, 2003. I am no longer doing so, but if you are desperate, I will provide a solution to any solvable FC deal (whether MS-numbered or not) for a nominal fee of $5. E-mail me to ask for a solution to the deal you want, though I don't suggest you pay for a solution to any of the first million FC deals, since you can now get them for free...

There is now a complete set of solutions to the first 1,000,000 deals (except for 11982 of course) on a new site based in Latvia, run by a gentleman named Yuri Bortnik (he replied right away when I asked about the site). The solutions all appear to be quite short, and the interface is very clean -- two clicks get you any solution up to 32000, and higher deal numbers can simply be entered in a search box. Yuri says that the "solutions are generated by computer. But a special human-friendly algorithm makes these solutions very sequential, logical and short of course." His longest solution is 53 moves, for deal 29596. Solutions are available in standard notation, or in a more detailed descriptive form. A very impressive job and a well-designed site. He has also added some stats on the first 64,000 deals, including a list of 0- and 4-freecell deals.

*** 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 deals 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

The depth of aces is a very 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), probably 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 8.51 cards covering the aces, only a few positions shallower than average. 52583 has all four aces available immediately, but requires the average two freecells to solve.

Pretty Good Solitaire includes a game called

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 deals, it takes much longer to push your average up very much.) If you're really interested in comparing yourself to other players, try

The all-time record on NetCELL is 20,000 (still active as of
December 19th, 2013) by a player called
PudongPete, who had earlier
posted the then-second-longest streak (now third) of 14,137 under the
name QingpuKid. The
previous record on NetCELL was 19,793, set by Bob K., a retired
chemist in the Atlanta area (under the name rgk5). He
previously had a record of 12,856 (now fourth-best) under the name
rgk1, which had
shattered the old record of 5301 by a player going by the name
Michelangelo. Bob started
playing around 1996, and has also had ten
other streaks of over 2000 wins. He did not record the deal which ended
his streak of 12,856, but says that the loss was due to a simple
mistake -- putting a red three on its homecell instead of on a black
four, and having nowhere to put a black 2 which was in a
freecell. A streak of over 1000 is needed to
make the top 100 all-time.

*** Are all of the solutions in the catalog correct?
**

Adrian Ettlinger ran 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.

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

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, with as few as 44 moves, which I never 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 (a competitive version no longer available) is that if someone was the first to post a 2-freecell solution to a particular deal, and someone else posted a shorter solution, the original poster lost all credit whatsoever for having posted it -- so there was 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 had been posted -- it was better to steal deals from someone else, especially if they were ahead of you in the rankings. Championship FreeCell also counted every individual card move in determining shortest solutions, which discouraged long sequence moves and further encouraged loose play such as moving every possible card to the foundations.

Until recently, little was known about the shortest solutions for deals. Danny A. Jones has used his various solvers to look for very short and minimal-length solutions for deals. With his standard Pri-DFS (prioritized depth-first search) solver, he originally found that all of the first million deals (except of course for the eight impossible deals) can be solved in 64 moves or fewer, using autoplay and supermoves as defined in MS FreeCell and FreeCell Pro. With his BFS (breadth-first search) and recursive-search Pri-DFS solvers, he later reduced this to only four deals for which he has not been able to find a solution of 50 moves or less; the longest is 57148 at 54 moves, followed by 739671 at 53 moves, and 255317 and 526267 at 51 moves each. When he extended his search to 25 million deals, all solvable deals could be solved in 66 moves or fewer. Solution length does not automatically correlate with difficulty (1941 has a fairly short solution), but most of the deals with the longest solutions are quite hard. For most deals, the solutions from his recursive solver are often considerably shorter than this at the price of memory and execution time. Danny was thinking at one point of creating a web site to post short solutions for FreeCell deals.

His BFS solver can sometimes (but not often, because of memory
limitations) find (probably) shortest solutions for standard
four-freecell deals. The caveat 'probably' is necessary because he uses
suit-reduction as a shortcut and can't guarantee a shortest solution.
As a simple example, his shortest solution for 1941 is 35 moves, only
one move shorter than K. H. Rodgers' solution in the catalog, which was
found by hand and dates back at least to 1997. For other deals, his BFS
solver produces more pronounced results. The shortest solution is not
definitely known for many deals: the shortest known solution to 617 is
41 moves (but can be shortened to 39 using full autoplay and
supermoves). Using a combination of his solvers and with maximal safe
autoplay (as in NetCELL) and supermoves (as in FreeCell Pro), he has
found 213 deals which can be solved in under 20 moves. The two
shortest, 15924803 and 17182509, are 13 moves each (even using the more
limited autoplay of MS FreeCell). Searching into the higher-numbered
FreeCell Pro deals, he has found five deals which his solver cannot
solve in under 60 moves; the longest solution of these is 24515390, at
66 moves. His BFS solver also solves zero-freecell deals. He has found
21,725 probably shortest zero-freecell solutions for deals in the first
ten million FCPro deals, plus an additional 24 deals later found by his
Pri-DFS solver.

