The Best Opening Domino, by the Numbers: 190,000 Simulated Hands
Everybody at the table has an opinion about what to lead. We have a game engine. So we dealt 190,000 hands of Fives, played every one of them out, and counted. Then we tested a hand that breaks the simple answer.
In Fives, the opening play is the only moment in the hand where you choose the entire board. Everything after that is a reaction to what's already down. In the first hand of a game you don't get the choice: whoever holds the highest double leads it. But every hand after the first is opened by whoever won the last one, with any bone they like. Win a hand, earn the open. So what should you do with it?
We asked the engine. Cookout Dominoes runs the same rules code on your phone and on the ranked server, and it can play a hand in well under a millisecond. We pointed it at the question and let it run.
How we did it
- Rules: two players, seven bones, first to 150, first double is the spinner, draw until you can play, go-out and blocked scores rounded to the nearest 5. The house rules on this site.
- Players: both seats were our OG Mode bot with its "human miss" model switched off, so every play is the strongest one-move-lookahead play it can find. No luck, no tilt, no distractions.
- Test 1, the 28 bones: for each bone in the set, 4,000 hands where the opener held that bone and led it. We recorded the opener's points minus the opponent's points for the hand (net), and who won the hand. 112,000 hands.
- Test 2, the policies: 8,000 identical dealt hands, each opened six different ways: heaviest bone, highest double, the bone that scores most right now, our Shark AI's full search, a random bone, and the lightest bone. Same deals, different rule, so the comparison is fair. 48,000 hands.
- Test 3, whole games: 6,000 complete games to 150, about 31,000 hands, to see what a game actually looks like.
Two honest caveats before the tables. These are strong bots, not your cousin, so real tables will be noisier and the edges smaller. And it's head-to-head; four-handed partners is a different game with different math.
Test 1: every bone as an opener
Sorted by net points per hand. "Opens for" is what the bone scores the moment it hits the table.
| Bone | Opens for | Net points / hand | Wins the hand |
|---|---|---|---|
| 5-5 | 10 | +9.6 | 59.3% |
| 6-4 | 10 | +9.0 | 53.9% |
| 3-2 | 5 | +6.7 | 55.3% |
| 4-1 | 5 | +3.1 | 54.9% |
| 0-0 | 0 | +3.0 | 59.6% |
| 5-0 | 5 | +1.8 | 53.8% |
| 1-1 | 0 | +1.5 | 59.8% |
| 3-3 | 0 | +1.1 | 60.6% |
| 4-4 | 0 | +0.6 | 59.4% |
| 1-0 | 0 | −0.5 | 54.8% |
| 2-2 | 0 | −0.6 | 60.3% |
| 5-2 | 0 | −1.0 | 53.3% |
| 3-0 | 0 | −1.2 | 55.5% |
| 5-1 | 0 | −1.3 | 54.2% |
| 6-6 | 0 | −1.4 | 60.6% |
| 5-3 | 0 | −1.6 | 53.5% |
| 2-0 | 0 | −1.7 | 54.9% |
| 3-1 | 0 | −2.3 | 55.1% |
| 2-1 | 0 | −2.7 | 55.3% |
| 4-0 | 0 | −2.8 | 54.9% |
| 6-0 | 0 | −3.0 | 54.3% |
| 6-5 | 0 | −3.1 | 53.0% |
| 5-4 | 0 | −3.6 | 52.7% |
| 6-1 | 0 | −3.6 | 54.9% |
| 6-2 | 0 | −4.8 | 53.9% |
| 4-3 | 0 | −5.2 | 53.5% |
| 4-2 | 0 | −6.2 | 52.2% |
| 6-3 | 0 | −6.4 | 53.7% |
Three things jump out.
1. In a random hand, the bones that score on the open are the bones that win
Every bone that scores when it hits the table is in the top six. Hold that qualifier, in a random hand; it matters below. The 5-5 and 6-4 open for a dime and end the hand about nine points ahead on average. The 3-2, 4-1 and 5-0 open for a nick and finish ahead too. Ten points on the first play is a tenth of the game, and the simulation says it doesn't get taken back.
2. Doubles win hands even when they don't win points
Look at the "wins the hand" column. Every double sits around 59 to 61 percent. Every non-double sits around 53 to 55. That's not about scoring. It's about shedding: a double is the hardest bone in your hand to play later, because it only fits one number, and if you're holding it when your opponent dominoes, it's the pips that pay them. Lead it and the problem is gone. Even the double blank, which scores nothing and looks like a nothing play, wins the hand 59.6 percent of the time and nets three points.
