Monday, June 30, 2025

Origin of the Game Gaps (Montana). Rules and How to Play Explained

Gaps, also known as Montana, is a solitaire card game that originated in the early 20th century as a variation of traditional patience games. It gained popularity because of its simple setup and engaging gameplay, which revolves around arranging cards in sequence by suit.

The game is played by organizing the cards into four suit sequences, from 2 to King, within a limited number of moves to clear gaps left by removed Aces. Players must carefully shift cards to fill empty spaces, making strategic decisions to complete the runs efficiently.


Understanding the rules and flow of Gaps helps players develop logical thinking and planning skills. This blend of chance and strategy explains why the game remains a well-liked pastime among card game enthusiasts.

History and Origin of Gaps

Gaps likely developed in the early 1900s as a variation of classic solitaire games. Its design is based on simple mechanics involving arranging cards in sequence while managing open spaces or "gaps." The exact origin is unclear, but it emerged as a household pastime.

The game was probably invented to add a different type strategy than its predecessors like Klondike. Its use of an entire deck and focus on sequences set it apart. Early card collections and rulebooks from the mid-1900s already listed Gaps under the solitaire family.

Evolution of the Game’s Name

The name "Gaps" derives from the key gameplay mechanic: moving cards into empty spaces, or gaps, to reorder the deck. Alternate names such as "Montana" and "Spaces" reflect regional variations and marketing choices.

"Montana" appears to have become popular in the U.S. during the mid-20th century, possibly named to evoke rugged simplicity. The name "Gaps" remains more common in Europe. These titles often accompany slight rule variations but retain the core gameplay.

Spread and Popularity

The game spread through family gatherings and was often included in collections of card games in books or magazines. Its simple but strategic nature appealed to both casual and serious players. Computer versions in the late 20th century further expanded its reach.

Notable Mentions in Literature

Gaps appears sporadically in card game literature starting in the 1930s. Early references often describe it as a useful form of solitaire for passing time. Some card game compendiums include Gaps alongside more widely known patience games.

Anglo-American and European publications discuss Gaps mainly in manuals for recreational card play. Though not the subject of extensive academic study, its listing in notable card indexes cements its place among classic solitaire variants.

Card Setup and Layout Explained

The game requires a specific arrangement of cards to begin play effectively. Players need to understand the deck composition, the initial tableau configuration, and the concept of gaps to start the game correctly.

Dealing the Initial Tableau

The game layout consists of four rows of twelve cards each, dealt face up. The cards are arranged horizontally, forming a grid that covers the playing surface.

The Aces are removed from the playing surface, creating the starting gaps. These gaps are essential as they serve as the initial spaces where cards can be moved during play. Players then organize moves around filling these gaps.

Definition of Gaps

In Gaps, "gaps" refer to the empty spaces created by removing the Aces. They are the key to manipulating cards on the tableau.

Each gap represents a potential spot where a card can be moved to help order the suits into proper sequences. Managing these gaps is crucial for strategy because only cards that can be placed into gaps can be moved, and this flexibility allows players to rearrange cards in ascending order by suit.

Objective of the Game

The main goal is to arrange cards in four suits, each forming a continuous sequence from 2 to King.

Winning occurs when all suits are completed in the correct sequence with no gaps between any cards.

Legal Moves and Restrictions

Cards can be placed only immediately to the right of a gap, and they must in sequence so to remain in ascending order from left to right (2 at left moving through King on right. Cards cannot jump over multiple gaps or cards.

Players cannot move cards into a gap that breaks suit and sequence. The game forbids rearranging cards beyond these rules, enforcing strict control over moves.

Sequence and Suit Rules

Cards are arranged by suit, and sequences must start from 2, progressing to King without interruption. The 2s act as the starting point in the four rows where they are placed.

Each row contains cards from the same suit ordered low to high without mixing suits across rows. This strict ordering means a 3 can only follow a 2 of the same suit, and so on.

How to Achieve Victory

Victory is achieved by organizing the cards from the 2 up to the King, each arranged by suit, in a continuous sequence without gaps.

Careful planning avoids getting trapped with immovable cards. Each move should bring the layout closer to the fully ordered state to win.