*** 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

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 deals, 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.

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

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 deals 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

Danny A. Jones has analyzed the effect on play if AllPlay is mandatory. If every card automatically goes to its homecell as soon as it can, most deals can still be solved, though play can sometimes be tricky. His solver analyzed the first 32,000 deals, and although the solutions are a little longer on average (52.94 moves, compared to 46.33 with safe autoplay), almost every deal can still be solved. The only exceptions are 1941 (perhaps the hardest of the 32,000 deals) and 11982 (which is impossible anyway). Danny later ran 1 million deals in less than an hour. Besides the eight deals which are impossible anyway, only two deals, 1941 and 98714 (a hard four-freecell deal), cannot be solved with AllPlay. The average solution length is 50.29 moves, with a maximum of 79 moves.

**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 (of course you can try the lists of difficult deals). Dennis Cronin's

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 the defunct Championship FreeCell. The people at Championship FreeCell estimated that nearly all deals (about 99% judging from their first sample of 500 deals) can be solved with only three freecells, about 80 percent with

Another more challenging way to play is
to
allow only kings to be moved to empty columns (as in FreeCell's
ancestor Eight Off, and related games such as Seahaven
Towers). This means that empty columns cannot be used as extra
freecells, and supermoves are impossible. Pretty Good Solitaire allows you to
change the rules to allow this option, which PGS calls KingOnly. I
think that KingOnly loses some of the flavor of FreeCell, and only
slightly reduces the win rate. Danny A. Jones has analyzed the 32,000
MS deals and found that only thirteen deals cannot be won using
KingOnly: 617, 7477, 11982, 16129, 17683, 18192, 20021, 20630, 21491,
26693, 29230, 29377, and 31465. Nine of these are four-freecell deals
(20021, 20630, and 29377 can be won with three); 11982 is impossible
even under normal rules, of course. His solver does not reach a
conclusion with 14292 or 23017. Eventually I ran a modified
version of Danny's solver on the first million deals; this took 82
hours of computer time over a period of several weeks. Danny
reprocessed the intractables, getting definite results for a few. In
the first million deals, there are 518 impossible with KingOnly
(including the eight which are impossible anyway) and 25 intractable.

An avid player wrote to me and asked for a solution to a particular
deal. When I sent the solution and explained the notation, she replied
that she was surprised to learn that you were allowed to move cards to
the homecells manually. She had solved thousands of MS deals relying
only on autoplay to get cards to the homecells. Danny A. Jones suggests
this is actually an easy way to make the game slightly more challenging
(we'll call it **AutoplayOnly**), and has analyzed its
effect on the win rate. Amazingly, all but five of the 32,000 MS deals
can be solved with autoplay only: in addition to 11982 which is
impossible anyway, the deals which require manual moves to the
homecells in order to be solved (even with the more sophisticated
autoplay rules described above, as used in NetCELL) are 617, 1941,
4603, and 31465. Three of these are among the most frequently cited
hard deals; 4603 is a fairly hard deal as well. Danny comments that
this scenario makes his computer solver "act like it was pulling a fat
rhino through fifty miles of quicksand." Later he did a full
analysis of the first two million deals, finding 131 deals which can
only be solved with manual moves to the homecells, with seven
intractables and sixteen deals already impossible under standard
rules. Of these 131 deals, 96 require four freecells to solve
with standard rules; the other 35 can be solved with three
freecells. None can be solved with two, so it appears that
virtually all such deals are above average in difficulty. With the
autoplay rules used by NetCELL, 50 more deals (48 of the
impossibles and 2 of the intractables) can be solved with AutoplayOnly,
leaving only 83 impossible and 5 intractable.

Maybe one reason 1941 is so hard is that it is the only solvable deal found so far which is unsolvable with both AutoplayOnly and AllPlay -- you have to make manual moves to the homecells to win, but you can't make all of them, and must choose the correct ones.

Since some of the deals which are impossible with either
KingOnly or
AutoplayOnly are often cited as extremely hard, searching for such
deals by computer may be a way to generate lists of extra-hard deals,
or at least candidates for extra difficulty. Since both KingOnly and
AutoplayOnly make the game a bit harder, what happens if you use both
options? Danny's solver says that 164 of the first 32,000 deals are now
impossible (with 83 intractable). The list includes many of the deals
usually regarded as very difficult.

Pretty Good Solitaire also has
games called **Challenge FreeCell**, and **Super
Challenge FreeCell**, described above in the question about ace depth. PGS also has variations of FreeCell
for two and three decks.

*100 Best Solitaire Games* by Sloane Lee and Gabriel Packard
(ISBN 1-58042-115-6), includes FreeCell and several variants, including
**Bonus FreeCell**, a version of Eight Off with alternate
packing (in other words, it is ForeCell with four extra
freecells). It's hard to see how adding four more
freecells, even initially occupied with cards, makes the game better:
the win rate may actually be 100%. There are also two games with half
of the cards dealt face down; they are no longer what I would even call
FreeCell; if the game isn't open, you're playing a variant of Klondike.

