FreeCell: Difference between revisions

FreeCell
A patience game
	A game of Freecell on KDE
Named variant	Baker's Game
Family	Freecell
Deck	Single 52-card
	See also Glossary of patience terms

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FreeCell is a solitaire card game played using the standard 52-card deck. It is fundamentally different from most solitaire games in that very few deals are unsolvable,^[1] and all cards are dealt face-up from the beginning of the game.^[2] Microsoft has included a FreeCell computer game with every release of the Windows operating system since 1995, which has greatly contributed to the game's popularity.^[3]

Rules

One standard 52-card deck is used. There are four open cells and four open foundations. Cards are dealt face-up into eight cascades, four of which comprise seven cards each and four of which comprise six cards each.

The top card of each cascade begins a sequence. Tableaus must be built down by alternating colors. Foundations are built up by suit. The Foundations begin with Ace and are built up to King.

Any cell card or top card of any cascade may be moved to build on a tableau, or moved to an empty cell, an empty cascade, or its foundation.

The game is won after all cards are moved to their foundation piles.

Supermoves

Unlike in many solitaire card games, the rules of Freecell only allow cards to be moved one at a time. Complete or partial tableaus may be moved to build on existing tableaus, or moved to empty cascades, only by a sequence of moves which recursively place and remove cards through intermediate locations.

For example, with one empty cell, the top card of one tableau can be moved to a free cell. The second card from the top of that tableau can now be moved onto another tableau. Then the original top card can be moved from the cell on top of it.

Such a sequence of moves is called a "supermove". Computer implementations often show this motion, but players using physical decks typically just move the tableau at once.

The maximum number $C$ of cards in a tableau that can be moved to another tableau equals the number of empty cells plus one, with that number doubling for each empty cascade: $C=2^{M}\times (N+1)$ , where $M$ is the number of empty cascades and $N$ is the number of empty cells.^[4] The maximum number that can be moved to an empty cascade is $C/2$ .^[4]

Numbered hands

Although software implementations vary, most versions label the hands with a number derived from the seed value used by the random number generator to shuffle the cards.^[2]

Microsoft FreeCell is so definitive for FreeCell players that many other software implementations include compatibility with its random number generator in order to replicate its numbered hands.^[2]^[5]

History and variants

One of the oldest ancestors of FreeCell is Eight Off. In the June 1968 edition of Scientific American, Martin Gardner described in his "Mathematical Games" column a game by C. L. Baker which is similar to FreeCell, except that cards on the tableau are built by suit rather than by alternate colors. Gardner wrote, "The game was taught to Baker by his father, who in turn learned it from an Englishman during the 1920s."^[6] This variant is now called Baker's Game. FreeCell's origins may date back even further to 1945 and to a Scandinavian game called Napoleon in St. Helena (not the solitaire game Napoleon at St Helena, also known as Forty Thieves).^[2]

Paul Alfille changed Baker's Game by making cards build according to alternate colors, thus creating FreeCell. He implemented the first computerised version as a medical student at the University of Illinois, in the TUTOR programming language for the PLATO educational computer system in 1978.^[7] Alfille was able to display easily recognizable graphical images of playing cards on the 512 × 512 monochrome display on the PLATO systems.^[8]

This original FreeCell environment allowed games with 4–10 columns and 1–10 cells in addition to the standard 8 × 4 game. For each variant, the program stored a ranked list of the players with the longest winning streaks. There was also a tournament system that allowed people to compete to win difficult hand-picked deals. Paul Alfille described this early FreeCell environment in more detail in an interview from 2000.^[9]

In 2012, researchers used evolutionary computation methods to create winning FreeCell players.^[10]

A variant where card sequence movement is not limited by available cells is known as Relaxed FreeCell.^[2]

Other solitaire games related to or inspired by FreeCell include Seahaven Towers, Penguin, Stalactites, ForeCell, Antares (a cross with Scorpion).