3. The 6-6 is a trap, and so is the 6-3
The big six wins the hand more often than almost anything, yet it's negative on points. Here's why. A double alone on the table with one side played still counts both halves. So after you open 6-6 and your opponent plays a six on it, the count is 12 plus whatever's on the far end. If that far end is a 3, the total is 15. Trees, for them, on the second play of the hand. And the 6-3 is the single worst bone to lead, because it leaves a 6 and a 3 open at once, which is the widest door in the set.
Every double has an answer
This is the table worth memorizing. When a double opens the hand and your opponent plays on one side, the double's unplayed side still counts both halves. So there is exactly one or two bones that score off each double. If you're leading a double, know what you're inviting. If you're answering one, know what you're looking for.
| You open with | The count showing | What scores on it | For |
|---|---|---|---|
| 0-0 | 0 | a 5 (the 5-0) | 5 |
| 1-1 | 2 | a 3 (the 3-1) | 5 |
| 2-2 | 4 | a 1 (the 2-1), or a 6 (the 6-2) | 5, or 10 |
| 3-3 | 6 | a 4 (the 4-3) | 10 |
| 4-4 | 8 | a 2 (the 4-2) | 10 |
| 5-5 | 10 | a blank (the 5-0) | 10 |
| 6-6 | 12 | a 3 (the 6-3) | 15 |
Which is the real reason the 5-5 is king. It pays you ten immediately, and the only bone that pays them back is the 5-0, one bone out of the 21 you can't see. The 6-6 pays you nothing and hands out a fifteen to one bone in 21. Same shape, opposite economics.
When the average lies: a hand full of ones
Everything above is an average over random hands that happen to contain the bone. In a random hand you hold about two of any number. That's not the hand that makes people argue. This one is:
We dealt this exact hand 5,000 times against random opponent hands and opened it four different ways.
| Opener | Net points / hand | Wins the hand | Opponent can't answer, must draw |
|---|---|---|---|
| 1-1 | +25.6 | 72% | 42% |
| 5-5 | +13.1 | 67% | 6% |
| 4-1 | +9.5 | 68% | 3% |
| 4-3 | +2.1 | 65% | 0% |
Leading the 1-1 is worth nearly double the 5-5 here. You hold five of the seven ones, so only the 1-5 and 1-6 are loose in the other 21 bones. Two times in five your opponent has neither, can't play on the double at all, and goes to the boneyard, and every bone they pull is a bone you collect when you domino. Meanwhile you have four more ones to feed the spinner on your terms. The 5-5 pays ten right now, then hands your opponent a 5 suit you can't follow, with your 1-1 stranded in your hand waiting for an end that may never come.
The rule the old heads already knew: lead the double of your long suit. The averages in Test 1 describe balanced hands. Your hand is not an average. Count your suits before you count the points.
Test 2: six ways to choose, same hands
Test 1 tells you which bones are good leads. It doesn't tell you what to do with an actual hand, where you might hold none of the top three. So we dealt 8,000 hands and opened each one six different ways.
| Opening rule | Net points / hand | Wins the hand | Avg. points on the open |
|---|---|---|---|
| Shark's search (looks ahead three plays) | +6.6 | 60.0% | 5.2 |
| Highest double | +5.5 | 66.5% | 2.2 |
| Best immediate score | +5.2 | 56.7% | 6.2 |
| Heaviest bone | +2.0 | 58.4% | 2.7 |
| Random bone | −0.2 | 56.4% | 1.3 |
| Lightest bone | −0.8 | 56.4% | 0.2 |
The rule you've heard most, lead your heaviest bone, is the worst of the four deliberate strategies. It's a habit from block dominoes, where pips in hand are all that matter at the end. In Fives the count matters on every play, and heaviest-first ignores it completely. It beat random by two points and lost to "just lead your highest double" by three and a half.
Highest double is the surprise. It scores the least on the open of any deliberate rule, and it wins the most hands by a distance: two out of three. That's the shedding effect from Test 1 with the volume turned up. If you care about winning the hand and taking the next open, lead your double.
Best immediate score takes the points now and wins fewer hands, because it often means leading a non-double like the 6-4 and keeping a double you'll be stuck with. It still nets more than heaviest-first, by a lot.
The Shark, which searches three plays deep over every hand the opponent might hold, splits the difference: it takes the points when the points are safe and leads the double when the double is the problem. That is the whole lesson in one row.