Filling the four freecells with the last four cards (as in ForeCell but
without the KingOnly rule; empty columns may be filled as usual) is
another way of making the standard game harder. We
mentioned results found by Danny A. Jones in the earlier section on
ForeCell; he analyzed the first million deals and found that 878,429
are solvable (121,566 are impossible, 5 intractable), a win rate of
87.8%.

I originally thought of this idea when I was playing
13-column FreeCell with no freecells: what if I had one freecell, but I
could only use it
once?

This led to the general idea of playing with freecells that
vanish after you move a card out of them;
I call this version **Ephemeral FreeCell**. This has not been
investigated much, but should work particularly well with wider
tableaux. There is lots of
scope for experimentation with combinations of permanent and ephemeral
freecells (you could also prefill all or some of the permanent
ones). This feature is available in the FreeCell
Virtuoso program, which is
planned as a replacement for FreeCell Pro. Charlotte
Morrison pointed out to me that the idea of one-use freecells appears
in the Pogo game **Rainy
Day Spider
Solitaire**; it has also appeared subsequently in other
casual/adventure solitaires, such as **Mystery
Solitaire: Secret Island**. Not
only does adding ephemeral freecells greatly increase the number of
combination games, it adds some extra strategic thinking to the game --
when should I play a card to a permanent freecell, and when to an
ephemeral one?

But the main reason I hope that ephemeral freecells might be such a useful device is that they could enable deals to be placed into many more categories of difficulty, using computer analysis. At the moment, we can group standard eight-column deals into eight categories, based on the minimum number of freecells each deal can be solved with (0 through 7). We can say that a deal is very hard if it can be solved with four freecells (but not 3), and hard if it can be solved with 3 but not 2. But we don't have an easy way to distinguish between, for example, the difficulty of deals like 1941 or 10692 with run-of-the-mill four-freecell deals. But I imagined that a FreeCell solver with the ability to analyze Ephemeral deals might make it possible to determine that some four-freecell deals can be solved with 3 reals and 1 ephemeral, or even 2 and 2.

I asked Danny A. Jones for help, and he has begun adapting his solver to handle Ephemeral FreeCell. Danny did a run (on August 11, 2012) of the first million MS deals, using three permanent freecells and one ephemeral one. Besides the eight deals known to be impossible with four freecells, there are only four more which cannot be solved if one of the freecells is ephemeral: 255317, 412030, 707659, and 888541. I have done some more runs of a million deals of various scenarios using his solver. In the scenario with two permanent and two ephemeral freecells, there are only 30 additional impossibles. One permanent and three ephemeral is a little harder: 58 of the first 32,000 and 1932 of the first million are impossible.

What if all of four of the freecells are ephemeral? This
is somewhat harder work for Danny's solver: it took 16 hours to process
the first 32,000 deals, and 272 of them were intractable. 25484
of the deals, just under 80%, were solved, with 6244 definitely
impossible. So four ephemeral freecells is just a hair
easier than two real freecells, but there's surprisingly little
correlation between the impossible lists for 8x2 and 8x0e4: quite a few
deals are solvable one way but not the other. The first
four 8x2 impossibles (1, 6, 21, 25) are all solvable as 8x0e4; the
reverse is true of 4, 9, and 12. 32 is the first deal
impossible both ways.

We can also look at the deals impossible with four freecells. Danny determined that all eight of the 8x4 impossibles in the first million MS deals can be solved as 8x4e1. Below is a screenshot of 11982 about to be played using 3 real (orange) and 2 ephemeral (pink) freecells. A full solution is:

11982 8x3e2

2d 2a 2b 2c 2e 78 28 4h 32 43

23 12 42 a4 1a 14 c4 12 b8 32

1b 17 35 b1 3b 31 35 a1 74 7a

73 71 d3 84 8h 87 82 e2 b2 83

85 8b 86 b8 68 6b 68 b6 38 58

56 51 51 63 61 61 43 42 4b

*** Can I play with a different number
of columns?**

Yes (this can also be done, of course, in a hand-dealt game with real cards). Playing with various numbers of tableau columns goes back to Paul Alfille's original version of FreeCell on PLATO, which allowed for every combination from 4 to 10 columns and 1 to 10 freecells (some of these are either virtually impossible or ridiculously trivial, though many players like the easy games either for relaxation, or as variants to be played very fast). We will use NetCELL's notation MxN to indicate a game played with M columns and N freecells (e.g. 10x2 is ten columns of 5 or 6 cards and two freecells). Several other computer versions allow for changing the number of columns, including Marc L. Allen's 1992 version, which allows between 6 and 10 columns. NetCELL has a large assortment of variant games from 4 to 13 columns wide, with as many as 10 freecells for the extremely narrow games:

freecells

columns 0 1 2 3 4 5 6 7 8 9 10

13 * * * *

12 * * * * *

11 * * * * * *

10 * * * * * * *

9 * * * * * * * *

8 * * * * * * * * *

7 * * * * * * * * *

6 * * * * *
* * * *

5 *
* * * * * * *

4 * * * * * * *

The game is much easier with nine or more columns: Danny A. Jones has analyzed games with nine columns or more and found that all 32,000 of the standard Microsoft deals are solvable with nine columns, even with only three freecells (in the first million deals, there are 19 impossible deals with three freecells and none with four freecells). With ten or eleven columns, most games are solvable with one freecell and almost all with two. With twelve or thirteen columns, most games are solvable with zero freecells and almost all with one. There are no impossibles in the first million deals at 10x3, 11x3, 12x2, or 13x2.