Unsolvable hands

In 2018, Theodore Pringle and Shlomi Fish found that, of 8.6 billion FreeCell Pro deals, 102075 deals were impossible to solve, or approximately one impossible deal out of 84,000 random deals.^[11] It is estimated that around 99.999% of possible deals are solvable.^[2] Deal number 11982 from the Windows version of FreeCell is an example of an unsolvable FreeCell deal, the only deal among the original "Microsoft 32,000" which is unsolvable.^[2]

Solver complexity

The FreeCell game has a constant number of cards. This implies that in constant time, a person or computer could list all of the possible moves from a given start configuration and discover a winning set of moves or, assuming the game cannot be solved, the lack thereof. To perform an interesting complexity analysis, one must construct a generalized version of the FreeCell game with 4 × n cards. This generalized version of the game is NP-complete;^[12] it is unlikely that any algorithm more efficient than a brute-force search exists which can find solutions for arbitrary generalized FreeCell configurations.

There are 52! (i.e., 52 factorial), or approximately 8×10⁶⁷, distinct deals. However, some games are effectively identical to others because suits assigned to cards are arbitrary or columns can be swapped. After taking these factors into account, there are approximately 1.75×10⁶⁴ distinct games.^[2]

References

^ Leonhard, Woody (2009). Windows 7 All-in-One for Dummies. John Wiley & Sons. p. 293. ISBN 9780470487631.
^ ^a ^b ^c ^d ^e ^f ^g ^h Keller, Michael (August 4, 2015). "FreeCell -- Frequently Asked Questions (FAQ)". Solitaire Laboratory. Retrieved February 7, 2017.
^ Glenn, Jim and Denton, Carey. The Treasury of Family Games (page 105). Reader's Digest, 2003 (ISBN 9780762104314)
^ ^a ^b "solitaire - FreeCell: How many cards can be moved at once?". Board & Card Games Stack Exchange.
^ "PySol - Rules for Freecell". PySolFC documentation. Retrieved 3 February 2018.
^ Gardner, Martin (June 1968). "Mathematical Games". Scientific American. 218 (6): 114. Bibcode:1968SciAm.218f.112G. doi:10.1038/scientificamerican0668-112.
^ Mark J. P. Wolf Before the Crash: Early Video Game History 2012 p212 "After Spacewar!, several more games appeared on the PLATO system, including DECWAR (1974, based on “Star Trek”), Empire (1974), a Dungeons & Dragons–inspired game named "dnd" released in 1979, Moria (1975), the original Freecell (1978), and a flight simulator named Airfight..."
^ Kaye, Ellen (October 17, 2002). "One Down, 31,999 to Go: Surrendering to a Solitary Obsession". New York Times.
^ Cronin, Dennis (May 4, 2000). "Interview with Paul Alfille". Freecell.net. Retrieved March 4, 2011.
^ Elyasaf, Achiya; Hauptman, Ami; Sipper, Moshe (December 2012). "Evolutionary Design of FreeCell Solvers" (PDF). IEEE Transactions on Computational Intelligence and AI in Games. 4 (4): 270–281. doi:10.1109/TCIAIG.2012.2210423. S2CID 801608. Archived (PDF) from the original on 2015-10-20.
^ The solvability statistics of the Freecell Pro 4-Freecells Deals
^ Helmert, Malte (March 2003). "Complexity results for standard benchmark domains in planning". Artificial Intelligence. 143 (2): 219–262. doi:10.1016/S0004-3702(02)00364-8.

Additional sources

"OHSU scientists say FreeCell can be adapted to spot early signs of dementia". Oregon Health & Science University. Retrieved June 1, 2017.
O'Hale, Marty M. (August 14, 2007). "The Four Virtues of FreeCell". The Escapist Magazine. Archived from the original on August 8, 2011. Retrieved June 9, 2012.

