Are All FreeCell Deals Solvable?

The famous #11982

When FreeCell shipped with Windows in the 1990s it offered 32,000 numbered deals, and its help file claimed, cautiously, that it was believed every one could be won. A group of players took that as a challenge and set out to solve all 32,000 by hand, an effort known as the Internet FreeCell Project. Over about a year they solved every deal except one: game #11982. Later computer searches, which try every possible sequence of moves, confirmed that it has no solution. It is the only impossible deal in the original set.

When later versions of Windows expanded the range to a million deals, exhaustive solvers found that eight of the first million are unwinnable: #11982, #146692, #186216, #455889, #495505, #512118, #517776 and #781948. Everything else, 999,992 deals, can be solved with the standard four free cells.

Those numbers refer to Microsoft's deal generator, a specific shuffle algorithm that other programs sometimes copy so that "game 11982" means the same layout everywhere. The numbers have no meaning for a program that shuffles differently, which brings us to CardCouch.

CardCouch's deal numbers are its own

Every FreeCell game on CardCouch has a number from 1 to 1,000,000, shown in the status line when the deal is laid out. The number seeds a shuffle, so the same number always produces the same layout, and you can replay a deal or send the number to a friend. But the shuffle is CardCouch's own, not Microsoft's, so our game #11982 is a completely different, ordinary deal, and the famous impossible layout is not sitting at that number here. The same goes for the other seven: there is no reason to avoid any particular number on CardCouch.

Because our million deals are effectively random shuffles, the same statistics apply: a very small handful are probably unsolvable, on the order of one in every hundred thousand, and we have not catalogued which. If you ever hit one you will know, because no amount of undoing helps. It will be a rare day.

To replay a deal, type its number into the Game number box beside New Game and press Deal number. On a phone the box is in the controls under the felt. Undo is unlimited, all the way back to the deal, so a lost position is never the end.

Why FreeCell is almost always winnable

• Nothing is hidden. All 52 cards are dealt face up into eight columns. There is no stock to draw from and no face-down cards to turn, so the outcome depends entirely on the order of your moves. That makes FreeCell a puzzle rather than a gamble.
• Four free cells give room to work. Any card can be parked in a free cell, which lets you dig under a buried Ace or reorder a column. Four cells is enough slack for nearly every layout; with three cells the unsolvable share rises sharply, and with one or zero cells most deals are lost.
• Empty columns multiply your moves. A sequence can be moved through free cells and empty columns together, up to (free cells + 1) × 2 to the power of empty columns cards at once. Two empty columns and four free cells let you move a run of 20. CardCouch enforces this supermove limit and counts the move as one.
• You can undo. Since nothing is random, a position you have lost can be rewound and taken a different way. Unlimited undo turns even a hard deal into a solvable one with patience.

The impossible deals are the layouts where the Aces and low cards are buried under long runs in the wrong order, so that every route to freeing one of them needs more temporary space than four cells and the columns can provide. They are rare precisely because the required tangle is so specific.

Lost a deal? It was probably still solvable

Given the odds, a deal you cannot finish is almost always a deal you have played into a corner. The common causes: filling free cells early with cards that had nowhere to go, emptying a column and immediately filling it with a low card, and building long runs that trap the last Aces underneath. The FreeCell strategy guide covers the habits that prevent this: free the Aces and twos first, keep cells empty as long as you can, and treat an empty column as more valuable than any single move.

If you want to test a deal properly, note its number, play it, and if you get stuck use Undo to back out to the decision that went wrong. Replaying the same number a second time with a clean plan is one of the best ways to get better at the game.