We now have some results for Ephemeral FreeCell.
The thirteen-column game is winnable almost 95% of the time with no
freecells (there are 51,531 impossibles in the first million).
With a single ephemeral freecell, only 29 deals are impossible (none in
the first 32,000: the first one is 35227). If the single
freecell is permanent, there are only five impossibles: 100730, 196724,
340351, 622692, and 680565. All of the first million deals are
winnable with 13x1e1, and even with 13xe2. The
twelve-column game is very
winnable too: there are 148,158 impossibles with no freecells, only 956
with a single ephemeral, and 394 with a single permament
freecell. All of the deals are winnable as 12x1e1.

Using less than eight columns makes the game more challenging. Danny A.
Jones' solver finds that there are at least 31,641 solvable 7x4 deals
(seven columns and four freecells), so that game is slightly harder
than the standard eight-column game with three freecells (8x3). What
about combining the variants, playing with seven columns and three
freecells? Of the 32,000 7x3 deals, at least 25,285 can be won; this is
approximately as difficult as the standard game with two freecells. It
is possible to play with six or even fewer columns, but the games
become extremely difficult unless more than four freecells are
allowed. A summary of win rates for all reasonable combinations
of columns and freecells can be found below in the statistics
section. You can scan the NetCELL score page
to see some results from real players; good games which can still be
won most of the time are 6x5 or 6x6, 5x7 or 5x8, and 4x10. The
NetCELL stats may vary quite a bit from our calculated win rates,
because of the effects of the NetCELL difficulty algorithm, especially
in variants with larger numbers of columns.

*** 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 packing
in alternate colors, 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 over 4% of deals it is
impossible to make any moves at all without any freecells (Danny A.
Jones found that 1,325 of the first 32,000 and 42,055 of the first
million are blocked at the start; the first few are 1, 23, 25, 28, 46,
and 51). 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.

Danny A. Jones says that the hardest deal he has ever encountered is
the zero-freecell FCPro deal 1003256. He says, "It's guaranteed to
quickly age manual solvers and turn computer solvers into memory hogs.
It goes against almost every optimization technique employed in my
normal solver. Think of your worst case of reordering cards to align
suits ... and then multiply it by 100+ for this deal! None of the
solvers in FcPro could find a solution -- not even after I helped by
providing the first 40 moves!" He also suggests playing 896777 without
making any manual moves to homecells (65 of the first million deals are
solvable this way; 8 more if autoplay takes effect before moving any
cards).

With fewer than eight columns, zero-freecell wins become even
rarer. Only one deal, 16110, out of the first 32,000 is
winnable with seven columns and zero freecells (2,780 are blocked at
the start, and 87,323 out of the first million). The overall win
rate appears to be about 1 in 100,000; there are 30 winnable 7x0 deals
in the first three million FCPro-numbered deals. With
six columns and zero freecells, no winnable deals have been found in
the first ten million FCPro deals.

Adding one ephemeral freecell to the eight-column game makes
902 of the first million deals solvable (a few of these are 58, 104,
105, 116, 150, and 163).

*** Why is it required to use freecells or
empty columns to move sequences?
**

Because the way the game, and most of its relatives (

11982 (solved with 4 freecells but relaxed rules)

4a 4b 41 4c a4 54 3a 3d b3 d3

8b 82 83 53 c5 8c 8d 81 31* 31

43* 48 24* 25 ch 7h 72 87 d8 18*

1c 17 15 16 1d 12 b5 25 21 24

2h 72 7a 72 34 d7 37 c3 63 51

5h 56 52 52 65 61 67

Many people enjoy playing Relaxed FreeCell with zero freecells (most are unaware that they are not following the standard rules, resulting in many false reports to us of additions to the zero-freecell list (previous question)). Danny has also analyzed the first 32,000 deals using zero freecells and relaxed rules. There are 1785 deals solvable under these conditions (the first few are 11, 38, 54, 56, and 58).

*** 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 (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 deals 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". Danny A. Jones's solver confirms that those two
deals are impossible as 52-card flourishes.

Deals from other programs have not been examined in detail for
52-card flourishes, but Scott Kladke found the NetCELL deal 10904-8
which can be solved fairly easily as a 52-card flourish.