@@ Line 1: / Line 1: @@
 {{short description|Solitaire card game}}
 {{Infobox card game
-|title    = FreeCell
+| title         = FreeCell
-|subtitle = A [[Patience (game)|patience]] game
+| subtitle      = A [[Patience (game)|patience]] game
-|image = Freecell KPatience Oxygen White.png
+| image         = Freecell KPatience Oxygen White.png
-|image_size = 250
+| image_size    = 250
-|caption  = A game of Freecell on [[KDE]]
+| image_caption = A game of Freecell on [[KDE]]
+| named_variant = [[Baker's Game]]
-|alt_names =
+| deck          = Single 52-card
-|NamedVariants=[[Baker's Game]]
+| family        = Freecell
-|deck    = Single 52-card
+| footnotes     = See also [[Glossary of patience terms]]
-|Family = Freecell
-|footnotes = See also [[Glossary of patience terms]]
 }}
-'''FreeCell''' is a [[Patience (game)|solitaire]] [[card game]] played using the [[standard 52-card deck]]. It is fundamentally different from most solitaire games in that very few [[Card_game#Deal|deals]] are unsolvable,<ref name="Leonhard2009">{{cite book |url=https://books.google.com/books?id=BjhFgc4DdjIC&pg=PA293 |title=Windows 7 All-in-One for Dummies |publisher=John Wiley & Sons |first=Woody |last=Leonhard |page=293 |year=2009 |isbn=9780470487631}}</ref> and all cards are dealt face-up from the very beginning of the game.<ref name="FCFAQ">{{cite web |url=http://solitairelaboratory.com/fcfaq.html |title=FreeCell -- Frequently Asked Questions (FAQ) |website=Solitaire Laboratory |last=Keller |first=Michael |date=August 4, 2015 |access-date=February 7, 2017}}</ref> Although software implementations vary, most versions label the hands with a number (derived from the seed value used by the [[pseudorandom number generator|random number generator]] to shuffle the cards).<ref name="FCFAQ" />
+'''FreeCell''' is a [[Patience (game)|solitaire]] [[card game]] played using the [[standard 52-card deck]]. It is fundamentally different from most solitaire games in that very few [[Card game#Deal|deals]] are unsolvable,<ref name="Leonhard2009">{{cite book |url=https://books.google.com/books?id=BjhFgc4DdjIC&pg=PA293 |title=Windows 7 All-in-One for Dummies |publisher=John Wiley & Sons |first=Woody |last=Leonhard |page=293 |year=2009 |isbn=9780470487631}}</ref> and all cards are dealt face-up from the beginning of the game.<ref name="FCFAQ">{{cite web |url=http://solitairelaboratory.com/fcfaq.html |title=FreeCell -- Frequently Asked Questions (FAQ) |website=Solitaire Laboratory |last=Keller |first=Michael |date=August 4, 2015 |access-date=February 7, 2017}}</ref> Microsoft has included a [[Microsoft FreeCell|FreeCell computer game]] with every release of the Windows operating system since 1995, which has greatly contributed to the game's popularity.<ref>Glenn, Jim and Denton, Carey. ''The Treasury of Family Games'' (page 105). Reader's Digest, 2003 ({{ISBN|9780762104314}})</ref>
-Microsoft has included a [[Microsoft FreeCell|FreeCell computer game]] with every release of the Windows operating system since 1995, greatly contributing to the game's popularity among users of personal computers, even leading to the creation of several websites devoted to FreeCell.<ref>Glenn, Jim and Denton, Carey.  ''The Treasury of Family Games'' (page 105). Reader's Digest, 2003 ({{ISBN|9780762104314}})</ref> Microsoft FreeCell is so definitive for many FreeCell players that many other software implementations strive for compatibility with its [[pseudorandom number generator|random number generator]] in order to replicate its numbered hands.<ref name="FCFAQ" /><ref>{{cite web |url=http://pysolfc.sourceforge.net/doc/rules/freecell.html |title=PySol - Rules for Freecell |website=PySolFC documentation |access-date=3 February 2018}}</ref>
 == Rules ==
+One standard 52-card deck is used.
-=== Construction and layout ===
+There are four open [[Solitaire terminology#Game layout|cell]]s and four open [[Solitaire terminology#Foundation|foundation]]s. Cards are dealt face-up into eight [[Solitaire terminology#Deal|cascade]]s, four of which comprise seven cards each and four of which comprise six cards each.
-*One standard 52-card deck is used.
