FreeCell -- Frequently Asked Questions (FAQ)
written by Michael Keller, Solitaire Laboratory
Copyright ©2009 by Michael Keller. All rights reserved.
Revised September 11, 2009
Thanks for questions and answers to:
Kate Ackley, Brian Barnhorst, David Bernazzani, Marion W.
Berryman, Bill Borland, Jurij 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, 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, 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.
The catalog of
solutions to the standard FreeCell deals, begun by Dave Ring and later
maintained by Wilson Callan, is now located on this site. The index is on the main page and it links to the catalog itself (which is quite
large, and broken into five pieces).
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?
* 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 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. 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 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 (called
KingOnly by Thomas Warfield). 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 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 of 71 deals including multiple tries. Some of the
deals can be clearly seen to be hopeless, but I estimated that the overall win
rate for ForeCell with perfect play was probably in the range of 65-75 percent.
This also turned out to be rather low; Danny A. Jones later analyzed the game
using his solver, and found that 27,395 of the 32,000 MS deals could be solved
using the rules of ForeCell. This suggests a win rate over 85 percent. In
195 of the deals (much less than 1 percent) no moves at all are possible.
Of the 4605 impossible deals, 3897 are impossible even if the KingOnly rule is
dropped; filling the freecells has a much larger effect than the KingOnly
rule.
* 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, 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, 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 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 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.
* 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. 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 is the only program I know which detects many
lost situations while a deal 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 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. 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
deals 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 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 almost two 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, Emilien Fenez, Milli Stelling, Fred Lamon,
Margaret Bannister, Theodore Gregg, Ken Gauvreau, Joyce DaFonte, and David B.
Bowie) who have played the entire set of
32,000; most 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 deals. 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
first 32,000 are the same as in earlier versions of MS FreeCell. 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
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 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?). The first really hard
deal past the first 32,000 deals is probably 35254. I've had seven people ask
for a solution or ask whether it is solvable (it is; the next impossible is past
100,000). Danny A. Jones suggests 57148 and 739671 as two of the hardest in the
first million.
* 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 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 (and the same
million as in Windows XP).
* 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 53.2% chance of
seeing no repeated numbers. 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.
* How can I get the solution
to a hard deal 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. Gary
Campbell's solver, now built into the Faslo FreeCell
Autoplayer, can often provide reasonably 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.
There is now a complete set of solutions to the
first 32,000 deals (except for 11982 of course) on a new site based
in Latvia, run by a gentleman named Jurij 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. Jurij says that the "solutions are generated by
computer. But a special human-friendly algorithm makes these solutions very
sequential, logical and short of course." A very impressive job and
a well-designed site.
* 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 many deals with
three freecells rather than four, and FCPro lets you do this. Most deals (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 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.
Pretty Good Solitaire includes a game called Challenge FreeCell, in which all of the twos and
aces are automatically dealt to the tops of the columns (twos in the four
leftmost columns, aces in the rightmost -- I would have done it the other way
around). This makes the deals slightly harder to solve, but almost all of them
are still solvable. Danny A. Jones ran an analysis in which he modified the
million XP deals in the same manner. Only 14 deals out of a million are
impossible (45813, 46589, 54150, 108905, 465251,
479573, 501129, 510749, 514842,
541924, 685515, 798261, 845934, and
855773. His solver found 846878 intractable. When he reversed the positions of
the aces and twos (aces in columns 1-4), 19 deals were unsolvable (including
some of the same deals as before, indicated in boldface) and 3 intractable
(including 855773 which is impossible the other way). PGS's Super Challenge FreeCell combines this modified
deal with KingOnly rules (only
kings may be played in empty columns -- see the question below about variants); most of the deals
are still solvable. Danny ran 40,000 deals, finding 56 impossible and 28
intractable. Even with two or three freecells, Challenge FreeCell is only
slightly harder than regular deals. With three freecells, Danny A. Jones' solver
found only 250 impossible deals (with 3 intractable) with the twos and aces in
the first eight positions. With two freecells, there are at least 24,161
solvable deals. With one freecell, however, his solver found only
3,785 solvable deals, and there are only four Challenge-modified deals (7079,
17873, 20393, and 20918) solvable with zero freecells.
* 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?
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 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. A few years ago, NetCELL 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. At least 70 streaks of over 1000 have been recorded on
NetCELL, but I would consider anything over 100 excellent in any standard
version of FreeCell. My own best streak of 79 straight only
made 141st place on the active list in June of 2006. Note that
NetCELL does not allow undos, so getting long streaks is harder than in standard
MS FreeCell, where you can fix a one-move mistake.
The all-time record on NetCELL is 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 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 several other streaks of over 1000 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. The second-longest streak ever is 14,137 by a player under the
name QingpuKid. A streak of at least 797 is needed to make the top 100
all-time, and 71 streaks over 1000 wins have been recorded.
* 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,
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 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.
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 is currently trying to decide if he should create 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 prduces 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 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; 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 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 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 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 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.
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 NetCELL, an online Java
version of FreeCell, has an ingenious algorithm to make deals harder or easier,
by dealing more high cards at the tops of columns and low cards at the bottoms
of columns (and vice versa). Originally the difficulty scale ran from 1 to
20, but he found that the higher numbers paradoxically were less difficult, and
the maximum level available on the server is now level 12. 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, and offers continuous tournaments (both long and short) every day with a
mixture of variant games. When playing single games, 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, with all cards equally likely at
each location) after 50 deals. I've managed 50 in a row in the standard 8x4
game; in order to break into the current top 100, you need to win over 100 in a
row (more than 650 to break the top 100 all time)!