Players should look for moves that free critical cards, enabling them to fill gaps in proper order. Recognizing when to temporarily move cards to open spaces is important.

In some cases, endgame success depends on correctly ordering the sequence so that no cards are stuck behind higher or lower cards out of place.

Cultural Impact and Legacy

Gaps holds a niche position among card games, valued for its clarity and strategic depth. Although not as popular as other solitaire games, it retains a loyal following due to its distinctive mechanics.

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Monday, June 9, 2025

Can every FreeCell solitaire game be won? Understanding the solvability of all deals

FreeCell solitaire has intrigued players for decades with its seemingly complex but solvable puzzles. Unlike many card games, FreeCell deals every game with all cards visible, giving players full information to strategize their moves.

Nearly every FreeCell solitaire game can be won, with only a tiny fraction of deals deemed unsolvable. This unique characteristic sets FreeCell apart from other solitaire variants, making it a favorite for those who enjoy logical problem-solving.

Understanding why most games are winnable involves exploring the game's structure and common strategies. This insight reveals how skill and planning influence the outcome more than luck.

Can Every FreeCell Solitaire Game Be Won?

Most FreeCell solitaire deals are solvable, but not all. Identifying the likelihood of solvability, known exceptions, and the factors influencing outcomes helps clarify the game's challenge level.

Mathematical Probability of Solvable Deals

Research shows that over 99.9% of FreeCell deals are solvable. Computer simulations running millions of games confirm that almost every randomized deal can be completed with perfect play.

The 52-card deck and open tableau design create many pathways to success. The statistical likelihood of winning is high because players can move cards freely between eight tableau columns and four free cells, allowing complex card rearrangements.

However, probability does not guarantee a human player will always succeed. The theoretical solvability assumes flawless strategy and patience, which is often difficult in practice.

Historical Analysis of FreeCell Game Numbers

Historically, the original Microsoft FreeCell implementation numbered games only up to 32,000, with only one known unwinnable deal (#11982). Later expansions and studies, including those by www.solitaire-web-app.com, extended this range considerably. www.solitaire-web-app.com hosts “FreeCell of the Day”, a selection of games which are all verified as winnable. Each deal was tested with automated solvers that employ advanced heuristics and exhaustive search algorithms.

FreeCell of the Day

Their method involves iteratively exploring move possibilities until a winning sequence is found or all options are exhausted. In all cases, a solution was identified, which confirms the solvability of the games included in this selection.

Known Exceptions and Unwinnable Games

Some specific FreeCell deals are mathematically unsolvable. Classic example: deal number 11982 in Microsoft’s original FreeCell collection cannot be completed, even by computers.

Unwinnable games occur when key cards become blocked in a way that no sequence of moves can free them. These exceptions are extremely rare but do exist.

Enumerations of FreeCell decks reveal that only a handful out of hundreds of thousands are proven unsolvable. They represent a tiny fraction of all possible deals.

Factors Affecting Game Solvability

The number of free cells and tableau columns affects solvability. Standard FreeCell uses four free cells and eight columns, optimizing maneuverability.

The order of cards on the tableau also impacts chances. Early mistakes in moving cards can reduce future options, even if the deal is theoretically solvable.

Skill in recognizing patterns and planning moves ahead significantly increases winning probability. Without strategy, players might fail even in easily solvable games.

How FreeCell Solitaire Is Designed

FreeCell solitaire is structured around a fixed layout and intricate rules controlling card movement. The initial setup and shuffling method directly affect the solvability of each game and the strategies required.

Rules Governing Game Setup

The game begins with 52 cards dealt face-up into eight columns, known as tableau piles. The first four columns contain seven cards each, while the remaining four have six. No cards are hidden, allowing players to see all cards at all times.

Four free cells act as temporary storage for single cards, aiding in maneuvering cards between tableau piles. Additionally, four foundation piles exist, one for each suit, where cards are built up in ascending order starting from the Ace.

Moves involve stacking cards in descending order and alternating colors on the tableau. Cards can be moved to free cells, tableau piles, or foundations but must follow strict sequencing rules.

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