-*There are four open [[Solitaire terminology#Game layout|cell]]s and four open [[Solitaire terminology#Foundation|foundation]]s.  Some alternate rules use between one and ten cells.
-*Cards are dealt face-up into eight [[Solitaire terminology#Deal|cascade]]s, four of which comprise seven cards each and four of which comprise six cards each.  Some alternate rules will use between four and ten cascades.
+The top card of each cascade begins a [[Solitaire terminology#S|sequence]].
-=== Building during play ===
-*The top card of each cascade begins a [[Solitaire terminology#Game layout|tableau]].
+Tableaus must be [[Solitaire terminology#Building|built]] down by alternating colors.
+Foundations are built up by suit. The Foundations begin with Ace and are built up to King.
-*Tableaux must be [[Solitaire terminology#Building|built]] down by alternating colors.
-*Foundations are built up by suit. The Foundations typically begin with Ace and are built up to King.
+Any cell card or top card of any cascade may be moved to build on a tableau, or moved to an empty cell, an empty cascade, or its foundation.
-=== Moves ===
-*Any cell card or top card of any cascade may be moved to build on a tableau, or moved to an empty cell, an empty cascade, or its foundation.
-*Complete or partial tableaus may be moved to build on existing tableaus, or moved to empty cascades, by recursively placing and removing cards through intermediate locations. Computer implementations often show this motion, but players using physical decks typically move the tableau at once.
+The game is won after all cards are moved to their foundation piles.
-The number of cards a player can move is equivalent to number of empty cells plus one, with that number doubling based on how many empty cascades there are. The mathematical equation for the number of cards that can be moved is (2<sup>M</sup>)×(N + 1), where M is the number of empty cascades and N is the number of empty cells.<ref>{{cite web |title=solitaire - FreeCell: How many cards can be moved at once? |url=https://boardgames.stackexchange.com/a/45157 |website=Board & Card Games Stack Exchange}}</ref>
-=== Victory ===
+=== Supermoves ===
+Unlike in many solitaire card games, the rules of Freecell only allow cards to be moved one at a time. Complete or partial tableaus may be moved to build on existing tableaus, or moved to empty cascades, only by a sequence of moves which recursively place and remove cards through intermediate locations.
-*The game is won after all cards are moved to their foundation piles.
+For example, with one empty cell, the top card of one tableau can be moved to a free cell. The second card from the top of that tableau can now be moved onto another tableau. Then the original top card can be moved from the cell on top of it.
-It is estimated that 99.999% of possible deals are solvable.{{citation needed|date=June 2020}} Deal number 11982 from the Windows version of FreeCell is an example of an unsolvable FreeCell deal, the only deal among the original "Microsoft 32,000" which is unsolvable.<ref name="FCFAQ" />
+Such a sequence of moves is called a "supermove". Computer implementations often show this motion<!-- and I bet there's a GIF of this somewhere -->, but players using physical decks typically just move the tableau at once.
+The maximum number <math>C</math> of cards in a tableau that can be moved to another tableau equals the number of empty cells plus one, with that number doubling for each empty cascade: <math>C = 2^M\times (N+1)</math>, where <math>M</math> is the number of empty cascades and <math>N</math> is the number of empty cells.<ref name="stackex">{{cite web |title=solitaire - FreeCell: How many cards can be moved at once? |url=https://boardgames.stackexchange.com/a/45157 |website=Board & Card Games Stack Exchange}}</ref> The maximum number that can be moved to an empty cascade is <math>C/2</math>.<ref name="stackex"/>
+== Numbered hands ==
+Although software implementations vary, most versions label the hands with a number derived from the seed value used by the [[pseudorandom number generator|random number generator]] to shuffle the cards.<ref name="FCFAQ" />
