Solitaire Odds Calculator

Not Every Card Left in the Deck Is Equally Likely to Help You

When you need a specific card — an ace to start a foundation, a red 6 to extend a column — the chance of finding it depends on exactly how many "outs" remain among the unseen cards and how many cards you're about to look at. This is the same hypergeometric math used to price flush draws in poker, adapted here for solitaire's dwindling stock pile.

The Formula

P(at least one hit) = 1 − C(N−K, n) / C(N, n)

N is the number of unseen cards left in the deck, K is the number of "out" cards among them that would help you, and n is how many cards you're about to draw or see. The calculation subtracts the probability of missing entirely from 1, which is easier to compute directly than summing every way of hitting one, two, or more outs.

Example Outcomes

P(at least one hit) for a 24-card unseen stock, computed from the hypergeometric formula
Outs remainingDrawing 1 cardDrawing 3 cardsDrawing 5 cards
28.33%23.91%38.04%
416.67%43.68%63.52%
625.00%59.68%79.84%

Figures computed directly from the formula above for a 24-card unseen pile; the calculator recomputes this exactly for any deck size, out count, and draw count you enter.

Where This Gets Used

  • Deciding whether to dig for a specific card — in Klondike, weighing whether flipping through the remaining stock is worth the moves it costs.
  • Comparing solitaire variants — games that let you see more cards per draw (three-card draw versus one-card draw) meaningfully change your odds of finding a needed card, exactly as this formula predicts.
  • General card-game odds — the same formula applies any time you need to estimate the chance of drawing at least one useful card from a shrinking, unseen pile.

How to Use This Calculator

  1. Enter Deck Size — the number of cards remaining in the unseen pile.
  2. Enter Outs — how many of those unseen cards would actually help you.
  3. Enter Draws — how many cards you're about to see.
  4. Select Calculate to get the exact probability of seeing at least one needed card.

Related Calculations

See the same hypergeometric logic applied to a live poker hand with the Texas Hold'em Equity Calculator, or check overall shuffle randomness with the Deck Shuffle Randomness Calculator.