Clock Solitaire Strategy and Odds: Can You Win?

Let's be honest from the start: there is no strategy for the strict game of Clock Solitaire. You never choose anything. Each card tells you where to put it and which card to turn next, so the game is decided the moment the deck is shuffled. A beginner wins exactly as often as someone who has played for sixty years.

That does not make this page empty, though. It is interesting to know why the odds are what they are, what a normal game looks like, and how one small house rule turns Clock Solitaire into a game with a real decision in it. If you need the basics first, start with the Clock Solitaire rules.

Why There Are No Decisions

In most solitaire games you look at the table and pick one move out of several. In Clock Solitaire there is only ever one thing you are allowed to do:

• The card you just turned can go to one pile only, the hour that matches its rank.
• The next card you turn must be the top card of that same pile.

Nothing is left to choose. Playing slowly, playing quickly, tapping the cards yourself or letting Auto-play run: the result is the same. If anyone tells you they have a system for Clock Solitaire, smile and deal them in.

The Odds: Exactly 1 in 13

The chance of winning the strict game is 1 in 13, a little under 8 percent. Here is the reasoning, with no math beyond a fraction.

The cards were shuffled, so every face-down card is a surprise. Each time you turn one, it is as if you were drawing the next card from a well-shuffled deck. The game keeps going until the fourth King is turned. So the question "Did I win?" is the same as the question "Was the very last card in that random order a King?" There are 52 cards and 4 of them are Kings. Four out of 52 is 1 out of 13.

These are averages. Luck comes in streaks, so you might win twice in an afternoon and then not at all for a week. A run of 20 games without a single win is quite ordinary: it happens about one time in five.

What a Normal Game Looks Like

Since twelve games out of thirteen are lost, it helps to know what "close" looks like. We played tens of thousands of deals to see where the lost games end.

On average a lost game ends with about 10 cards still hidden, so most of the clock does get filled in. More than half the time you finish within nine cards of winning, which is why this game so often feels like a near miss. Once in a great while all four Kings sit near the top of the center pile and the game is over almost before it starts. That is not a fault in the shuffle. It is just rare bad luck.

Three Kings Showing: The Exciting Part

The game gets tense as soon as the third King is in the center. From then on, every card you turn might be the last. A handy way to judge your chances at any moment: if three Kings are out and N cards are still face down, your chance of winning is 1 in N, because the last King must be the last of those N cards. With 10 cards left it is 1 in 10. With 2 cards left it is an even coin flip. Our game shows both numbers in the corners of the table so you can follow along.

Adding a Real Choice: The One-Swap Rule

If you would like a say in the result, turn on One swap for the fourth King in Settings. When the fourth King comes up too early, you may tuck it face down under any pile around the clock that still has face-down cards, and take that pile's top card instead. You get one swap per game. The variations page has the full rule.

Now there is something to think about: which pile should hide the King?

The best pile is the fullest one

Always tuck the King under the pile with the most face-down cards. During the swap, each pile shows a tag such as "2 down" so you can compare them at a glance.

Here is why. The King goes to the bottom of the pile you choose, so it will not be seen again until every other card in that pile has been turned. A pile with three cards on top of the King keeps it buried longer than a pile with one. In fact the numbers work out very neatly:

Rule of thumb: after the swap, your chance of winning is the number of face-down cards on the pile you chose, divided by all the face-down cards on the table. If 12 cards are face down and you pick a pile holding 3 of them, you have a 3 in 12 chance, or 1 in 4. Pick a pile holding only 1 and your chance drops to 1 in 12.

The Hint button does this arithmetic for you. It marks the best pile and tells you your chance of winning from there.

How much does choosing well matter?

Two things stand out. First, the swap itself is a big help: even a careless swap wins nearly four times as often as the strict game. Second, choosing the fullest pile is worth roughly one extra win in every twelve games compared with choosing badly. It is a small decision, but it is yours.

When two piles are tied

If several piles have the same number of face-down cards, it makes no difference which one you pick. Your chances are identical. Choose your lucky number.

A Few Friendly Habits

• Play for the pleasure of it. The fun is in watching the clock fill in and holding your breath when the third King is out.
• Count how far you got. Beating your own record for "fewest cards left" is a nice private goal in a game you cannot steer.
• Use Auto-play when you want to relax. It turns the cards at a calm pace, and pauses by itself if a swap decision comes up.
• Don't blame yourself. A loss in Clock Solitaire is never your mistake. It is one of the few games where that is completely true.

If you find you want more to think about, that is a sign you are ready for a different kind of solitaire. In FreeCell nearly every deal can be won by planning ahead, and classic Klondike is a pleasant mix of luck and judgment. Clock Solitaire will still be here for the quiet moments.