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Is Every Solitaire Game Winnable? The Odds in Klondike

No. Some deals of Klondike cannot be won however well you play, and nobody knows the exact share of games a perfect player would win when the face-down cards are hidden. Here is what the research does know, and under which rules.

The short answer

Not every game of solitaire can be won. Even a player who could see every card, face down or not, would find no way to win about one deal in five of draw-three Klondike. In ordinary play, where the hidden cards stay hidden until they turn up, the share of games won is lower still, and its exact value is unknown.

Why the odds are so hard to pin down

In 2004 a team of Stanford and Cornell researchers, Xiang Yan, Persi Diaconis, Paat Rusmevichientong and Benjamin Van Roy, called it “one of the embarrassments of applied mathematics” that nobody could work out the odds of winning such a common game. There are three reasons.

  • There are too many deals. A deck of 52 cards can be ordered in 52! ways, about 8 × 1067. Nobody can check them all, so every figure below comes from a sample of random deals.
  • Games are long and branch a lot. Every deal needs at least 52 moves, one for each card that has to reach a foundation, and many positions offer several moves at once.
  • Hidden cards turn it into a game of chance. With 21 cards face down at the start, the best move depends on cards you cannot see. A perfect strategy would have to weigh every way those cards could lie.

Two different questions

The studies below answer one of two questions, and it matters which.

  • How many deals can be won at all? This is measured on “thoughtful” solitaire, a version in which the player knows where every card is from the start. It gives a ceiling: no player of ordinary Klondike can do better.
  • How many deals does good play win? This is measured by playing ordinary Klondike, with the hidden cards hidden, by a program or a person. It gives a floor: a better strategy could only win more.

The true chance of winning ordinary draw-three Klondike with the best possible play lies somewhere between the two.

What the studies found

StudyRulesResult
Blake and Gent (2026)Every card known; draw three; no pass limit81.945% ± 0.084% of deals can be won
Blake and Gent (2026)Every card known; draw one; no pass limit90.480% ± 0.116% of deals can be won
Yan and others (2004)Every card known; draw three; no pass limitAn expert won 36.6% of 2,000 games; a program won 70.2% of 200
Bjarnason, Fern and Tadepalli (2009)Hidden cards; draw three; no pass limitPrograms won over 35%; random play won 7.1%
Jupiter Scientific (2013)Hidden cards; draw three; no pass limitOne careful player won 189 of 442 games, 43%

The ceiling: about 82% in draw three

Charlie Blake and Ian Gent built a solver that settles whether a given deal can be won with every card known. Run on a large sample of random deals, it found that 81.945% of draw-three deals can be won, give or take 0.084%, and 90.480% of draw-one deals, give or take 0.116%. Their rules allow any number of passes through the stock and allow cards back from the foundations. So close to one deal in five of draw three, and one in ten of draw one, is lost before the first move.

The experts and the program

The 2004 study measured the same thoughtful game from the other side. A mathematician who had studied it for years played and recorded 2,000 games and won 36.6% of them, taking about 20 minutes a game. Their best program won 70.2% of the 200 games it played, almost twice as many, at about an hour and three quarters a game. The authors could also prove that no strategy wins more than 98.81% of deals; the later solver put the true share at about 82%.

The floor: over a third with hidden cards

For the game as people play it, Ronald Bjarnason, Alan Fern and Prasad Tadepalli wrote programs that plan ahead by sampling the ways the hidden cards might lie. In 2009 they reported a program that wins over 35% of draw-three games, the first reported lower bound for ordinary Klondike. For comparison, choosing moves at random won 7.1% of a million deals.

A report by Jupiter Scientific in 2013 took a human route: one careful player played 442 games of draw three, without looking at hidden cards, and won 189, or 43%. That is a single player and a small sample, so the figure is a rough lower bound rather than a measurement of the game.

What makes a deal easier or harder

  • Cards per draw. The more cards you turn at a time, the fewer deals can be won: in Blake and Gent’s count, about 90.5% for one card, 88.6% for two and 81.9% for three, with every card known. See Turn 1 vs Turn 3 for why.
  • Limits on passes. Every figure above allows unlimited passes through the stock. A limit can only remove chances, never add them, so with three passes or one the share of winnable deals can only be the same or lower.
  • Cards back from the foundations. Allowing them helps a little. With every card known, draw three goes from 81.524% of deals without it to 81.945% with it.
  • Undo. Many computer versions let you take moves back. If you use undo to peek at a hidden card and then play differently, you are moving toward the thoughtful game, and the ceiling above starts to apply.

What it means when you play

A lost game does not always mean a mistake: nearly a fifth of draw-three deals cannot be won by anyone. Judge your play by your results over many games, not by a single deal, and compare like with like: the same draw, the same limit on passes. And if most of your losses come from cards you never reached, the strategy tips are about exactly that.

Play Klondike now

Deal a game in your browser: Turn 1 Klondike (draw one) or Turn 3 Klondike (draw three).

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