Closest CallDice pool odds: counting successes
Roll a handful of dice and count the ones that show 5 or 6. Here is how often you get the successes you need.
Successes on 5 or 6
In a dice pool you roll several six-sided dice and count each die that reaches a target face, instead of adding them up. The most common rule counts a 5 or a 6 as a success, so each die succeeds one time in three.
| Dice in the pool | At least 1 success | At least 2 | At least 3 | At least 4 | Average successes |
|---|---|---|---|---|---|
| 1 | 33.3% | n/a | n/a | n/a | 0.33 |
| 2 | 55.6% | 11.1% | n/a | n/a | 0.67 |
| 3 | 70.4% | 25.9% | 3.70% | n/a | 1.00 |
| 4 | 80.2% | 40.7% | 11.1% | 1.23% | 1.33 |
| 5 | 86.8% | 53.9% | 21.0% | 4.53% | 1.67 |
| 6 | 91.2% | 64.9% | 32.0% | 10.0% | 2.00 |
| 7 | 94.1% | 73.7% | 42.9% | 17.3% | 2.33 |
| 8 | 96.1% | 80.5% | 53.2% | 25.9% | 2.67 |
| 9 | 97.4% | 85.7% | 62.3% | 35.0% | 3.00 |
| 10 | 98.3% | 89.6% | 70.1% | 44.1% | 3.33 |
What the chart tells you
- Three dice give you one success on average, but you still roll none at all 29.6% of the time.
- For a better than even chance of at least one success you need 2 dice; for at least two you need 5; for at least three, 8.
- To be 90% sure of at least one success you need 6 dice.
- Each extra success is much harder than the last. With six dice, at least one success comes up 91.2% of the time, at least two 64.9%, at least three 32.0% and at least four only 10.0%.
- Every die showing a success is rare: all of five dice at 5 or 6 happens 0.412% of the time, or 1 in 243.
Other target numbers
Some games count a 4, 5 or 6 as a success, and some count only a 6. This is the chance of at least one success for each rule.
| Dice in the pool | Success on 4, 5 or 6 | Success on 5 or 6 | Success on 6 only |
|---|---|---|---|
| 1 | 50.0% | 33.3% | 16.7% |
| 2 | 75.0% | 55.6% | 30.6% |
| 3 | 87.5% | 70.4% | 42.1% |
| 4 | 93.8% | 80.2% | 51.8% |
| 5 | 96.9% | 86.8% | 59.8% |
| 6 | 98.4% | 91.2% | 66.5% |
| 7 | 99.2% | 94.1% | 72.1% |
| 8 | 99.6% | 96.1% | 76.7% |
| 9 | 99.8% | 97.4% | 80.6% |
| 10 | 99.9% | 98.3% | 83.8% |
How to work it out
For at least one success, count the rolls with none. One die misses 4 times in 6 when it needs a 5 or 6, so n dice all miss with chance 4/6 multiplied by itself n times. Take that from 1. For two or more successes you also have to take away the rolls with exactly one, which is where a chart saves time.
Where this matters
Dice pools are used in many tabletop role-playing games and miniature war games: your character's skill or your unit's strength sets how many dice you roll, and the difficulty sets how many successes you need. The chart shows why adding one die to a small pool matters far more than adding one to a large pool.
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
- At least one six in 1 to 10 rolls
- 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.