RandoziDice Probability Calculator
How likely is 15 or more on 3d8? Pick your dice, a modifier and a target, and see the exact odds instead of guessing.
Chance of rolling at least 8
41.67 %
Lowest
2
Average
7
Highest
12
| Total | Exactly | At least | At most |
|---|---|---|---|
| 2 | 2.78 % | 100 % | 2.78 % |
| 3 | 5.56 % | 97.22 % | 8.33 % |
| 4 | 8.33 % | 91.67 % | 16.67 % |
| 5 | 11.11 % | 83.33 % | 27.78 % |
| 6 | 13.89 % | 72.22 % | 41.67 % |
| 7 | 16.67 % | 58.33 % | 58.33 % |
| 8 | 13.89 % | 41.67 % | 72.22 % |
| 9 | 11.11 % | 27.78 % | 83.33 % |
| 10 | 8.33 % | 16.67 % | 91.67 % |
| 11 | 5.56 % | 8.33 % | 97.22 % |
| 12 | 2.78 % | 2.78 % | 100 % |
Dice duel: one die against another
Chance that A beats B
15/36
Both dice are fair and independent. Every pair of faces is counted one by one: no simulation.
Dice pool: at least k successes
Chance of at least 2 successes
7/27
Expected successes
1
| Successes | Exactly | At least |
|---|---|---|
| 0 | 8/27 (29.6296 %) | 1 |
| 1 | 4/9 (44.4444 %) | 19/27 |
| 2 | 2/9 (22.2222 %) | 7/27 |
| 3 | 1/27 (3.7037 %) | 1/27 |
Exact whole-number counts, not a simulation. Rules differ between games: this only counts dice that show the threshold or higher.
Reroll 1s once
Average result with the reroll
3.9167
| Final result | Chance |
|---|---|
| 1 | 1/36 (2.7778 %) |
| 2 | 7/36 (19.4444 %) |
| 3 | 7/36 (19.4444 %) |
| 4 | 7/36 (19.4444 %) |
| 5 | 7/36 (19.4444 %) |
| 6 | 7/36 (19.4444 %) |
Share this setup
The numbers travel in the part of the link after the # sign: it stays in your browser, is never sent to a server and does not change the page address that search engines see. A panel with decimals or numbers outside its limits is left out of the link.
How it works
- Set the number of dice and how many sides each one has, for example 2 dice with 6 sides.
- Add a modifier if your roll has one, such as +3, and type the total you need.
- Choose “at least”, “at most” or “exactly” and read the probability and the average roll.
- Scroll the table to see the chance of every possible total, and copy it to share with your group.
- In the dice pool, read the chance of exactly k successes and the expected number of successes, or open the “Reroll 1s once” panel for a die whose 1s are rolled again.
- Use “Copy link to this setup” to share every panel with the same numbers; they travel after the # sign of the link and are never sent to a server.
What people use it for
Tabletop games
Check whether a +5 to hit really beats a difficulty of 15 more often than a +3 does.
Board games
Compare the odds of rolling 8 or more on 2d6 with 10 or more on 3d6.
Teaching
Show students why 7 is the most common total of two dice.
Questions
- How are the odds computed?
- Every face of every die is equally likely. The tool combines the dice one at a time, adding up all the ways each total can happen, so 2d6 gives 6 ways out of 36 to roll a 7, which is 16.67 %. There is no simulation and no randomness: the result is exact. The odds table is limited to 1,000 possible totals, so 20d50 works and 20d100 does not.
- What does the modifier do?
- It is added to the sum of the dice. The target you type is compared with the final total, modifier included. A +3 modifier on 1d20 makes “17 or more” the same as rolling 14 or more on the die.
- Can I compare two different dice, or count successes in a pool?
- Yes, with the two panels under the main result. “Dice duel” gives the chance that one die beats, beats or ties, or ties another (a d6 against a d8, for example). “Dice pool” gives the chance of at least k successes when each of up to 30 dice succeeds on a roll at or above a threshold you set.
- Does it handle advantage, rerolls or exploding dice?
- Mostly no. The main result is the sum of a fixed number of identical dice, and rules that keep the best die or add extra dice are not included. One reroll rule is covered, in the “Reroll 1s once” panel, where each 1 on a single die is rolled again one time and the second result is kept. Its exact chances for a d6 are 1/36 for a 1 and 7/36 for each of 2 to 6, so the average goes from 3.5 to 3.9167.
- What do “exactly k successes” and “expected successes” mean?
- In the dice pool, each die succeeds on a roll at or above the threshold. The table gives the exact chance of k successes for every k from 0 to the number of dice, next to “at least k”. For 3d6 succeeding on 5+, exactly 1 success has a chance of 12/27 (shown reduced as 4/9) and at least 1 has 19/27. The expected number of successes is the number of dice times the chance that one die succeeds: 3 × 1/3 = 1.
- What does “Copy link to this setup” contain?
- Only whole numbers (dice, sides, modifier, target, duel faces, pool values and reroll faces) in the part of the link after the # sign, with a version tag. That part stays in your browser: it is not sent to a server and does not change the page address. Numbers with decimals or outside a panel's limits are left out of the link, and a link with invalid values is ignored when opened.