Later, Jason, using a new program he calls Flourish Explorer, extended
the analysis through the first million deals, and found a total of 435
candidates for 52-card flourishes. Danny's solver has found
solutions for 354 of those; 19 are impossible and 62 are so far
unsolved. The search for candidates is very fast (Jason searched
100 million deals in 159 seconds, making a search of the entire 8
billion deals possible in about 3 hours), but the process of looking
for actual solutions is very slow (over 17 hours for the analysis of
the 435 candidates). Danny's solver also found a
solution to 7239 using only three freecells.

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

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. Some
FC programs allow
worrying back as part of the standard rules; Solitaire Virtuoso
provides it as an optional rule. Worrying back has a very small
influence on the win
rate, at least in the standard four freecell game: Tom Holroyd did some
computer analysis and found 11 deals (impossible with the standard
rules) that can be won by worrying back at least one card from a
foundation back onto an occupied column (11982 is still impossible,
though). Danny A. Jones extended the analysis up to 100
million, increasing the total to 69 deals winnable only by worrying
back:

(Holroyd) 4266168, 6332629, 7334559, 8381178, 10784666, 11953120,
13380013, 14194581, 15995200, 18739641, 19231830, (Jones) 19617733,
20001314, 24150534, 24795893, 26461140, 26960143, 27437151, 27616230,
30871801, 33293110, 33613814, 33900707, 34640348, 35784277, 40795834,
41445789, 45179955, 47883810, 48820590, 48830158, 49229215, 50279472,
50369429, 50532958, 50589757, 51869627, 53102422, 53126087, 53687601,
58996156, 59619214, 60555498, 61300229, 61830786, 62331953, 62641958,
63379066, 63478203, 64929238, 65924723, 66766350, 68311834, 70306173,
72865887, 74736875, 75265810, 78986182, 80505989, 81912256, 82943794,
85627209, 86265437, 89238318, 89819335, 90320629, 90801896, 95048417,
95464480

Here's a neat solution by Danny's solver, in which diamonds are
worried back three times to solve number 47883810 (D indicates a move
from the diamond foundation pile):

#47883810
49 moves

2a 3b 7c 17 41 34 23 2d 21 2h

a1 7h 7a 72 7h 74 D4 b4 8b 87

a8 D8 D4 74 27 32 dh 82 87 3a

37 c3 8c 27 6d 68 26 38 62 a3

26 43 52 56 45 48 4a 42 14

*** 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)

(2)

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.

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

FreeCell Pro is a Windows 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

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 deals 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 deal 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 runs under Windows NT/2000 and Windows 95/98/ME/XP.

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.

Since Microsoft FreeCell for Vista has now corrected its handing of supermoves, a few of the catalog solutions recorded with FreeCell Pro will no longer play back correctly. In particular, when moving a sequence of four cards from a column to an empty column, when there is another empty column and one empty freecell, is broken up into three separate two-card moves by FC Pro to match what older versions of MS FC did.

*** What are the minimum
requirements
for a good computer version of FreeCell?
**The biggest flaw in Microsoft FreeCell is its dialog box which
pops up every time you want to move to an empty column, asking if you
want to move a single card or a sequence of cards. Moves of single
cards to empty columns (when a move of more than one card from a column
is possible) are very rare (the standard notation allows for this, but
there is not a single instance of it in the catalog of over 400
solutions; I do not remember ever doing so when playing MS FreeCell),
and it can always be done anyway in two steps by moving the single card
to a freecell first, then to the empty column. This dialog box was
eliminated very early in the development of FreeCell Pro, and most good
versions of FreeCell either automatically move the maximum number of
cards to an empty column, or use a drag-and-drop interface (though this
is not as good an interface for FreeCell; NetCELL, strangely, allows
drag-and-drop for single card movement only). Yahoo's version of
FreeCell makes a different mistake -- it uses the selection method, but
requires the player to select the top of the sequence to be moved,
rather than simply choosing the column to be moved from (the rare cases
where it is desirable to move part of a sequence to an empty column can
also be handled by individual moves to freecells; a well-designed
program would use shift-click or control-click to select an exact
partial sequence -- I have never seen this implemented). A first-rate
program would allow the user to customize the selection method to
behave exactly as preferred (FreeCell Pro allows the user to choose
what action, if any, is taken on double clicks).

Every program should have autoplay of all cards which are safe to move to the homecells (preferably using the strong NetCELL autoplay rules described at the end of section 2); this speeds up play, especially at the finish. Being able to turn off autoplay completely is a nice optional feature. Poorly designed programs often make one of two errors: either not having autoplay at all, or playing every possible card to the homecells (as discussed earlier under AllPlay, this makes many deals much harder and on rare occasions impossible).

Every program should have selectable, numbered deals; part of
the
culture of FreeCell is the discussion of hard or unusual deals. Many
versions of FreeCell, even non-Windows versions, have adopted the
Microsoft deal numbers, at least for the first million deals.

