Closest CallAt least one six in N rolls
How likely a six is to turn up when you get more than one try.
One to ten rolls
Each roll of a six-sided die shows a six 16.7% of the time. Rolling one die several times and rolling several dice at once are the same thing, so this chart covers both. It works for any single face, not only the six.
| Rolls (or dice) | At least one six | No six at all | Exactly one six | Two or more sixes |
|---|---|---|---|---|
| 1 | 16.7% | 83.3% | 16.7% | 0.00% |
| 2 | 30.6% | 69.4% | 27.8% | 2.78% |
| 3 | 42.1% | 57.9% | 34.7% | 7.41% |
| 4 | 51.8% | 48.2% | 38.6% | 13.2% |
| 5 | 59.8% | 40.2% | 40.2% | 19.6% |
| 6 | 66.5% | 33.5% | 40.2% | 26.3% |
| 7 | 72.1% | 27.9% | 39.1% | 33.0% |
| 8 | 76.7% | 23.3% | 37.2% | 39.5% |
| 9 | 80.6% | 19.4% | 34.9% | 45.7% |
| 10 | 83.8% | 16.2% | 32.3% | 51.5% |
What the chart tells you
- It takes 4 rolls to be more likely than not to see a six: 51.8%. With 3 rolls the chance is 42.1%.
- Six rolls do not guarantee a six. The chance is 66.5%, so about one time in three you roll six times and miss every time.
- Each extra roll adds less than the one before. The second roll adds 13.9% to your chance; the tenth adds only 3.23%.
- For a 90% chance you need 13 rolls, for 95% you need 17, and for 99% you need 26. No number of rolls makes it certain.
- On average the first six arrives on the 6th roll, but it is most likely to arrive on the very first.
How to work it out
It is easier to count the rolls with no six. One die avoids a six 5 times in 6. For every die to avoid it, multiply 5/6 by itself once per die. Take that away from 1 and you have the chance of at least one six. For four dice: 5/6 × 5/6 × 5/6 × 5/6 = 625/1,296, which leaves 671/1,296, or 51.8%.
A double six with two dice
The same method answers a question gamblers argued over in the 1600s. A pair of dice shows double six on 1 in 36 throws. In 24 throws of the pair, the chance of at least one double six is 49.1%; it takes 25 throws to pass an even chance (50.6%).
Where this matters
Many board games ask for a six to start, to leave a space or to score a hit, and many war games roll a handful of dice looking for at least one success. If you need a six and have three dice, you will get it 42.1% of the time; with five dice, 59.8%.
More dice odds
- Dice odds library: every chart in one place
- Two dice (2d6) odds chart
- Three dice (3d6) odds chart
- 4d6 drop the lowest: ability score odds
- d20 with advantage and disadvantage
- Five of a kind and other five-dice odds
- Attacker against defender dice odds
- Two twenty-sided dice (2d20) odds chart
- Dice calculator: the exact odds for any total with any number of dice, plus a dice roller.
Every figure on this page was computed by counting all possible outcomes. Game names mentioned here are trademarks of their owners; this site is not affiliated with or endorsed by them.