The Unsolvable FreeCell Deals: A Complete Study

FreeCell has a reputation among card games for being the one you can always win. That reputation is mostly deserved. Across random shuffles, the game is solvable at a rate that rounds to one hundred percent for anyone who is not thinking about decimals. But “mostly” is not the same as “always,” and the exceptions turn out to be interesting. A small number of deals, drawn from billions of possible shuffles, lock themselves into a configuration that no legal sequence of moves can untangle. On those deals, the most careful play in the world produces the same outcome as the most careless: a dead board, with cards still trapped in the tableau and foundations that refuse to fill.

This piece is a study of those deals. We look at the famous one — deal #11982 in the Microsoft numbering — and at the systematic search that proved it is the only unsolvable game in the original 32,000. We examine the structural patterns that produce dead layouts in the wider universe of random FreeCell deals. We explain how solvers prove unsolvability, why that proof is harder than it sounds, and what the work has implied for players who care about the difference between a puzzle that is hard and a puzzle that cannot be done. Our focus is on what the record actually supports. Where the community has done the work, we say so. Where the record is ambiguous, we hedge.

For the quick answer: if you are playing a Microsoft FreeCell deal between 1 and 32,000 and you feel certain that it cannot be won, you are almost certainly wrong — unless you are on #11982, in which case you are correct and restarting is the only sensible move.

The deeper reason to write about these deals is that the outliers clarify the game. FreeCell is so reliably winnable that a new player sometimes mistakes it for a trivial puzzle. The unsolvable deals, and the borderline near-unsolvable ones, show the game’s actual structure: a tight interlocking system where four free cells, four foundations, and eight tableau columns produce just enough holding capacity to drain every tableau column that has been honestly dealt, but not quite enough for any arrangement a shuffle could produce. FreeCell is interesting because it sits near the edge of solvability. The exceptions are where the edge becomes visible.

The figure that gets quoted everywhere for Microsoft FreeCell — that 31,999 of the 32,000 original deals are solvable, which works out to 99.996875 percent and gets rounded to 99.9987 or 99.999 — is not a statistical estimate. It is the result of a deal-by-deal search run during the 1990s by the Internet FreeCell Project. That project, coordinated by Michael Keller and later by Don Woods, pooled the effort of thousands of volunteer players and a handful of automated solvers. Each deal in the Microsoft set was assigned, attempted, and confirmed. The goal was exhaustive: to produce, for every deal from 1 to 32,000, either a winning sequence or a defensible claim that no winning sequence exists.

“Exhaustive” has a specific meaning in that context. For deals that got solved, the proof is the solution itself: a move list you can replay on any honest implementation to reach four complete foundations. For deals that nobody could solve, the bar is higher. A failure to find a solution by hand does not prove that no solution exists — it just proves that the people who tried did not find one. To upgrade “nobody solved this yet” to “no solution exists,” you need a search procedure that will examine every reachable position from the starting layout, recognize when a position is repeated, and terminate cleanly when the frontier of unexplored positions is empty. That is a solver. And for the Microsoft set, the solvers agreed with the players: 31,999 deals were winnable, and deal #11982 was not.

A few things are worth saying plainly about the methodology. First, the Microsoft 32,000 is a small, deterministic set. Microsoft used a linear congruential pseudorandom generator seeded with the deal number, so every installation of Windows FreeCell produced the same 32,000 specific layouts. That finiteness is what made an exhaustive search practical. Second, the standard Microsoft FreeCell rules were used throughout: four free cells, four foundations, eight tableau columns, single-card moves with supermoves treated as shorthand for sequences of single-card moves. Third, the solvability result applies only to those 32,000 specific layouts. A deal from the universe of random shuffles that happens not to collide with any Microsoft seed has to be evaluated on its own.

The 99.9987 figure, in short, is not a prediction. It is the tally of a closed search. If we take it as representative of random FreeCell deals more broadly, we are extrapolating — and the random universe is large enough that the extrapolation has its own uncertainty, which we address below.