FreeCell is an open solitaire -- the identity of every card is supposed
to be visible at the start; this can be a problem with aces in
particular if the cards are tightly packed together. Spreading the
cards in each column far enough apart is the easiest way to do this (a
large enough screen, as in FreeCell Pro, can easily hold the maximum
possible 18 cards in a column). Microsoft FreeCell, which uses a very
small screen, allows any card to be identified by a right-click, which
momentarily displays the entire card (this is an easy feature to
program and is quite useful in other games where there are often many
cards in a column, where the spacing between cards in a column is
automatically adjusted when it contains more cards than normal). Some
programs use specially designed cards with extra suit indices on the
upper right corner, visible even with minimal spacing between the
cards. Some very bad versions of FreeCell give the player no way of
identifying an ace which is covered by another card; this perverts the
nature of the game, which is strategic planning without guesswork.

*** What are some other programs
which
allow you to play FreeCell?**

FreeCell Pro is now over eleven years old and starting to show
its age (no new versions have appeared in six years and it is not
currently
being developed). A relatively new program is the **Faslo Freecell Autoplayer**
developed by S.S. Reddi and Gary Campbell, which incorporates Gary's
very strong solver. It has many of the same features
familiar to FCPro users, including deal numbers up to 4294967295 which
are compatible with MS FreeCell and FreeCell Pro. There are
also new features not found in FCPro: its game playing function can ** detect
losses up to four moves ahead of time**, even when there
are moves still available. FFA also has a Hint function which
almost instantly suggests the next move (or two if desired) if the deal
is still solvable; this was one of the most-requested features for
FCPro, which was never implemented there. (Since the suggested
moves come from the solver, they are always going to be good
suggestions, unlike some other programs which merely suggest a legal
move). You can use backspace to undo moves anytime, even after a
loss is signaled. One of the coolest features (another
FCPro suggestion never implemented) is that when the program signals
impossible, you can backspace one move at a time until it signals
solvable (no need to rerun the solver and click OK as in
FCPro). Displayed solutions are much shorter and cleaner
than those of FreeCell Pro, and incorporate multi-card
moves. Solutions can be played through using the right (and
left) arrow keys. Gary also notes that deals (and full
or partial solutions) can be output to the Windows clipboard (and then
to a text file) using the F9 key, and F6 reads a deal from the
clipboard, so you can type a hand-dealt deal (or a deal from a
non-MS-compatible program) into a text file, select, copy, and read
into FFA for play and analysis. (The format is a little
tricky; the best method is to save an F9 template as a text file and
replace the layout text with the deal you want to input). The
program can be downloaded and used for free, though donations to Gary
for its development are gratefully accepted. This
powerful program may become the new standard for FC analysis programs;
at the present its major limitation is that it only handles the
standard four-freecell game. Gary's website
includes a detailed tutorial.

Two other new programs with solvers are being developed in Java. Junyang Gu is developing a solver. A group of students at Vrije Universiteit (Amsterdam, The Netherlands), led by their professor Daan van den Berg, are trying to use the results of human-played FreeCell deals to develop a solver.

There are quite a few packages for Windows which include
FreeCell (and sometimes variants) among their many games. BVS Solitaire Collection
is a large package of 435 solitaire games, with many powerful features,
including an **autoend **function which tells you when
you are stuck. Their version of FreeCell allows some of the
rules to be changed, but does not appear to allow variable numbers of
columns and freecells. The deals are numbered, but are not
compatible with MS deal numbers. The program allows either
drag-and-drop or select-source-and-destination movement interfaces.

Solitaire City
is a program recently expanded to 13 games (53 including variants),
including FreeCell, Klondike, and Spider. Their version of
FreeCell includes seven game variations, six of which can be played
against the clock to score points and compete against others (tables of
the highest scores in each game are published on the website). The
variants are standard, easy (similar to low levels of NetCELL where
low-ranking cards tend to be dealt later), hard (the reverse, like high
levels of NetCELL), and one, two, and three freecells. Because
the competition is speed-based, the designer, Peter Wiseman, chose not
to implement autoplay, and numbered deals are only available as a
seventh variant. The deal numbers go up to 4294967295, and
are compatible with MS deal numbers (higher numbers also match those of
FreeCell Pro). Solitaire City includes a number of features,
including autoend, a tutorial for each game, and a move hint feature
which seems to give intelligent suggestions.

*** Is it cheating to use computers?
**

Well, most of us are using a computer to deal and keep track of the deals, 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).