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 deals (about 99% judging from their first
sample of 500 deals) 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 600 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.
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 (it bears the
same relationship to Eight Off that standard FreeCell does to Baker's Game).
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%.
* 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.
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.
* Why
is it required to use freecells or empty columns to move sequences?
Because the way the game,
and most of its relatives, were designed, is that cards can only be moved one at
a time. A variation where a sequence of cards can be moved as a unit, regardless
of the number of freecells available (though freecells can still hold only one
card at a time), is sometimes called Relaxed
FreeCell. Danny A. Jones has analyzed the 320 deals out of the first 25
million FreeCell Pro deals which are impossible under standard rules. Amazingly,
all but four of them can be solved in Relaxed FreeCell, including 11982. The
deals which are still impossible are 2607073, 12421023, 18667482, and 24121426.
Since the win rate of the standard game is already extremely high, it does not
seem necessary to make the rules any easier (although solving the impossibles
like 11982 using relaxed rules is sometimes quite challenging).
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 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 130 impossible
deals up to 10 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%. Mark E. Masten has confirmed this
with a run of 15 million deals, with 13,397,816 wins (89.32%) out of 15
million. Much of the game's difficulty comes from only being allowed
to move kings to empty columns; if the KingOnly rule is waived, the win rate
jumps to over 98%. Using Tom Holroyd's Patsolve solver, the first 32,000
MS deals (dealing cards in the same order to ten columns instead of eight) were
analyzed with both rules. Under standard KingOnly rules 28,564 deals are
winnable (89.26%); with any card playable to an empty column 31,502 deals are
winnable (98.44%). The help file for the original version mentions a
harder variant (which is not implemented there): eight columns of six with the
four remaining cards dealt to all four depots; this is identical to ForeCell
except that the tableau columns are packed in suit. Danny A. Jones has
analyzed this variant and found that only 3,382 deals are winnable out of the
first 32,000 MS deals; in 1,276 deals no moves at all are possible.
(2)
Penguin, invented by David Parlett, and found in several of his books
(Teach Yourself Card Games For One,
published in 1994, is excellent, though now out of print, though
easy to find used at a reasonable price). 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 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 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 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 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.
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
401 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).
* Is
there a version of FreeCell for Macintosh or other systems?
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, 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).
* 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. A new solver by Gary Campbell, which runs as a command file under DOS,
has recently been released.
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 (the link for this
has disappeared). XCell also has a built-in solver.
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, 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, 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. Eight of the one million deals in FreeCell for Windows XP
are unsolvable. Danny A. Jones has extended the analysis to 20
million using his own solver (of the first 25 million, 320 are impossible), and
Ryan L. Miller (running Tom Holroyd's Patsolve solver in FreeCell Pro for more
than 22 days of computing time, with some assistance from me, Danny A. Jones,
and Gary Campbell) has extended it to 100 million. Of the first 100 million,
1282 are impossible, a win rate of nearly 99.999%, or about 1 loss in 78,000
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 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 79% (at least 25,381 of the first 32,000 deals are solvable),
and 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 his solver
for these results. The win rate for zero
freecells (discussed in section 3) is about 0.2%.
The approximate win rates (as
percentages) for variant games with different numbers of columns (across top)
and freecells (down left) are:
|
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
| 0 |
|
|
|
0.001 |
0.22 |
6 |
30 |
64 |
85 |
95 |
| 1 |
|
|
0.01 |
0.88 |
19 |
65 |
93 |
99 |
99+ |
99+ |
| 2 |
|
0.003 |
0.88 |
25 |
79 |
99 |
99+ |
99+ |
100 |
100 |
| 3 |
|
0.23 |
16 |
79 |
99 |
99+ |
100 |
100 |
100 |
100 |
| 4 |
0.02 |
4 |
62 |
99 |
99+ |
100 |
|
|
|
|
| 5 |
0.25 |
25 |
94 |
99+ |
99+++ |
|
|
|
|
|
| 6 |
2 |
65 |
99+ |
100 |
|
|
|
|
|
|
| 7 |
12 |
93 |
99+ |
|
|
|
|
|
|
|
| 8 |
38 |
99 |
|
|
|
|
|
|
|
|
| 9 |
71 |
99+ |
|
|
|
|
|
|
|
|
| 10 |
92 |
|
|
|
|
|
|
|
|
|
| 11 |
99 |
|
|
|
|
|
|
|
|
|
| 12 |
99+ |
|
|
|
|
|
|
|
|
|
| 13 |
99+ |
|
|
|
|
|
|
|
|
|
| 14 |
100 |
|
|
|
|
|
|
|
|
|
* 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. 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 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
ten freecells to solve. From the starting position below, move all 26 red
cards to the homecells. The resulting position, with 26 black cards, needs ten
freecells to win.
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
TH TD 9H 9D 8H
8D
5C 5S
7H 7D 6H 6D 5H
5D
6C 6S
4H 4D 3H 3D 2H
2D
7C 7S
AH AD
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 24 moves.
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 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.
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.
* 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 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 (FCPro uses 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 the New Deal function can actually select every single possible deal.
*
What is the fewest number of cards one can have
left remaining and still lose?
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