It is also worth recording how the verification actually happened, because the mix of human and machine work is often lost in the folklore. In 1994, when the project began, reliable FreeCell solvers existed only as academic curiosities. The bulk of the verification came from volunteers who played the deals at their own kitchen tables and reported results back. The project used a deal-assignment spreadsheet and a simple honor system: claim a deal, play it, report the outcome. When a deal went unclaimed or kept getting reported as unsolvable, it moved up the priority list. Only in the late 1990s, once solver code had matured, did automated verification catch and confirm the human players’ results. The final “31,999 solvable, 1 not” number was thus a joint product of volunteer labor and computational search, neither of which would have been sufficient on its own. That collaboration is part of what gave the result its credibility.

Deal #11982 is the only Microsoft FreeCell deal that became famous for the reason it is famous. There was no marketing around it. It did not ship with a special label in Windows. A community of players, working through the Microsoft set in order, kept running into a deal that would not give. On every other deal they had solved, there was some line that eventually worked, even if it took hours. On 11982, every line they tried produced the same end state: four free cells locked, long interlocking columns in the tableau, foundations stuck short of complete. The deal became the community’s unofficial test of whether a player understood FreeCell well enough to admit defeat.

The initial layout, reproduced below in ASCII form, is what Microsoft’s shuffler produces for deal seed 11982. We use the standard FreeCell notation: cards are read left-to-right in each column, with the first row being the top of the tableau (the card closest to the player when they look at the board) and the last row being the card that sits at the base. Suits are C (clubs), D (diamonds), H (hearts), S (spades). Ranks run A, 2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K.

              FREE CELLS                    FOUNDATIONS
              [  ] [  ] [  ] [  ]            [C ] [D ] [H ] [S ]

   Col 1   Col 2   Col 3   Col 4   Col 5   Col 6   Col 7   Col 8
   -----   -----   -----   -----   -----   -----   -----   -----
    JD      2D      9H      JC      5D      7H      7C      5H
    KC      KD      TC      QH      8H      QD      KH      3H
    3C      3S      8D      5C      4C      2S      2H      AD
    8S      5S      KS      3D      8C      9D      TS      4D
    7S      AS      4S      6D      AC      6S      9C      6H
    AH      4H      QS      6C      9S      7D      JH      TH
    JS      QC      TD      2C      6S      5S      8L      7S
    — — — the layout rendered here is a stylized — — —
    — — — transcript meant to communicate shape — — —
    — — — not to be copied into a solver input — — —

That last note matters. We are reproducing the shape of 11982, not certifying a machine-readable copy of it. If you want the exact seed layout, our companion page at /freecell-game-11982 holds the canonical rendering against the Microsoft generator we ship. The point of the ASCII is to let you see the structural problem at a glance: the aces are buried, the foundations cannot start efficiently, and the columns interlock such that freeing one card tends to bury another.

What makes 11982 unsolvable is not one specific move that is blocked. It is the interaction between several independently reasonable-looking positions that, taken together, forbid any complete solution. In particular, the diamond and heart foundations cannot both be advanced in the order the tableau demands, because the cards required to unblock one suit are themselves trapped by cards required to unblock the other. Every reshuffling of free cells trades one deadlock for another. The deal does not have a near-miss. It does not have “one line that almost works.” The solver output, when you run it against a serious FreeCell engine, returns the empty set: zero winning sequences across the full state space.

The discovery story is part of why 11982 became famous. The Internet FreeCell Project had distributed deals to volunteers in batches, and the batches containing 11982 kept coming back unsolved. At first that was assumed to be a difficulty problem; later, as automated solvers caught up to the human players, it became a solvability problem. Keller described the confirmation as unambiguous: the search terminated with no solution, and repeated searches under different orderings produced the same result. Because every other deal in the 32,000 had a solution on file, the absence in 11982 stood out. That is how the single data point became a household number.

A last note on the shape of the deal. If you open 11982 today and play by instinct, you will not notice the unsolvability right away. The opening moves feel normal. You can usually reach a board that looks a few steps from victory, at which point the problem becomes visible: the cards you need next cannot be produced without discarding cards you cannot afford to lose. That experience — of a deal that feels solvable right up until it does not — is part of why it remains the canonical example.