+Microsoft FreeCell is so definitive for FreeCell players that many other software implementations include compatibility with its random number generator in order to replicate its numbered hands.<ref name="FCFAQ" /><ref>{{cite web |url=http://pysolfc.sourceforge.net/doc/rules/freecell.html |title=PySol - Rules for Freecell |website=PySolFC documentation |access-date=3 February 2018}}</ref>
 == History and variants ==
-One of the oldest ancestors of FreeCell is [[Eight Off]]. In the June 1968 edition of ''[[Scientific American]]'', [[Martin Gardner]] described in his "Mathematical Games" column a game by C. L. Baker that is similar to FreeCell, except that cards on the tableau are built by suit rather than by alternate colors. Gardner wrote, "The game was taught to Baker by his father, who in turn learned it from an Englishman during the 1920s."<ref>{{cite journal |title=Mathematical Games |journal=Scientific American |first=Martin |last=Gardner |date=June 1968 |volume=218 |issue=6 |page=114 |doi=10.1038/scientificamerican0668-112}}</ref>  This variant is now called [[Baker's Game]]. FreeCell's origins may date back even further to 1945 and to a Scandinavian game called Napoleon in St. Helena (not the solitaire game [[Napoleon at St Helena]], also known as Forty Thieves).<ref name="FCFAQ" />
+One of the oldest ancestors of FreeCell is [[Eight Off]]. In the June 1968 edition of ''[[Scientific American]]'', [[Martin Gardner]] described in his "Mathematical Games" column a game by C. L. Baker which is similar to FreeCell, except that cards on the tableau are built by suit rather than by alternate colors. Gardner wrote, "The game was taught to Baker by his father, who in turn learned it from an Englishman during the 1920s."<ref>{{cite journal |title=Mathematical Games |journal=Scientific American |first=Martin |last=Gardner |date=June 1968 |volume=218 |issue=6 |page=114 |doi=10.1038/scientificamerican0668-112|bibcode=1968SciAm.218f.112G }}</ref>  This variant is now called [[Baker's Game]]. FreeCell's origins may date back even further to 1945 and to a Scandinavian game called Napoleon in St. Helena (not the solitaire game [[Napoleon at St Helena]], also known as Forty Thieves).<ref name="FCFAQ" />
+Paul Alfille changed Baker's Game by making cards build according to alternate colors, thus creating FreeCell. He implemented the first computerised version as a medical student at the University of Illinois, in the [[TUTOR (programming language)|TUTOR programming language]] for the [[PLATO (computer system)|PLATO]] educational computer system in 1978.<ref>Mark J. P. Wolf ''Before the Crash: Early Video Game History'' 2012 p212 "After Spacewar!, several more games appeared on the PLATO system, including DECWAR (1974, based on “Star Trek”), Empire (1974), a Dungeons & Dragons–inspired game named "dnd" released in 1979, Moria (1975), the original Freecell (1978), and a flight simulator named Airfight..."</ref> Alfille was able to display easily recognizable graphical images of playing cards on the {{nowrap|512 × 512}} monochrome display on the PLATO systems.<ref name="nyt">{{cite news |url=https://query.nytimes.com/gst/fullpage.html?res=9F05E6DE143DF934A25753C1A9649C8B63 |title=One Down, 31,999 to Go: Surrendering to a Solitary Obsession |work=New York Times |last=Kaye |first=Ellen |date=October 17, 2002}}</ref>
+This original FreeCell environment allowed games with 4–10 columns and 1–10 cells in addition to the standard {{nowrap|8 × 4}} game. For each variant, the program stored a ranked list of the players with the longest winning streaks. There was also a tournament system that allowed people to compete to win difficult hand-picked deals. Paul Alfille described this early FreeCell environment in more detail in an interview from 2000.<ref>{{cite web |url=http://www.freecell.net/f/c/alfille.html |title=Interview with Paul Alfille |work=Freecell.net |first=Dennis |last=Cronin |date=May 4, 2000 |access-date=March 4, 2011}}</ref>