While there are probably at least a dozen in Windows, I know of a few versions for Macintosh: the first freestanding version was David Bolen's Super Mac Freecell (the old home page seems to be gone and the program may no longer be supported). Two newer versions I have not seen are a Dashboard Widget version by Daniel Erdahl, and an OS X version by Alisdair McDiarmid, which includes support for the first million MS deals (modified by Lowell Stewart). Several large packages for Macintosh also include FreeCell: Rick Holzgrafe's Solitaire Till Dawn (which includes FreeCell among its 40 games), Eric's Ultimate Solitaire (which includes FreeCell among its 23 -- also available for Windows 95), and Ingemar Ragnemalm's 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 Ace of Penguins, a Linux version by D. J. Delorie (Karl Ewald, who mentioned this version, says that it does not even support selectable deal numbers -- this is so easy to do, and so desirable a feature, that its absence in any version of computer solitaire is in my view inexcusable), nor 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. Among the other Windows versions are the Windows 95 version Xcell. There used to be a version of FreeCell (and other solitaires) for Web TV, from Epsylon Games; this did not work well on an ordinary browser, and I received conflicting reports on how well it worked on Web TV. The site vanished entirely in 2001. A package which runs on a wide variety of platforms is a new edition of the Solitaire Antics package, called Solitaire Antics Ultimate, by Masque Publishing. The new edition, on CD-ROM, has over 200 games, including FreeCell, plus a very powerful game editor, and runs under Windows (95 through XP), Macintosh, Windows CE, and Palm OS (the latter two allow it to run on many handheld PCs). Other packages available for both Windows and Macintosh are Burning Monkey Solitaire, which has 30 games including FreeCell [apparently no longer available], Solitaire Plus!, which also has 30 different games including FreeCell, and dogMelon's Classic Solitaire, available for Windows, Palm, and Macintosh (all including FreeCell, with varying numbers of games).

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

There were also a number of FreeCell packages available for handheld and palmtop PC's including the HP, Psion and Palm Pilot. In fact there were at least three versions of FreeCell for Palm Pilots (all of them appear to have vanished): one from Electron Hut (this had the same deal numbers as Microsoft FC), another called Acid FreeCell from Red Mercury, and a portable version of NetCELL. Microsoft made a version of the Windows Entertainment Pack (including FreeCell) for the Windows CE operating system, for $34.95. This ran on various handheld PCs (H/PC) such as the Hewlett Packard HP360/620 LX and Sharp Mobilon, but no longer seems to be available. Micah Gorrell wrote a free version of FreeCell for the Palm Pre; I'm not sure if this is still available. Gorrell later wrote an omnibus program called Solitaire Universe for HP Touchpads. This has free versions of FreeCell, TriPeaks, and Klondike (deal 3), and can be expanded to include more than 50 other games and variants.

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. A new solver by Gary Campbell, which originally ran as a command file under DOS, has recently been integrated into the Faslo program mentioned above.

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
had a built-in solver (the links for these have all
disappeared).

There are a number of unpublished solvers I know about. Danny A. Jones
has a very powerful one, which he has used extensively to find
solutions and win rates for this FAQ. His standard solver, running
under Windows XP on a 1.8 GHz Pentium 4, can solve the first million
deals in under an hour.

**5. More Statistical Facts and Curiosities
* How often can I win?
**

Adrian Ettlinger, using Don Woods' solver with some extensions of his own, 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, 130 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, 7705172, 7748399, 7777900, 7795097, 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.

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.

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 (199 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 list of difficult deals page.

Based on analysis of the first 32,000 deals, we can also give some results for smaller numbers of freecells. With two freecells, the win rate is about 79-1/2% . It has been found, as a result of recent work by Shlomi Fish (following earlier work by Danny A. Jones), that 25,381 of the first 32,000 deals are solvable and 6,619 are impossible. The last of these to fall was number 982, which was intractable for quite a while but eventually proved impossible. Shlomi Fish and his colleague Jonathan Ringstad (who provided computing resources and support at the University of Oslo) have extended their analysis through the first 400,000 deals, finding 317,873 solvable and 82,126 impossible. Only deal number 384243 has still proved intractable. More details are available in the September 2, 2012 posting on Fish's blog.

With one freecell,
the win rate is slightly less than
20% (at least 6289 of the first 32,000 are solvable) -- thanks again to
Danny A. Jones and Shlomi Fish and their solvers for these results. The
win rate for zero freecells (discussed in section 3)
is about
0.22%.

The approximate win rates (per 1000 deals) for variant games with
different numbers of freecells (across top) and columns (down left) are:

**White
boxes with zeros indicate variants where no winnable random deals are
known. Red boxes with asterisks have win rates less than 1 in
1,000. Blue boxes with At Signs have win rates greater than
99.95%. The lavender box with a double At Sign has a win rate
greater than 99.999999% (there is one known random 8x5 deal which is
impossible). Violet boxes with exclamation points indicate that
no impossibles have been found.
**

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

At least seven, it appears. All of the 130 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.

**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 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). No other such deals have been found in searches through 100 million deals. Note that 14720822 has only 13 cards covering the aces. Why is it so hard? Look at how many odd-numbered cards are at the bottoms of the columns, and how many of the even-numbered cards are clumped at the top.

David A. Miller has worked on making even harder deals than
Adrian
Ettlinger's, and has constructed some deals which appear to 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
**Ryan L. Miller points out that a position can be reached,
without filling any freecells, that requires

**AC AS KS QS JS TS 9S 8S
2S 2C KC QC JC TC 9C 8C
3C 3S **KH KD QH QD JH JD

4C 4S

5C 5S

6C 6S

7C 7S

He also says that it appears that at least 37 freecells are
needed
so that *no unsolvable position can ever be reached*. With 36
freecells, a blocked position can be reached in which the bottom row
consists of all of the aces and queens, and the second row all kings
and twos (each king covering an ace and each two a queen), and the
other 36 cards are in freecells. Here's his example; this is actually a
zero-freecell deal which can be trivially solved in 23 moves if played
correctly.