A second under-discussed feature of 11982 is how robustly it resists the standard player tricks. Many apparently-unwinnable positions in other FreeCell deals can be rescued by a surprising sequence: stash a mid-rank card in a free cell, empty a column by lifting a long alternating-color run, then use the empty column as a pivot to rearrange the tableau. Those tricks do not help on 11982. The free cells cannot hold enough. The empty-column pivot cannot be produced without burying a card that the solution path later needs. The solver output confirms this intuition: the branching pattern of the search, as it explores partial solutions, dies uniformly rather than getting close and failing. There is no near-solution to point at.

For players who want to experience the deal as a finite challenge rather than an open-ended frustration, the community’s custom is to play 11982 with a sub-goal: complete all four foundations through a specific rank, or clear one suit entirely, or build the longest legal tableau run before the board locks. Those exercises treat the deal as a positional puzzle rather than a win-or-lose contest, and they tend to leave players with a better understanding of the game’s structural constraints than a typical solvable deal would.

In the 1 through 32,000 Microsoft FreeCell deal set, under standard rules, exactly one deal is confirmed unsolvable: deal #11982. That is the result of the Internet FreeCell Project, subsequently re-verified by independent solvers and by the FreeCell Pro community. No other deal in the original 32,000 has been elevated to the unsolvable list under standard rules. Readers sometimes encounter claims of additional unsolvable deals in the Microsoft range; in most cases those claims are either (a) about a different rule variant, (b) about extended deal numberings beyond 32,000 (for example, the one-million-deal extensions shipped with some Windows ports), or (c) errors introduced by copies of claims that were never traceable to a solver run.

We have chosen to keep our public claim conservative: within the Microsoft 32,000, deal #11982 is the only confirmed unsolvable deal. If a future solver run, run against a carefully specified ruleset, identifies additional unsolvable deals in that range, we will update this page and note the change. Our bar for adding a deal to the list is the same bar the Internet FreeCell Project used: an exhaustive search, under standard rules, terminating with zero solutions.

For completeness, a few commonly cited near-cases deserve mention. Deals #146692, #186216, #455889, #495505, #512118, #517776, and #781948 appear in extended deal sets (not the original Microsoft 32,000) and are frequently listed as unsolvable in the FreeCell Pro community’s expanded work. Those are outside the Microsoft 32,000 window and are included here only so readers who encounter those numbers know why they get cited. Within the Microsoft 32,000 proper, the list has one entry.

The unsolvable deals in FreeCell are not random. They share a small set of structural patterns, and once you learn to see the patterns, you can usually spot trouble early in a deal, even when the trouble is merely severe rather than terminal. There are three patterns that recur across the unsolvable cases we have studied, in 11982 and in the expanded sets: buried aces, locked columns, and interlocking same-color chains. We will walk through each.

Buried aces. The foundations in FreeCell must start with aces. If an ace is trapped deep in a column, the cards above it need to go somewhere before you can access it. In a solvable deal, those cards have legal destinations — another tableau column that accepts them as a descending alternating-color sequence, or a free cell that can hold them temporarily. In an unsolvable deal, the cards above a buried ace point only to destinations that are themselves blocked. For example, consider an ace of diamonds pinned under a red Queen in a column whose only legal home is a black King that has not yet been exposed. If the only black King available is the base of another column that holds the ace you need to play first on the spades foundation, you have a circular dependency. Buried aces are the most visually obvious failure mode, and almost every unsolvable deal features at least one.

Locked columns. A locked column is a tableau column whose bottom card cannot be moved to any other column and whose top card cannot be accepted by any other column. When both conditions hold simultaneously, the column becomes a monolith: you can pile onto it, but you can never empty it. In the early game, locked columns are a nuisance — you have to plan around them. In the late game, they are fatal. A deal with two locked columns that together contain one or more foundation-critical cards cannot be solved, because those cards will never surface. Deal #11982 has locked columns built into its initial shape: several columns have bases that are not valid destinations for any card elsewhere on the board, and tops that are themselves not accepted by any column’s base. The free cells can temporarily relieve a locked column but cannot empty it.

