FreeCell Solvability: Why You Can Win Almost Every Deal

What "solvable" means in FreeCell

A deal is solvable if at least one legal sequence of moves delivers all 52 cards to the foundations. In most solitaires that question is muddied by hidden information — you might play perfectly against the cards you can see and still lose to the ones you cannot. FreeCell removes the ambiguity entirely. Every card is face up from the deal, there is no stock and no redeal, so a deal's fate is decided the moment it is shuffled. Either a path exists through the tangle or it does not, and a computer can check exhaustively.

Computers have checked. Solver programs have chewed through millions of numbered FreeCell deals, and the verdict is remarkably one-sided: of the first one million deals in the standard numbering, only eight have been proven to have no solution — a solvability rate of 99.9992%. Play a fresh deal here every day and, statistically, you would wait several lifetimes to be dealt a genuinely impossible one.

Compare that with the rest of the solitaire family: roughly a fifth of Klondike deals are unwinnable no matter what, and Baker's Game — FreeCell's stricter suit-building sibling, which you can also play on this site — is commonly estimated to be solvable only around three-quarters of the time. FreeCell's four free cells and alternate-color building sit in a mathematical sweet spot that keeps nearly every shuffle honest.

Deal #11982: the exception that proved the rule

When Windows 95 shipped FreeCell with 32,000 numbered deals, the help file included a teasing line suggesting that every deal might be winnable — and challenged players to prove otherwise. The internet took the bait. In 1994, Dave Ring organized the Internet FreeCell Project, splitting the 32,000 deals among about a hundred volunteers who played and re-played their assigned numbers, reporting each one solved or stuck.

One by one the deals fell — except #11982. No volunteer could crack it, and the deal became a minor internet legend, passed around as a dare. The human verdict was later confirmed the hard way: exhaustive computer search of every reachable position shows that deal #11982 has no winning line at all. Its cards simply interlock — the low diamonds and clubs sit beneath blockers that can never be relocated in time, no matter how cleverly the free cells are juggled.

The story cuts both ways for players. It proves FreeCell is not literally always winnable — but it also means 31,999 of 32,000 deals were beaten by ordinary players with patience and undo. When your game locks up, the overwhelming likelihood is that the position is still alive and the mistake was somewhere in your line. That is precisely why replaying a lost FreeCell board is worthwhile in a way replaying a lost Klondike deal is not.

The supermove formula

Solvable does not mean easy, and the bridge between the two is the supermove. Strict FreeCell rules move one card at a time; empty free cells and empty columns act as temporary parking that lets you relocate a whole ordered run in a single gesture. The capacity is:

(empty free cells + 1) × 2^{empty columns}

Each free cell holds one card of the run while the rest move, hence the +1. Each empty column can stage half of a larger run, doubling capacity. One wrinkle this app enforces, as do most faithful implementations: when the run is moving onto an empty column, that column is the destination rather than a helper, so the capacity is halved.

Read the bottom row and the stakes become obvious. With everything open, you can carry a 20-card run — nearly half the deck — in one motion. Fill all four cells with parked cards and that same position moves one card at a time. The difference between those two states is usually the difference between a deal that solves smoothly and one that grinds to a halt with the solution still on the table.

Solvable is not the same as easy

A 99.999% solvability rate does not mean 99.999% of deals feel the same. Solver data shows a wide difficulty spread within the solvable pile: most random deals admit many different winning lines and forgive a couple of loose moves, while a small minority thread through a single narrow sequence where one premature free-cell parking ends the game. Among the original Microsoft numbers, deal #1941 built a reputation as one of the nastiest solvable boards in the set — winnable, but only along lines that look suicidal until they suddenly are not.

The practical upshot for regulars: expected effort, not expected outcome, is what varies day to day. An average deal falls in well under a hundred moves once you see the shape of it; a hard one may take several undo-assisted attempts across a coffee break or three. Players who track their statistics here usually find their win rate climbs toward the high nineties not by getting faster, but by refusing to abandon the rare stubborn deal — because unlike almost any other solitaire, persistence in FreeCell is nearly always mathematically justified.

What solvability means for how you play

Knowing that better than 99.99% of deals can be won should change your behavior at the table in three concrete ways.

First, stop blaming the shuffle. In FreeCell a loss is information: somewhere in your line was a move that spent a cell too early, buried a low card, or broke a run you would need later. Second, use undo as a solver's tool rather than a confession — backing up five moves and trying a different order is how the Internet FreeCell Project volunteers beat 31,999 deals with no computer help. Third, protect your supermove capacity like a resource, because it is one: every occupied cell halves-to-fifths the runs you can carry, and an empty column is worth more than any single move it could be spent on.

For the habits that put these principles into practice — opening board scans, cell discipline, and column timing — see the FreeCell strategy guide, or brush up on the mechanics in the rules guide. And if you want to feel how much the math matters, try Baker's Game — same layout, suit-only building, and a solvability rate that drops from 99.999% to roughly 75%.