FreeCell

FreeCell is a solitaire card game played with a 52-card standard deck. Although implementations vary, most versions label the hands with a number (derived from the random number seed used to generate the hand). FreeCell is fundamentally different from most solitaire games in that most deals can be solved (for example, see the Windows version).

Rules

Construction and layout:
*One standard 52-card deck is used.
*There are four open cells and four open foundations. Some alternate rules use between one to ten cells.
*Cards are dealt evenly into eight cascades. Some alternate rules will use between four to ten cascades.

Building during play:
*The top card of each cascade begins a tableau.
*Tableaus must be built down by alternating colors.
*Foundations are built up by suit.

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. While computer implementations often show this motion, players using physical decks typically move the tableau at once.

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

For games with the standard layout (four open cells and eight cascades) most games are easily solved. The Windows version article contains a section that discusses unsolved games.

History

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. This variant is now called Baker's Game. FreeCell's origins may date back even further to 1945 and a Scandinavian game called Napoleon in St. Helena (not the game Napoleon atSt. Helena, also known as Forty Thieves). [ [http://www.solitairelaboratory.com/fcfaq.html FreeCell FAQ] ]

Paul Alfille changed Baker's Game by making cards build according to alternate colors, thus creating FreeCell. He implemented the first computerised version of it in the TUTOR programming language for the PLATO educational computer system in 1978. Paul managed to display easily recognisable graphical images of playing cards on the 512×512 monochrome display on the PLATO systems.cite news|title=One Down, 31,999 to Go: Surrendering to a Solitary Obsession|publisher=New York Times|last=Kaye|first=Ellen|date=2002-10-17|url=http://query.nytimes.com/gst/fullpage.html?res=9F05E6DE143DF934A25753C1A9649C8B63]

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 describes this early FreeCell environment in more detail in an interview from 2000. [ [http://www.freecell.net/f/c/alfille.html Interview with Paul Alfille] ]

Complexity

The FreeCell game has a constant number 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 we must construct a generalized version of the FreeCell game with 4×"n" cards. This generalized version of the game is "provably hard". It was proven to be (NP-complete) in 2000 and this result was first published in 2001. [Malte Helmert, Complexity results for standard benchmark domains in planning, Artificial Intelligence Journal 143(2):219-262, 2003.] The result implies that writing a computer algorithm that efficiently finds solutions for arbitrary FreeCell configurations of the generalized version would answer the P = NP problem, a major scientific breakthrough. A perfect FreeCell playing program running in polynomial time would earn the discoverer a $1,000,000 prize for solving one of the Clay Mathematics Institute's Millennium Prize Problems. However, most researchers believe that no such efficient computer algorithm exists.

Solvers

One of the passions of several FreeCell enthusiasts was to construct computer programs that could automatically solve FreeCell. Don Woods wrote a solver for FreeCell and several similar games as early as 1997.

Another known solver is Patsolve of [http://members.tripod.com/professor_tom/ Tom Holroyd] . Patsolve uses atomic moves, and since version 3.0 incorporated a weighting function based on the results of a genetic algorithm that made it much faster.

Shlomi Fish started his [http://fc-solve.berlios.de/ own solver] beginning in March 2000. This solver wassimply dubbed "Freecell Solver" .

Gary Campbell wrote a solver for FreeCell for DOS in 8086 Assembly. This solver weighs in at 12 kilobytes, and is quite fast.

References