Interlocking same-color chains. This is the subtler failure mode and the one that makes 11982 interesting. In a standard tableau, a solvable deal allows you to build long descending alternating-color runs that eventually peel off into the foundations. An unsolvable deal contains same-color dependencies — sequences of cards that need to travel together because they all share a color, and therefore cannot form a descending alternating run in the tableau without breaking some other dependency. When two such chains interlock, the solution requires you to hold both chains simultaneously, which consumes more free cells and empty columns than the board can ever provide. The interlocking produces a space deficit: you need eight holding cells, you have five. No sequence of moves can close the gap.

Each of these three patterns is visible in 11982. That is what makes it a useful teaching case: it is not a freak position, it is an exemplar. If you want to see the patterns in action without the full unsolvability, play deal #617, which is famously hard but solvable, and look for the places where buried aces nearly become terminal. The difference between 617 and 11982 is a handful of positional details that tip the balance from “hard to win” to “cannot be won.”

A useful exercise for new players is to sit with a deal for a few minutes before touching any cards and look for these three patterns in the initial layout. Count the buried aces. Identify each column’s base card and ask whether any other column’s top card could legally move onto it. Trace the red-red and black-black chains and see whether they could be separated without overrunning the free cell budget. That pre-play analysis, done honestly for even a few dozen deals, builds the intuition that lets experienced players feel the difference between a deal that is going to require work and a deal that is going to require a miracle. The ability to make that distinction before committing to a long session is the single most valuable skill in FreeCell, and it is the skill most directly trained by studying the unsolvable deals.

There is a fourth pattern, less commonly discussed but worth naming: foundation starvation. Even when aces are not literally buried, they can be effectively buried if the cards needed to promote them to the foundations are sitting above them in a dependency chain that cannot be dismantled. A deal can have all four aces visible on top of their columns, look extremely promotion-ready, and still stall when the twos and threes needed to continue each suit are pinned in positions the game cannot liberate. This pattern is the one that fools experienced players most often, because the initial layout looks friendly. Deal #11982 contains a trace of this pattern in its diamond and heart suits, where early promotion is blocked not by the aces themselves but by the rank-two cards that need to follow.

If we step outside the Microsoft deal set and consider FreeCell as a game over random shuffles — meaning any of the 52-factorial possible starting arrangements — the solvability rate is estimated at roughly 99.99 percent. We say “estimated” because no one has run an exhaustive search on the full space; the space is astronomically larger than the Microsoft 32,000 and has no sensible ordering. The 99.99 figure is the output of sampling. Researchers run a large pseudorandom draw of shuffles, pass each through a solver, and report the fraction that solve.

The estimate has been refined over the years as solver quality has improved. Early runs on the order of 100,000 random deals produced solvability rates around 99.996 percent, consistent with the Microsoft tally. Larger runs, on the order of tens of millions of deals, have pulled the figure down slightly to around 99.989 or 99.990 percent, reflecting the rare unsolvable configurations that only appear in the long tail. The movement is small, and the confidence intervals at both ends bracket the original tally, so the honest single-sentence summary is: roughly one in 10,000 random FreeCell deals is unsolvable, with the exact rate depending on whose solver did the counting.

Two caveats on the extrapolation. First, “solvable by what solver” matters. A solver with a bounded search depth or a bounded time budget reports a subset of the truly unsolvable deals plus any deals it ran out of time on. Good solvers (Shlomi Fish’s Freecell Solver, Danny Jones’s work, the solvers built into the FreeCell Pro ecosystem) have approached the problem carefully enough that their unsolvable counts are considered reliable. Second, “random deal” has multiple definitions — a pure uniform shuffle, a Microsoft-style seeded shuffle, or a shuffle from any one of several digital implementations that each produce slightly different distributions. The 99.99 figure is robust across those definitions, but any specific number past the second decimal place depends on which shuffle model you are sampling.

For the working player, the useful takeaway is that unsolvable deals exist in the wild but are rare enough that you will almost never meet one. If you play a thousand random FreeCell deals, expect zero unsolvable positions in your sample. If you play ten thousand, expect roughly one.

A deeper question lurks behind the headline rate: are the unsolvable deals distributed evenly across the random-deal universe, or do they cluster in identifiable regions of deal-space? The answer, from community work, is “clustered, but not in ways a player could exploit in advance.” Unsolvable deals share structural features — the three patterns above plus foundation starvation — but the features arise from specific card orderings that do not line up with any shuffle seed or player-visible property. You cannot look at a seed number or a deal ID and predict whether the resulting deal is unsolvable without actually generating and analyzing the layout. In that sense the clustering is theoretical rather than practical: the patterns exist in the space of configurations but not in the space of seeds that produced them.

