Domino Draw Probability Calculator
Pick a set size and a hand size to see the odds of drawing doubles into your opening hand.
Draw probability
The math behind the odds
Drawing a domino hand is sampling without replacement: once a tile is in your hand, it can’t also be drawn by an opponent. The hypergeometric distribution gives the exact probability of ending up with a particular number of “successes” — here, doubles — in a hand of a given size, drawn from a set of a known total size and a known number of doubles.
The calculator first works out your set’s total tile count and doubles count from the highest pip value you choose, then applies the hypergeometric formula to your hand size. Because the same tile can’t be drawn twice, the odds shift slightly from a simpler back-of-the-envelope estimate — this tool does the exact calculation.
Frequently Asked Questions
What kind of probability does this calculate?
It uses the hypergeometric distribution — the correct model for drawing a fixed number of tiles from a set without putting any back, when some tiles (the doubles) count as “successes.” It's the same math used for card-drawing odds in a deck of cards.
Why doubles specifically?
Doubles are a natural, well-defined group in any domino set — there are exactly n+1 of them in a double-n set — which makes them a clean example for the calculation. The same formula works for any other group of tiles you define; only the group size (K) changes.
What does “P(at least one double)” mean?
It's the chance your hand contains one double or more, which is 1 minus the chance of drawing zero doubles at all. For a standard double-six set with a 7-tile hand, that works out to roughly 90% — doubles are common enough that most hands have at least one.
What if I want the exact number, not “at least one”?
Enter a number in the “exact number of doubles” field and the tool also reports the probability of landing precisely that count — useful for comparing, say, the odds of exactly one double against exactly two.
Educational tool only. Results are exact probabilities for a fair, well-shuffled set; real-world dealing should approximate this closely but isn’t guaranteed to.