AS AC AH AD QD QH QC QS

2D 2H 2S 2C KH KD KS KC

3S 3C 3H 3D JS JC JH JD

4H 4D 4S 4C TH TD TS TC

5S 5C 5H 5D 9S 9C 9H 9D

6H 6D 6S 6C 8H 8D 8S 8C

7S 7C 7H 7D

*** 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

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. The versions of Microsoft FreeCell, up through Windows XP, used supermoves correctly when there is one empty column and at least one empty freecell, but failed 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 works correctly in all supermove situations, but when recording moves, converts complex supermoves into a series of individual moves compatible with the original versions of MS FC (the most common is a four-card sequence moved from a column to an empty column, when there is another empty column and one empty freecell.

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 deals 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, but the algorithm used by Microsoft and compatible programs repeats halfway through (FCPro uses a programming trick to get around this, and another trick to double this to 8589934592; it appears that these are all different). The solitaire package Hardwood Solitaire III, which includes FreeCell among its 100 games, actually allows in theory for any possible deal to be generated, but at the cost of having to enter a deal number of up to 68 digits. I do not know if Hardwood's New Deal function can actually select every single possible deal.

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 (another example can be seen in deal number 2582 in the next question, if you play 32 instead of 42 on move 99!):

#15196 David A. Miller

5h 5h 8h 67 23 2a 27 27 27 2b

12 82 52 47 8c 83 48 c8 b8 63

6b 6c 67 a6 16 1a 12 b2 a2 5a

5h 7h 78 7b 75 65 76 1d 16 c6

b6 4h 7b 7h 3h 3h dh 4h 3c 3d

3h 8h 2h 37 31 1h ch 8c 8h 4h

6h 5h 21 2h 8h 2h 2h 62 6h 5h

85 8h 38

Madeleine Portwood writes that it seems to be possible to block all 13
cards of one suit in about 1 in 10 deals. There must be an ace in the
bottom (deepest) row with a card of the same suit directly above it,
and either another card of the same suit (or a king of another suit)
directly above that, or two cards of the suit to be blocked at the
bottom of another column -- this allows all of the other cards to be
cleared.

Here's a different pattern, with 14 cards left, all hearts or diamonds:

#187 David A. Miller

3a 54 5b 35 35 3c 3d 61 71 71

7h c3 73 a7 27 8a d8 58 6h 5c

56 5d a5 65 25 d6 2a 24 2d 15

16 c2 82 81 a8 21 2a 43 d2 4c

4d 42 47 6h dh 5d 5h 3h c3 6h

67 64 62 86 82 a8 48 5h 3a 3h

14 12 4h 8h 2h 7a 7h 7c 4d 4h

7h 6h 83 87 7h bh 2b 2h 48 47

7h 27 2h 12

From a practical standpoint, I don't know of any magic number of cards
left which makes victory certain (or even nearly certain). I've seen
separate claims for 40 cards left and 36 cards left being sure wins,
but I doubt either of these is true even as a general rule of thumb.

*** Is it possible to play an entire suit to the homecells ahead
of all of the other suits?
**

Yes. In fact, here is a solution in which all of the diamonds are played first, then all of the clubs:

#36 Michael Keller

81 8d 8c 8b 8a 52 a5 8a b8 d8

18 6b 1h 64 6d 67 c7 6c d6 c6

56 56 b6 a4 26 2a 2b 2h ah bh

57 1a 1h 71 7b 7c 7d 75 7h a7

d7 2a 27 26 c5 85 b2 68 6h a2

48 1a 1h 67 6h 1b 1h 6c 6h 16

26 12 54 5h 31 83 8h 45 4d 4h

d4 81 8h 18 38 31 3h 13 36 84

8h ah 7h bh ch 2h 56 41 45

Jason A. Crupper bettered this with a solution in which all four suits are played in order (32 instead of 42 on the next-to-last move blocks all 13 remaining spades):

#2582 Jason A. Crupper

8a 8b 83 8c 8d 83 b3 7b 78 a7

c7 d7 5a 25 25 1c 18 1d ch b1

4b 4h 4c 45 d5 b4 85 72 78 c8

71 27 2b 82 6c 68 68 b8 67 26

2b 2h 7h ah 7a 7h ch bh 1h 8b

8h 2h 12 1c b1 18 a1 61 32 3a

3b 32 56 3d 41 4h 5h bh ch dh

2h 7h 23 2h 78 7h 2b 2h 84 8h

53 6h 1c 1h 3h 1d 1h 38 3h 57

5h 35 3h 4h bh 4b 4h 2h 42 3c

Revised March 26, 2021