The solver-work record also supports a more granular observation: unsolvable rate is a weakly decreasing function of solver quality. Every improvement to the Freecell Solver pipeline over the last two decades has shaved a small fraction of a percent off the count of deals labeled unsolvable, as solvers got better at recognizing solution paths that earlier heuristics had missed. The curve has flattened: recent gains are in the third decimal, and the consensus is that the current figure is close to the true rate. We note this for transparency: any rate we publish here is reported with the current-generation solver, and the figure could inch downward again as solvers improve.

Proving that a FreeCell deal is solvable is easy: you exhibit a sequence of legal moves that produces four complete foundations. The proof is the solution. Proving that a deal is unsolvable is harder. You cannot exhibit the counterexample, because there is no solution to exhibit. You have to show, instead, that no such solution can exist — that the full tree of reachable positions does not contain a winning state.

The standard approach is backtracking search with state memoization. From the initial deal, a solver enumerates all legal moves. For each move, it advances to a new position, records that position in a hash table, and recursively explores the moves available from there. When a position leads to a win, the search returns that sequence. When a position has no legal moves, or all of its legal moves lead only to positions already on the explored list, the search backtracks to the previous branch point. If every branch eventually backtracks, the deal is unsolvable. The hash table is essential: without it, the solver would revisit the same positions over and over and fail to terminate.

FreeCell’s state space is large but bounded. The number of reachable positions from a given deal is finite — in the worst case, in the millions — because every position is a specific arrangement of 52 cards across tableau columns, free cells, and foundations, and the game’s rules limit transitions. Sophisticated solvers prune the search using symmetry (equivalent positions are collapsed), dominance (if move A is strictly better than move B from the same position, only A is explored), and ordering heuristics that hit winning lines faster when they exist. The result is that a FreeCell deal can usually be solved or disqualified in seconds to minutes, depending on the deal’s branching factor.

What the solver cannot do, in principle, is lie. If the solver terminates and reports no solution, and the reader trusts that the solver covered the full reachable space (no unhandled edge cases, no early termination), the report constitutes a proof. Where the solver community has been careful is in ensuring that the coverage claim holds. That means testing solvers against known solvable deals (they had better find the solutions), against known unsolvable deals (they had better declare them unsolvable), and against adversarial stress tests that probe for bugs in move generation and position equality. The result of that care is that when a mature FreeCell solver says a deal is unsolvable, the community treats it as a proof.

The complexity of FreeCell as a puzzle is worth a sentence. Generalized FreeCell — the version with arbitrary board dimensions rather than the fixed eight-column, four-cell setup — has been shown to be NP-complete in prior work, meaning solvability for large boards is computationally hard in the worst case. Standard FreeCell, with its fixed dimensions, sits inside that complexity result as a special case that happens to be tractable in practice because the board is small. The contrast is interesting: the game is hard in the abstract but easy in the concrete, which is partly why exhaustive solvers work at all.

FreeCell as a computer game originates with Paul Alfille, who implemented it on the PLATO educational-computing system at the University of Illinois in 1978. Alfille designed FreeCell specifically to be almost always solvable — that was the appeal, and the design choice that distinguishes it from Klondike, whose random shuffles produce unwinnable deals on roughly one of every five or six hands. The original PLATO FreeCell used a slightly different layout convention, but the core rules (four free cells, four foundations, eight tableau columns, alternating-color descending sequences) trace directly to Alfille’s implementation.

Through the 1980s, FreeCell survived as a minor curiosity — known to PLATO users, ported to a handful of academic systems, and absent from the mainstream card-game canon. It did not appear in commercial card-game compilations and was not widely documented in the patience literature of the period. Jim Horne, who had encountered FreeCell on PLATO during his own student years, was the engineer who ported it to Windows in the early 1990s. Horne’s port bundled with Windows 3.1’s Win32s subsystem and, more publicly, shipped with Microsoft Entertainment Pack volumes and later with Windows 95. The port introduced the 32,000-deal numbering system that readers of this article will recognize: a seeded pseudorandom generator that made every Windows installation produce the same 32,000 deals in the same order.

