Gaps Solitaire (Montana)

TSBy The Strategy Desk·Published April 5, 2026

Gaps Solitaire — also known as Montana — is a captivating patience card game where all 52 cards are dealt face-up into a 4×13 grid. After removing the four Aces to create gaps, you slide cards into the empty spaces to build complete suit sequences from 2 through King in each row.

How Gaps Works

A card can move into a gap only if it is one rank higher and the same suit as the card immediately to its left. For instance, if the 7♥ sits to the left of a gap, only the 8♥ can fill it. Gaps in the leftmost column accept any 2, since rows must start with a 2. A gap to the right of a King or another gap is “dead” — nothing can go there.

Redeals

When you run out of moves, you can redeal (up to 2 times). Cards that form a correct sequence from the left of their row — starting with a 2 — are locked in place. All other cards are gathered, shuffled, and redealt. Aces are removed again to create fresh gaps. Use your redeals wisely — they're limited!

History & Origins

Gaps has collected an unusual list of aliases: Montana, Spaces, Vacancies, and occasionally Addiction — each name highlighting a different aspect of the game. The earliest printed rules we have found sit in early-twentieth-century American patience compilations, which framed it as a puzzle rather than a card game, since there is no stock, no waste pile, and no hidden information. A four-by-thirteen grid contains exactly the fifty-two cards of the deck, and lifting the four aces produces four gaps the player rearranges the rest of the grid into. The Montana nickname appears in American newspapers in the 1930s, possibly a reference to the wide-open-spaces feel of the cleared grid, and Vacancies / Spaces come from English parlor sources. The three-deal variant — two redeals on top of the initial shuffle — became the standard ruleset once the game migrated into computer editions, because it pushed the win rate into a range players found both satisfying and fair. That is the edition we have followed here.

Strategic Principles

Gaps is a planning game wearing the clothes of a card game. Each move is mechanically trivial — slide one card into one gap — but the sequence in which we move cards decides whether the grid solves or deadlocks. We begin every game by locating the four twos and asking whether any of them can reach a leftmost-column gap on this deal. A two that cannot reach column one is a row-killer: the row it belongs to cannot be built in this deal and will have to wait for a redeal.

Once we know which rows can open with twos, we plan gap-chains several moves ahead. A single move creates a new gap behind the card we moved — and that new gap may or may not be productive. If moving the 6♥ into gap A opens a new gap behind it that accepts the 9♠ we need, we take the move. If the new gap is dead (next to a king, or next to another gap), we have wasted the move and frozen a useful neighbor. We look two moves ahead minimum, three when the board is crowded.

Kings are Gaps' structural villains. Every king is the end of a chain, and the gap immediately to its right is permanently dead for the rest of the deal. So we track where the kings sit and treat the spaces behind them as frozen terrain. If two kings end up adjacent after our manipulations, we have effectively lost two gap slots. The art is keeping gaps mobile — always in positions where some card in the grid can legally fill them — because once all four gaps are dead, we must redeal.

After a redeal, card order matters enormously. The redeal preserves the locked prefixes — the consecutive run from column one to wherever the sequence breaks — and reshuffles everything else into the open slots. Longer prefixes lock more cards, which means the next deal starts with less chaos and better odds. So when we are approaching a forced redeal, we stop chasing random moves and specifically work to extend each row's locked prefix by one or two cards. Those last-minute extensions can turn a hopeless redeal into a solvable one.

Difficulty & Win Rate

Gaps has a tunable difficulty curve based on redeals. With zero redeals (a single deal), the theoretical win rate drops below five percent — most shuffles create dead-king neighborhoods that cannot be unwound in one pass. With the standard two redeals (three total deals), solver analyses put the win rate at roughly forty-five percent under careful play, which is where most published references place the game. Unlimited-redeal variants push the rate toward ninety percent, but lose the “race against the redeal” tension that gives Gaps its character. Human players typically land in the thirty-to-forty percent range as they learn to extend locked prefixes before redealing. Gaps is more forgiving than Forty Thieves or Baker's Dozen, but more punishing than FreeCell — a middleweight patience with genuine skill differentiation.

Common Mistakes

The classic Gaps mistake is impatient redealing — triggering a redeal while the current deal still has productive moves, or triggering without first extending locked prefixes. Each redeal is a finite resource, and wasting one on a board we had not fully solved is the fastest route to a loss. A second common error is moving cards into leftmost-column gaps without checking which two we are committing to that row; placing the wrong two locks a row into a suit whose sequence cannot complete. A third mistake is creating king-adjacent gaps — moving a card into a slot whose exit gap will land next to a king, burning two gap slots with one move. We also see players ignore multi-step chains, taking the first legal move they spot rather than scanning all four gaps to find the move that unlocks the most downstream moves. Finally, many players underestimate the value of locked- prefix extension at the end of a deal: an extra thirty seconds spent sequencing columns one through four can lock twelve extra cards before the redeal, dramatically improving the next shuffle's solvability.

How This Game Compares

Gaps is structurally unique among common patiences. Compared to Klondike or FreeCell, it dispenses with foundations, stocks, and tableau stacking entirely — there is only the grid and the gaps. Compared to TriPeaks or Golf, which are discard-based, Gaps is arrangement-based: cards never leave the board, they just slide around. The closest cousin is probably Eliminator or Accordion, both of which treat the shuffled deck as a grid to be rearranged, but Gaps is more constrained — every slide must match both suit and rank-plus-one. The game it feels most like, despite sharing no mechanics, is a sliding-tile puzzle: the deal is the scramble, the gaps are the blank tiles, and the goal state is “each row in ascending suit order.” That lineage may explain why Gaps feels more like a puzzle and less like a card game than any other patience in the common rotation.

Variant Notes

Gaps has spawned several rule tweaks. “Montana (strict)” forbids redeals entirely and accepts a sub-five-percent win rate as the price of honest difficulty. “Addiction” allows unlimited redeals, which pushes the game toward solvable-in-principle territory. “Spaces” sometimes requires the leftmost-column gap to accept only the two of a specified suit, turning each row into a suit-committed sequence from the first move. “Paganini” uses a double deck and eight rows, producing a grid-patience epic that takes twenty minutes to solve. Our implementation follows the classic three-deal standard: one initial deal, two redeals, leftmost-column gaps accept any two, correctly sequenced prefixes lock during redeals, and the four kings act as chain terminators with dead gaps to their right. Players who enjoy Gaps may also want to try Cruel, another redeal-driven patience.

Strategy Tips

• Prioritize placing 2s in the leftmost column early to start building sequences.
• Avoid creating dead gaps next to Kings — plan moves to keep gaps productive.
• Build sequences from the left side of each row to lock more cards during redeals.
• Save redeals for when you're truly stuck — sometimes one more move opens up.

Learn More

• How to Play Gaps — Complete rules and strategy guide
• Gaps (Montana) Strategy Guide — Tips and winning tactics
• Play Cruel Solitaire — Another patience game with redeals
• Play FreeCell — The classic free cell solitaire
• Types of Solitaire — Explore 20+ solitaire variants