Hardest FreeCell Games: The Deals That Need All Four Free Cells

The hardest FreeCell games are the ones you can't win with fewer than four free cells. We checked the first 2,000 classic deals one by one, and only 18 of them can't be won with three, among them the famous games #617 and #1941. Game #11982 is harder still: it needs five cells, so it can't be won in a normal four-cell game. Most deals are far easier: 79.1% of them can be won with two free cells or fewer.

Below are the full numbers, the hardest deals, a look at what makes game #1941 so tough, and what all this means when you play with fewer cells.

How we measured difficulty

Whether a deal feels hard depends on the player, so we used a measure a computer can settle. Michael Keller's FreeCell FAQ, the long-running reference on the game, says the best way he has found to measure difficulty objectively is to count how many free cells a deal needs. By that yardstick a deal that needs four cells is very hard, and one that needs three is hard.

Here is how we measured it with Poozee's FreeCell engine:

1. Same deals as Microsoft. Poozee numbers its games with the same shuffle as Microsoft FreeCell, so game #617 here is game #617 there.
2. Fewer cells, step by step. For each deal we tried four free cells, then three, two, one and none, until one failed. With fewer cells you can also move fewer cards at once, just as in FreeCell versions that let you pick the number of cells.
3. A win or a proof. At each step the search either found a winning line, which we replayed move by move in the game's rules engine, or it went through every position that can be reached and found no win. Cards went home automatically only when no other card could still need them, as in Poozee's FreeCell, which never costs a win.

For 20 deals (1.0%), the search could neither win with one cell fewer nor rule it out within 2 million positions per try. We count those at the fewest cells that won, so they may be one cell too high. None of them is among the hardest deals below.

How many free cells the first 2,000 deals need

Two cells is the typical deal. One deal in five can be won with a single free cell, and one in five needs three. The FAQ estimates that about 79% of the 32,000 classic deals need two cells or fewer, and the first 2,000 come out at 79.1%. It puts four-cell deals at about one in 150; in the first 2,000 there are 18, about one in 111.

At the easy end, only 6 of the first 2,000 deals (#164, #892, #1012, #1081, #1150, #1529) can be won with no free cells at all.

The hardest deals in the first 2,000

The 18 deals that need all four cells are #169, #178, #285, #454, #575, #598, #617, #657, #775, #829, #988, #1025, #1136, #1443, #1495, #1661, #1734, #1941. For every one of them, the search checked every position you can reach with three cells and found no win.

Three of them are harder again. In a normal four-cell game you can win most four-cell deals without ever having all four cells full at once, because the fourth cell's job is to let you move longer runs. Games #617, #657 and #1941 don't allow that: at some point you need a card in every cell.

So by this measure, #617, #657 and #1941 are the three hardest of the first 2,000 deals.

What the FreeCell FAQ says, checked

The FAQ names several deals by how many cells they need. Our search agrees with every one we checked:

Why game #1941 needs all four cells

Here is the layout. Columns are numbered 1 to 8 from left to right, and the last card in each column is the one you can move first. To play it on Poozee, open FreeCell, click Game #, enter 1941 and press Deal.

The Aces are only a little deeper than usual: 14 cards cover them, and across the first 2,000 deals the average deal has 11.0. The trouble is the Kings. Column 3 holds the A♦, the A♠ and the 2♥, and on top of them sit the K♣, the K♦ and the 7♥. And the K♥ is the last card of column 1, with the 5♣ and the 4♥ between it and the A♥. A King can only go to a free cell or an empty column, and there is no empty column yet.

Here are the first ten moves of a winning line our search found. Every move is a single tap in Poozee's FreeCell, "Cells full" counts the full free cells right after the move, and "Then home" lists the cards the game then sends to the foundations by itself.

After five moves all four cells are full, three of them with Kings, and three Aces are home by move 6. That's the price of this deal: to reach the low cards you have to park Kings, and parked Kings stay parked until an empty column opens up.

The line wins in 35 moves, and the cells barely get a rest. All four cells are full after 24 of the 35 moves, including from move 13 to move 29, 17 moves in a row in which every card you move has to go onto a column or home. The K♥ and the K♦ never leave their cells until the last move sends everything home. Only one King gets out earlier, on move 30, when the K♣ moves to an empty column.

Take one cell away and there is no way through. With three cells, only 23,631 different positions can be reached from the deal, and not one of them leads to a win. Even with four cells you can't keep one in reserve: if you never fill all four at once, there are 38,451 positions you can reach that way, and none is a win. Game #617 is the same story (13,582 positions with three cells, 33,365 with the fourth cell kept empty, no wins).

Four cells, but never all full

Poozee's FreeCell always gives you four cells, but you can still play "with fewer" by never filling more than you allow yourself. That is easier than a real three-cell game, because the cells you leave empty still count when you move a run. Here is the lowest limit each of the first 2,000 deals can be won with in the four-cell game:

Of the 2,000 deals, only 3 (#617, #657, #1941) make you fill all four at once. And 100 deals can be won without ever putting a card in a free cell. For 983 of the 2,000 deals (49.2%), the limit is lower than the number of cells the deal needs in a real game with fewer cells. (The limit was left unsettled for 2 deals in the four-cell game; they count at the lowest limit that won.)

Game #1 shows the difference. It needs three cells: with two cells it has 70,882 reachable positions and no win. Yet our game #1 walkthrough wins it in Poozee's four-cell game without ever having more than two cells full, because the two empty cells let it move runs of several cards at once.

How to play with fewer free cells

These habits come straight from the numbers above:

• Keep the fourth cell in reserve. 1,997 of the first 2,000 deals can be won without ever filling all four cells. If a move would fill the last one, look for another move first: the odds are very good that a line exists without it.
• An empty cell is worth more than a parking spot. Each empty cell adds one card to how many you can move at once, so a cell you leave empty keeps working. That is why almost half the deals can be won with a lower limit in the four-cell game than in a game that really has fewer cells. How to play FreeCell has the full table of how many cards you can move.
• Count the cards on the Aces, but don't trust it too much. Among the first 2,000 deals, deals that needed one cell had 9.8 cards on their Aces on average, two-cell deals 11.0, three-cell deals 12.0 and four-cell deals 14.0. 31.6% of deals with 16 or more cards on their Aces needed three or four cells, against 12.5% of deals with 7 or fewer. Deep Aces make a hard deal more likely, but #285 needs all four cells with only 10 cards on its Aces.
• Watch for Kings on low cards. In #1941 the Kings, not the Aces, are what fill the cells. A King you park early can stay in its cell for most of the game, so before you park one, know which column you will empty for it.
• Want a challenge? Set a limit. In Poozee's FreeCell you can't remove a cell, but you can promise yourself never to fill more than two: 93.7% of the first 2,000 deals can still be won that way. With a limit of one it's 52.2%, so every other deal.

Pro tip: If you play a FreeCell version with only three cells, every one of the first 2,000 deals except 18 can still be won. Losing a three-cell game almost always means a better line existed, so press undo and look for it.

Keep playing

Try the hardest ones yourself in FreeCell: enter 617, 657 or 1941 under Game #. If they're too much, warm up with the game #1 solution, which never has more than two cells full. For the one classic deal no number of moves can save, read why game #11982 can't be won, and for the habits that win the other 31,999, see the FreeCell strategy guide.