Dominoes statistics: what 20,000 simulated games reveal
Folk wisdom says doubles are a burden and going first helps. We ran 20,000 games to find out by how much.
Guides · Updated
Every dominoes player has heard the same few pieces of advice. Get rid of your doubles early. Dump heavy tiles. Going first is an advantage. They are repeated so often that nobody asks how true they are, or by how much.
So we measured. Using the same rules engine and computer opponent that run the game on this site, we played 20,000 two-player rounds of dominoes, 10,000 of Block and 10,000 of Draw, and recorded what happened. These are the dominoes statistics that came out, including one finding where the obvious reading of the data turned out to be backwards.
Key findings
- In two-player Block, 57% of rounds end blocked. Blocking is the normal outcome, not the exception. In Draw it happens in only 5.7% of rounds.
- The player who leads wins 58% of Block rounds and 55.6% of Draw rounds, a clear first-move advantage in both.
- Every extra double you hold costs you. A player who did not lead won 45.5% of Block rounds with no doubles and 32.9% with three or more.
- In Block, a light hand is worth 18 points of win rate. Non-leaders with the lightest hands won 49.2% of the time; with the heaviest, 31.2%.
- In Draw, starting weight barely matters. The same comparison moved only a few points, within the margin of error.
- Draw rounds run about 60% longer. 17.7 tiles reach the table on average, against 11.2 in Block.
How often does dominoes end in a block?
In two-player Block dominoes, 57% of rounds end with the board blocked and nobody able to move; only 43% end with a player going out. In Draw dominoes, where players can take from the boneyard, just 5.7% of rounds block.
| How the round ended | Block | Draw |
|---|---|---|
| A player went out | 43.3% | 94.4% |
| Board blocked, lighter hand won | 54.0% | 5.4% |
| Board blocked, hands tied | 2.7% | 0.3% |
That Block figure surprises people, but the arithmetic makes it almost inevitable. Two players take seven tiles each, so 14 of the 28 tiles are never in play. Each number appears on seven tiles, and with half of them sitting unseen at the side of the table, numbers run dry quickly. Once both open ends show numbers nobody holds, the round is over.
It changes what Block is about. If more than half of your rounds are decided by counting the pips left in each hand, then a large part of the game is not racing to go out at all: it is making sure that, when the board locks, you are the one holding less. The scoring rules explain exactly how a blocked round is counted.
Does going first matter in dominoes?
Yes, noticeably. The player who led won 58.0% of decisive Block rounds and 55.6% of decisive Draw rounds. With both seats played by the same computer opponent, the only difference between them was the deal, so that edge belongs to the lead itself.
Two things produce it. The leader plays a tile before their opponent has done anything, so they start the race holding six tiles against seven. And the tile they lead with is almost always a double: in 99.7% of deals someone held one, because the chance that 14 dealt tiles contain no double at all is about 1 in 345. A double is the hardest kind of tile to get rid of, as the next section shows, and the leader gets to shed their best one for free.
The edge is bigger in Block than in Draw. That fits: in Block every tile you start with is a tile you must eventually play or be counted against, so starting one tile lighter matters more. In Draw the boneyard dilutes it.
Are doubles bad in dominoes?
This is the finding where the data tried to mislead us, and it is worth walking through.
Group every player by how many doubles they were dealt and compare win rates, and you get this:
| Doubles dealt | Block, all players | Draw, all players |
|---|---|---|
| 0 | 45.8% | 51.6% |
| 1 | 51.8% | 53.6% |
| 2 | 51.6% | 49.9% |
| 3 or more | 46.5% | 44.3% |
Read at face value, one or two doubles is the sweet spot and having none is bad. That would contradict a century of advice. It is also wrong, and the reason is the lead.
The player holding the highest double leads, and leading is worth several points of win rate on its own. So a player dealt no doubles almost never leads, and gets counted against the advantage they didn’t have. A player with one or two doubles often does lead, and their doubles get credit for it. The doubles weren’t helping; they were standing next to something that was.
Remove the lead from the picture by looking only at the player who did not lead, and the real pattern appears:
| Doubles dealt | Block, non-leader | Draw, non-leader |
|---|---|---|
| 0 | 45.5% | 51.8% |
| 1 | 44.2% | 47.2% |
| 2 | 40.5% | 39.7% |
| 3 or more | 32.9% | 34.5% |
Now it is a clean slope in both games. Each double costs you, and three or more costs you a lot: from no doubles to three-plus, the win rate falls by 12.6 points in Block and 17.3 in Draw. The old advice is right, and more right than the raw numbers suggested.