Test 3: what a game actually looks like
Six thousand games to 150, both seats strong. If you've ever wondered whether your table is normal, here's normal.
| Hands per game | 5.2 on average. Five is the most common; nearly every game finishes in four to seven. |
| Points per hand, both players | About 50. |
| Plays that score | 28% of all plays. Better than one in four. |
| What the scores are | 44% nicks, 41% dimes, 13% trees, 2.6% twenties, 0.4% quarters, 0.1% thirties. Board count only; the go-out bonus is separate. |
| Earthquakes (35 or more on the board) | Not once in 31,000 hands. It takes a 6-6, 5-5 and 4-4 on three ends and a 5 on the fourth. The earthquakes you'll actually see come from a domino that stacks go-out pips on a board score. |
| Draws per hand | 4.5. Somebody goes to the boneyard most turns. |
| Passes per hand | 0.14. Passing is rare because you draw first. |
| Hands that end blocked | 17.2%, about one in six. Blocked ties: 0.2%. |
| Who opens the first hand | A double, 99.6% of the time. The 6-6 specifically, 50.4% of games. |
| First-hand opener wins… | the hand 60.7% of the time. The game, 51.3%. The edge is real for one hand and gone by the end. |
| Loser's final score | 103 on average. 25% of games end with the loser at 130 or better. 5% end with the loser under 50. |
Two of those are worth carrying to the table. First, more than a quarter of plays score, and 84% of scores are a nick or a dime. Fives is a game of small, constant money, and the player who collects the fives beats the player waiting for a quarter. Second, the first-hand advantage is a hand-long advantage, not a game-long one. Losing the big-six draw is not a reason to be mad.
How to use this at the table
- Count your suits first. Four or more of one number and you hold its double? Lead the double. The points can wait; the starve can't.
- On a balanced hand, lead the 5-5, 6-4 or 3-2 if you hold one. Take the points. The only bone that punishes the 5-5 is the 5-0.
- Otherwise lead your highest double and check the answer table first. Leading a 6-6 when the 6-3 is unaccounted for is a gift. Leading a 4-4 when you hold the 4-2 yourself is free.
- Never lead the 6-3, 4-2 or 4-3 unless it's all you have. Two open numbers with no points is the worst thing you can put on an empty table.
- Forget "heaviest first." If a heavy bone happens to also be a scorer or a double, fine. If it's the 6-5, hold it.
Reproduce it
The raw output is published at results.json: every bone, every policy, every game statistic above, with the seed scheme and the counts. The simulator is part of the Cookout Dominoes codebase, which is not public; what we publish is the complete results file and the method described above, so the numbers can be checked and the setup reproduced by anyone with a Fives engine of their own. If your table plays to 200, or nine bones, the tables will move a little. The ordering won't move much. And if you've got a hand you think breaks one of these rules, send it. The ones hand above came from exactly that kind of argument.
Questions people ask
What is the best domino to start with?
It depends on your hand. If one number dominates it, four or more bones of the same suit, lead that suit's double: your opponent often can't answer and has to draw. On a balanced hand, lead the 5-5, then the 6-4, then the 3-2, the bones that score on the way down. Across 4,000 simulated hands per bone the 5-5 averaged 9.6 net points, the 6-4 9.0 and the 3-2 6.7. In the first hand of a game you don't get to choose: the highest double opens.
Should you play your heaviest domino first?
No. On 8,000 identical hands, always leading the heaviest bone netted about 2 points per hand, the worst of every deliberate policy we tested. Leading your highest double netted 5.5 and won the most hands. Leading the bone that scores the most right now netted 5.2. Heaviest-first is a block-dominoes habit that doesn't survive the count.
Is the 6-6 a good opening domino?
It opens the first hand if anyone holds it, so you rarely get a choice. When you do, it is slightly negative on points: it scores nothing itself and any 6-3 played on it scores 15 for your opponent. It does win the hand more often than average, because getting rid of the big six early means you are never stuck holding it.
Does the player who goes first win more in dominoes?
For the hand, yes: in 6,000 simulated games the player who opened the first hand won that hand 60.7 percent of the time. For the game, barely: they won 51.3 percent. A game to 150 runs about five hands, and the edge washes out.
How often does a dominoes hand end blocked?
About one hand in six. In our simulation 17.2 percent of hands ended with both players unable to play, and only 0.2 percent of hands ended in a blocked tie where nobody scored.
How many hands does a game to 150 take?
Five, usually. The simulated average was 5.2 hands, with five hands the most common length and almost every game finishing in four to seven.