+In 2012, researchers used [[evolutionary computation]] methods to create winning FreeCell players.<ref>{{cite journal |url=http://www.genetic-programming.org/hc2013/Sipper-Paper.pdf |archive-url=https://web.archive.org/web/20151020115006/http://www.genetic-programming.org/hc2013/Sipper-Paper.pdf |archive-date=2015-10-20 |url-status=live |title=Evolutionary Design of FreeCell Solvers |journal=IEEE Transactions on Computational Intelligence and AI in Games |first1=Achiya |last1=Elyasaf |first2=Ami |last2=Hauptman |first3=Moshe |last3=Sipper |volume=4 |issue=4 |pages=270–281 |date=December 2012 |doi=10.1109/TCIAIG.2012.2210423|s2cid=801608 }}</ref>
-Paul Alfille changed Baker's Game by making cards build according to alternate colors, thus creating FreeCell. He implemented the first computerised version as a medical student at the University of Illinois,<ref>{{cite web |title=History of FreeCell Solitaire |url=https://solitaired.com/freecell#historyoffreecellsolitaire |website=Solitaired |access-date=4 November 2020}}</ref> in the [[TUTOR (programming language)|TUTOR programming language]] for the [[PLATO (computer system)|PLATO]] educational computer system in 1978.<ref>Mark J. P. Wolf ''Before the Crash: Early Video Game History''  2012 p212 "After Spacewar!, several more games appeared on the PLATO system, including DECWAR (1974, based on “Star Trek”), Empire (1974), a Dungeons & Dragons–inspired game named "dnd" released in 1979, Moria (1975), the original Freecell (1978), and a flight simulator named Airfight..."</ref> Alfille was able to display easily recognizable graphical images of playing cards on the {{nowrap|512 × 512}} monochrome display on the PLATO systems.<ref name="nyt">{{cite news |url=https://query.nytimes.com/gst/fullpage.html?res=9F05E6DE143DF934A25753C1A9649C8B63 |title=One Down, 31,999 to Go: Surrendering to a Solitary Obsession |work=New York Times |last=Kaye |first=Ellen |date=October 17, 2002}}</ref>
+A variant where card sequence movement is not limited by available cells is known as Relaxed FreeCell.<ref name="FCFAQ" />
-This original FreeCell environment allowed games with 4–10 columns and 1–10 cells in addition to the standard {{nowrap|8 × 4}} game. For each variant, the program stored a ranked list of the players with the longest winning streaks.  There was also a tournament system that allowed people to compete to win difficult hand-picked deals.  Paul Alfille described this early FreeCell environment in more detail in an interview from 2000.<ref>{{cite web |url=http://www.freecell.net/f/c/alfille.html |title=Interview with Paul Alfille |work=Freecell.net |first=Dennis |last=Cronin |date=May 4, 2000 |access-date=March 4, 2011}}</ref>
+Other solitaire games related to or inspired by FreeCell include [[Seahaven Towers]], [[Penguin (solitaire)|Penguin]], [[Stalactites (solitaire)|Stalactites]], ForeCell, Antares (a cross with [[Scorpion (solitaire)|Scorpion]]).
-In 2012, researchers used [[evolutionary computation]] methods to create winning FreeCell players.<ref>{{cite journal |url=http://www.genetic-programming.org/hc2013/Sipper-Paper.pdf |title=Evolutionary Design of FreeCell Solvers |journal=IEEE Transactions on Computational Intelligence and AI in Games |first1=Achiya |last1=Elyasaf |first2=Ami |last2=Hauptman |first3=Moshe |last3=Sipper |volume=4 |issue=4 |pages=270-281 |date=December 2012 |doi=10.1109/TCIAIG.2012.2210423}}</ref>
+== Unsolvable hands ==
-Other solitaire games related to or inspired by FreeCell include [[Seahaven Towers]], [[Penguin_(solitaire)|Penguin]], [[Stalactites_(solitaire)|Stalactites]], ForeCell, Antares (a cross with [[Scorpion_(solitaire)|Scorpion]]), and several others.
+In 2018, Theodore Pringle and Shlomi Fish found that, of 8.6 billion FreeCell Pro deals, 102075 deals were impossible to solve, or approximately one impossible deal out of 84,000 random deals.<ref>[https://fc-solve.shlomifish.org/charts/fc-pro--4fc-deals-solvability--report/ The solvability statistics of the Freecell Pro 4-Freecells Deals]</ref> It is estimated that around 99.999% of possible deals are solvable.<ref name="FCFAQ" /> Deal number 11982 from the Windows version of FreeCell is an example of an unsolvable FreeCell deal, the only deal among the original "Microsoft 32,000" which is unsolvable.<ref name="FCFAQ" />