The reason is structural. A single like the 6–3 can be played against a six or a three. A double can only be played against one number, so it has half the chances to find a home, and when that number dries up the double is stranded. It is also heavy: the double-six is the most expensive tile in the set to be caught holding. Play your doubles while their number is still live.
Does a light hand help you win?
In Block, enormously. In Draw, hardly at all. Again looking at the player who did not lead:
| Starting pip total | Block, non-leader | Draw, non-leader |
|---|---|---|
| Light (under 36) | 49.2% | 42.4% |
| Average (36 to 48) | 40.6% | 44.9% |
| Heavy (over 48) | 31.2% | 46.0% |
The 18-point spread in Block follows directly from the blocking figure. When 57% of rounds are settled by whoever holds fewer pips, a hand that starts light is already halfway to winning a blocked round.
Draw is different because your hand does not stay the hand you were dealt. You take an average of 6.8 tiles from the boneyard over a round, so your starting weight is diluted by tiles you had no say in. The small upward drift in the Draw column is inside the margin of error for groups this size, so the honest reading is no clear effect. (This one also looks different in the raw data, where heavy Draw hands appear to win 54% of the time. That turns out to be the lead again: heavy hands tend to contain the high doubles that lead.)
How long does a round of dominoes last?
| Per round, on average | Block | Draw |
|---|---|---|
| Tiles placed on the table | 11.2 | 17.7 |
| Tiles drawn from the boneyard | 0 | 6.8 |
| Points scored by the winner | 9.3 | 15.3 |
Because each Draw round is worth about two-thirds more, a match to the same target takes roughly two-thirds more rounds of Block than of Draw. Draw rounds are longer and worth more because the loser is more likely to be caught holding a hand that grew from the boneyard.
Checking the simulation against the maths
A simulation is only as good as its engine, so before trusting any of this we checked it against figures that can be worked out exactly. Three of them:
| Quantity | Exact probability | Simulated |
|---|---|---|
| A seven-tile hand holds no doubles | 9.8% | 9.7% |
| A seven-tile hand holds three or more doubles | 22.0% | 22.0% |
| Neither player is dealt a double | 0.29% | 0.3% |
They agree. The deal is behaving exactly as a fair shuffle should, which is the part of the engine every other number depends on.
What this means for how you play
- In Block, play to be light when it locks. Blocking is the likely outcome, so shed heavy tiles early and treat every pip you hold as a pip you may be scored on.
- Get doubles out while their number is live. A double stranded on a dead number is the costliest mistake in the game.
- Don’t over-read a bad deal in Draw. The boneyard reshapes your hand, so a heavy start is far less of a handicap than it is in Block.
- Expect the leader to have an edge, and do not mistake losing a round you didn’t lead for playing badly.
Our strategy guide turns these into six principles in the order they matter, and the coach in the game uses the same evaluation as the computer opponent, so it will tell you when you are holding a double too long.
How we ran it
Each round was the first round of a freshly seeded two-player match, using a standard double-six set with seven tiles dealt to each player. The player holding the highest double leads with it (or the heaviest tile if nobody holds one). In Block the undealt tiles are never used; in Draw players draw until they can play, and the boneyard may be drawn empty. A blocked round goes to the lighter hand, and equal hands are recorded as a tie.
Both seats were played by the same computer opponent, the one called Sharp in the game, which weighs each move on pips shed, doubles, the spread of numbers in hand and control of the open ends. Using the same player on both sides means any difference between seats comes from the deal and the lead, not from skill. Because every shuffle comes from a seeded generator, every one of these 20,000 rounds can be replayed exactly.
Two limits are worth stating plainly. These are games between identical computer players, not people: human play is less consistent, and a real table’s numbers would be noisier. And the findings describe two-player double-six games; more players or a bigger set change the arithmetic. With 10,000 rounds per game the overall percentages are accurate to about one point either way, and the smaller groups in the doubles and weight tables to about two or three.
If you want to test any of this yourself, play a few rounds of each and keep count. You will see the blocking rate in Block within an evening.