Threes Dice Game: Rules, Scoring and Best Strategy
Threes is a quick dice game where the lowest score wins and every 3 you roll counts as zero. You roll five dice, keep at least one each time, and roll the rest until all five are set aside. It takes a minute to learn, and each roll forces a small decision. Here are the rules, the scoring and a strategy we worked out by computer.
What You Need
- Five six-sided dice.
- Two or more players.
- Paper to keep score.
No dice? Use the Dice Roller: roll five dice first, then however many you have left.
How to Play
- Roll all five dice.
- Keep at least one. After every roll you must set aside at least one die. You may set aside more.
- Roll the rest. Keep rolling the dice that are left, setting aside at least one each time, until all five dice are set aside.
- Add up your score. A 3 counts as zero. Every other die counts its number of pips. Your score is the total of your five kept dice.
- Lowest score wins. When everyone has had a turn, the lowest score wins the round. Ties roll off or share the round.
So the best possible score is 0, from five 3s. A 1 is the next best die, and a 6 is the worst.
Simple Strategy
We calculated the best play for every possible roll. It comes down to a few rules:
- Always keep every 3. They are free.
- Keep a 1 only near the end. Keep it if it leaves you two or fewer dice to roll. Earlier on, rerolling usually beats a 1.
- Keep a 2 only as one of your last two dice. Keep it when it leaves you one die or none to roll.
- If you must keep something, keep only the single lowest die and reroll the rest. Never keep a 4, 5 or 6 unless you have to.
Why keep a 1 so rarely? Because the dice you still hold have value. Here is the average number of points still to come with best play:
| Dice you still have to roll | Expected extra points with best play |
|---|---|
| 5 (start of turn) | about 6.3 |
| 4 | about 5.8 |
| 3 | about 5.2 |
| 2 | about 4.4 |
| 1 | 3 |
Going from three dice to two saves only about 0.8 points on average, so keeping a 1 at that stage costs you. Going from two dice to one saves about 1.4 points, so a 1 is worth keeping then.
What Scores Win
With best play, the average score is about 6.3. In our simulation of 400,000 turns, the final scores looked like this:
| Final score with best play | Chance |
|---|---|
| 0 (all threes) | about 1% |
| 2 or less | about 12% |
| 5 or less | about 46% |
| Median score | 6 |
Against one other player, 5 or less wins more often than not. A zero is a rare treat. For more on how dice odds work, see our guide to dice probability.
Variants and House Rules
- Betting rounds: everyone puts a token in the pot and the lowest score takes it. Ties carry over to the next round.
- Know the score to beat: if you roll after others, you can take more risk when you need a very low score, or play safe when the target is high.
Where the Game Comes From
Threes is a folk game passed on by word of mouth, with no known inventor. It belongs to the same family as other quick games with five dice, such as Farkle and poker dice, where you set dice aside after each roll.
For another game of risk and reward, try Pig. More quick games are in our list of easy dice games.
FAQ
How do you play Threes with dice?
Roll five dice. After each roll, set aside at least one die and roll the rest, until all five are set aside. A 3 counts as zero and every other die counts its pips. Lowest total wins.
What is the best score in Threes?
Zero, from five 3s. With best play it happens about 1% of the time.
Should you keep a 1 in Threes?
Only near the end of your turn. Keep a 1 if it leaves you two or fewer dice to roll. With three or more dice left, rerolling is better on average.
What is a good score in Threes?
The average with best play is about 6.3, and half of all turns end at 6 or less. A score of 5 or less is usually good enough to win against one opponent.
How many dice do you need for Threes?
Five six-sided dice, shared by all players.