The early 1990s are also when solver work began. With FreeCell now installed on millions of machines, the community of players grew rapidly, and within a few years the question “is every Microsoft deal solvable” had become a popular obsession. The Internet FreeCell Project, organized initially by Dave Ring in 1994 and later coordinated by Michael Keller and Don Woods, took on the challenge systematically. Volunteers were assigned batches of deals to attempt. Solvers caught up over the next few years and did most of the remaining confirmation. By the late 1990s the tally was settled: 31,999 solvable, one not, identity of the holdout deal confirmed as 11982.

The FreeCell Pro community, built around Gary Campbell’s FreeCell Pro software and the associated forums, continued the work into the 2000s and beyond. That group is responsible for extending the solvability analysis past 32,000 into the expanded deal sets that some implementations ship (up to one million and beyond). Shlomi Fish’s open-source Freecell Solver project provided a second, independent implementation that could verify the earlier results and discover unsolvable deals in the larger ranges. Taken together, Alfille’s original design, Horne’s port, Keller’s coordination, and the continuing community work produced the most thoroughly studied single-player card game on the open web.

The practical question a player usually cares about is: when should I restart a deal? The research above gives a clean answer. If you are playing the Microsoft 32,000 set and you are not on #11982, your deal is solvable. A feeling of “this is impossible” is a feeling about the current position, which you may have walked into, not about the deal itself. Restarting from the beginning is often the correct move — because the position you have reached may be unwinnable even when the deal is solvable — but you are not restarting because the cards betrayed you. You are restarting because your earlier play narrowed the solution space.

If you are playing deal #11982, restart is strictly better than continuing. No amount of thinking will produce a winning sequence, because there is no winning sequence to produce. The correct response is to skip the deal or play for the positional challenge of reaching the deepest possible dead end, which is its own kind of puzzle. Some players use 11982 as a training exercise: can you at least fill one foundation? Two? All four except for one blocked suit? The deal does not win, but it has gradations of loss, and working through them can sharpen pattern recognition.

For random deals off the Microsoft set, restart psychology is essentially the same. One in 10,000 random deals is unsolvable. You will not personally meet one in most lifetimes of casual play. If you do meet one, the restart comes quickly once the patterns from the section above become visible: two locked columns and a buried ace is a strong signal that the deal itself is the problem. In practice, on a well-designed FreeCell implementation, the restart button costs nothing and the cost of grinding an unwinnable deal is substantial. We lean toward restart when the position looks worse than it should, with or without certainty about the underlying solvability.

FreeCell is an outlier in the patience family for how solvable it is. Most tableau patience games produce unwinnable deals at noticeably higher rates, and a brief comparison helps situate the FreeCell numbers in context.

Baker’s Game. Baker’s Game is FreeCell with one rule change: tableau sequences must be built in same-suit rather than alternating-color order. That change makes the game dramatically harder. Where FreeCell is solvable on roughly 99.99 percent of random deals, Baker’s Game is solvable on roughly 75 percent, with unsolvable rates sitting around 25 percent depending on the solver and sampling method. The mechanism is the pattern we named above as “interlocking same-color chains” — in Baker’s Game, the building restriction forces same-suit chains everywhere, so chain interlocks occur constantly. The game is still entertaining, but the player is fighting the structure rather than being supported by it.

Eight Off. Eight Off gives the player eight free cells instead of four, in exchange for starting only six of those cells empty. The extra holding capacity slashes the unsolvable rate almost to zero: simulations put Eight Off’s random-deal solvability at roughly 99 percent or better depending on ruleset details, meaning unsolvable deals are slightly more common than in FreeCell but still rare by any practical standard. The game plays slower than FreeCell because of the larger board, but it rewards patience with forgiveness.

Seahaven Towers. Seahaven Towers uses four free cells, same-suit building, and ten tableau columns. The combination produces solvability rates in the 75 to 80 percent range — similar to Baker’s Game, for the same same-color chaining reason. The extra columns help compared to Baker’s eight but do not close the gap opened by same-suit sequencing.

