Roll the dice
Roll with .
Three six-sided dice are on the table. Tap them, press Roll or hit the Space bar, and you get three faces and their total, from 3 to 18. The average is 10.5, and the totals near the middle come up far more often than the extremes: 10 and 11 are the most common, while 3 and 18 each need all three dice to cooperate.
One die gives a flat result: every face is equally likely. Add a second and the middle starts to dominate. With three dice, the shape already looks like a bell. That is why 3d6 has long been used when a game wants “usually average, sometimes exceptional”: early role-playing games rolled 3d6 for each ability score, in order, and some systems still resolve every action by rolling 3d6 under a skill.
In the early seventeenth century, gamblers in Tuscany noticed that a total of 10 came up more often than 9 with three dice, although both can be made in six different ways (for 9: 1-2-6, 1-3-5, 1-4-4, 2-2-5, 2-3-4, 3-3-3). Galileo explained why: the dice are distinct, so 1-2-6 can happen in six orders, while 3-3-3 happens in only one. Counted properly, 10 has 27 ways out of 216 and 9 has 25. The table below lists every total, counted the same way.
216 equally likely combinations, counted one by one. Average total: 10.5.
| Total | Ways (of 216) | Chance | This or more |
|---|---|---|---|
| 3 | 1 | 0.46% | 100% |
| 4 | 3 | 1.4% | 99.5% |
| 5 | 6 | 2.8% | 98.1% |
| 6 | 10 | 4.6% | 95.4% |
| 7 | 15 | 6.9% | 90.7% |
| 8 | 21 | 9.7% | 83.8% |
| 9 | 25 | 11.6% | 74.1% |
| 10 | 27 | 12.5% | 62.5% |
| 11 | 27 | 12.5% | 50% |
| 12 | 25 | 11.6% | 37.5% |
| 13 | 21 | 9.7% | 25.9% |
| 14 | 15 | 6.9% | 16.2% |
| 15 | 10 | 4.6% | 9.3% |
| 16 | 6 | 2.8% | 4.6% |
| 17 | 3 | 1.4% | 1.9% |
| 18 | 1 | 0.46% | 0.46% |
The dice for this page are already on the table, and the sentence under them says how many and how many sides. No setup needed.
Tap the dice, press Roll or hit the Space bar. They tumble, land, and the result appears at the top.
Tap a die to keep it while the others re-roll; Release all frees them. To roll something else, tap the number of dice or sides in the sentence.
We build tools that are as simple and intuitive as possible, with a few bonuses here and there. Tell us what would make this one better.
10 and 11, tied. Each comes up 27 times in 216, or 12.5% of rolls.
One in 216, about 0.46%. Only triple six makes 18, and only triple one makes 3.
10.5, three times the average of one die.
Yes. It is free to use, funded by advertising, with no account and no app to install.
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