 == Solver complexity ==
-The FreeCell game has a constant number of cards. This implies that in constant time, a person or computer could list all of the possible moves from a given start configuration and discover a winning set of moves or, assuming the game cannot be solved, the lack thereof. To perform an interesting complexity analysis one must construct a generalized version of the FreeCell game with {{nowrap|4 × ''n''}} cards. This generalized version of the game is [[NP-complete]];<ref>{{cite journal |title=Complexity results for standard benchmark domains in planning |journal=Artificial Intelligence |first=Malte |last=Helmert |date=March 2003 |volume=143 |issue=2 |pages=219–262 |doi=10.1016/S0004-3702(02)00364-8|doi-access=free }}</ref> it is unlikely that any algorithm more efficient than a brute-force search exists that can find solutions for arbitrary generalized FreeCell configurations.
+The FreeCell game has a constant number of cards. This implies that in constant time, a person or computer could list all of the possible moves from a given start configuration and discover a winning set of moves or, assuming the game cannot be solved, the lack thereof. To perform an interesting complexity analysis, one must construct a generalized version of the FreeCell game with {{nowrap|4 × ''n''}} cards. This generalized version of the game is [[NP-complete]];<ref>{{cite journal |title=Complexity results for standard benchmark domains in planning |journal=Artificial Intelligence |first=Malte |last=Helmert |date=March 2003 |volume=143 |issue=2 |pages=219–262 |doi=10.1016/S0004-3702(02)00364-8|doi-access= }}</ref> it is unlikely that any algorithm more efficient than a brute-force search exists which can find solutions for arbitrary generalized FreeCell configurations.
-There are 52! (i.e., 52 [[factorial]]), or approximately 8{{e|67}}, distinct deals. However, some games are effectively [[isomorphism|identical]] to others because suits assigned to cards are arbitrary or columns can be swapped. After taking these factors into account, there are approximately 1.75{{e|64}} distinct games.<ref name="FCFAQ" />
+There are 52! (i.e., 52 [[factorial]]), or approximately 8{{X10^|67}}, distinct deals. However, some games are effectively [[isomorphism|identical]] to others because suits assigned to cards are arbitrary or columns can be swapped. After taking these factors into account, there are approximately 1.75{{X10^|64}} distinct games.<ref name="FCFAQ" />
 == References ==
-{{reflist|30em}}
+{{reflist}}
 == Additional sources ==
 {{Commons category|FreeCell}}
 * {{cite web |url=https://news.ohsu.edu/2006/07/17/computer-card-game-detects-cognitive-changes |title=OHSU scientists say FreeCell can be adapted to spot early signs of dementia |publisher=Oregon Health & Science University |access-date=June 1, 2017}}
-* {{cite web |url=http://www.escapistmagazine.com/articles/view/issues/issue_110/1342-The-Four-Virtues-of-FreeCell.2 |title=The Four Virtues of FreeCell |publisher=The Escapist Magazine |date=August 14, 2007 |access-date=June 9, 2012 |author=O'Hale, Marty M.}}
+* {{cite web |url=http://www.escapistmagazine.com/articles/view/issues/issue_110/1342-The-Four-Virtues-of-FreeCell.2 |title=The Four Virtues of FreeCell |publisher=The Escapist Magazine |date=August 14, 2007 |access-date=June 9, 2012 |author=O'Hale, Marty M. |archive-date=August 8, 2011 |archive-url=https://web.archive.org/web/20110808093819/http://www.escapistmagazine.com/articles/view/issues/issue_110/1342-The-Four-Virtues-of-FreeCell |url-status=dead }}
 == See also ==
-*[[Eight Off]]
+* [[Eight Off]]
 * [[Baker's Game]]
-*[[Klondike (solitaire)|Klondike]]
+* [[Klondike (solitaire)|Klondike]]
-* [[Penguin_(solitaire)|Penguin]]
+* [[Penguin (solitaire)|Penguin]]
 * [[List of solitaires]]
 * [[Glossary of solitaire]]
-{{Solitaire}}
+{{Patience}}
 {{DEFAULTSORT:Freecell}}
@@ Line 80: / Line 85: @@
 [[Category:Open packers| ]]
 [[Category:Patience video games]]
-[[Category:PLATO games]]
+[[Category:PLATO (computer system) games]]
 [[Category:Single-deck patience card games]]
+[[Category:NP-complete problems]]