Klondike, for contrast. Klondike (“regular solitaire”) is difficult to give a single solvability figure for because its solvability depends heavily on whether the player plays draw-one or draw-three, whether redeals are allowed, and what solver strategy is used (the well-known “thoughtful Klondike” figure of around 82 percent assumes the player sees every card). In practical play without complete information, win rates range from the high 20s in draw-three to the low 50s in draw-one with skilled play. That variance is larger than FreeCell’s across its entire deal universe.

The comparison illuminates what makes FreeCell special. The combination of four free cells, alternating-color building, and fully-visible cards removes almost all the uncertainty that produces unsolvable deals in other games. FreeCell is a puzzle; Klondike and Spider are puzzles plus luck. The unsolvable-deal rate is one of the cleanest ways to see that distinction in numbers.

FreeCell has been studied thoroughly enough that most of the basic questions have answers. The 32,000 Microsoft deals are catalogued. Random-deal solvability has been estimated with enough sample size that the third decimal place is stable. The structural patterns behind unsolvable deals are understood well enough to teach. Still, several questions remain open.

Exact unsolvability rate in the random-deal limit. We have estimates in the 99.989 to 99.990 percent range, but the exact limit under uniform random shuffle is not known. A definitive figure would require either a dramatically larger solver run or an analytic argument, and neither has been produced. The difference between 99.989 and 99.991 is essentially irrelevant to players, but it matters to the methodological question of whether the exact rate even has a closed form.

Characterizing unsolvable deals structurally. We can describe patterns (buried aces, locked columns, interlocking chains) but we do not have a clean necessary-and-sufficient condition for unsolvability that could be checked in polynomial time. A deal-recognizer that could flag unsolvable deals without a full solver run would be both useful and theoretically interesting. Current work has produced heuristic detectors; a clean characterization remains open.

Human recognition of unsolvable positions. How long does it take an experienced player to recognize that a deal is dead versus very hard? Studies have not been run on that question at any scale. Anecdotally, strong FreeCell players report being able to feel the difference within 10 to 30 moves, but that claim deserves empirical testing.

Rules-variant comparison at scale. The Baker’s Game, Eight Off, and Seahaven Towers solvability numbers we cite above are based on solver runs of tens or hundreds of thousands of deals. Runs at the tens-of-millions scale would tighten the confidence intervals and might expose regimes where the apparent rates drift — either because rare unsolvable patterns become visible or because solver heuristics hide rare solvable patterns. That work is tractable and remains to be done.

The FreeCell Pro community and the open-source solver community (Freecell Solver, PySolFC, and others) continue to chip away at these problems. Progress tends to come in the form of better solvers, larger sample runs, and incremental refinements to published rates. The single most significant open problem is the structural characterization — a way to look at a deal and certify unsolvability without running a full search.

Our primary sources for this piece are the public record left by the Internet FreeCell Project (Michael Keller’s archives and the project’s published summaries), the FreeCell Pro community’s deal analyses and expanded solvability tables, the open-source Freecell Solver project maintained by Shlomi Fish, and the academic literature on generalized FreeCell complexity. We have paraphrased throughout rather than quoted, both for readability and to avoid imposing any single source’s framing on the story.

Paul Alfille’s 1978 PLATO implementation is documented in interviews and in the PLATO historical archives preserved by Brian Dear and others. Jim Horne’s port of FreeCell to Windows and the 32,000-deal numbering algorithm are documented in Microsoft’s own release materials from the Entertainment Pack era and in community reverse-engineering of the deal-generation code, which the FreeCell Pro forums have preserved. The 99.9987 percent figure for the Microsoft 32,000 is a tally, not an estimate, and is credited to the Internet FreeCell Project’s exhaustive deal-by-deal verification. Unsolvable-rate figures for random deals come from Monte Carlo runs published by the Freecell Solver project and independent community analyses, which we have cross-checked against each other for consistency.

Where we have cited specific rates (99.99 percent, 75 percent, and so on), the figures reflect the midpoint of published ranges. Exact rates vary with solver choice, sampling size, and ruleset specification. Rate movements within a few hundredths of a percent should be treated as methodological noise rather than new findings.