Dice Odds for 3d6
Dice Odds d20 vs. 3d6
| 1d20 | 3d6 | |||
|---|---|---|---|---|
| Pct | Odds | Pct | Odds | |
| 1 | 5% | 19.0 : 1 | - | - |
| 2 | 10% | 9 : 1 | - | - |
| 3 | 15% | 5.7 : 1 | 0.5% | 215 : 1 |
| 4 | 20% | 4 : 1 | 1.9% | 53 : 1 |
| 5 | 25% | 3 : 1 | 4.6% | 20.6 : 1 |
| 6 | 30% | 2.3 : 1 | 9.3% | 9.8 : 1 |
| 7 | 35% | 1.8 : 1 | 16.2% | 5.2 : 1 |
| 8 | 40% | 1.5 : 1 | 25.9% | 2.9 : 1 |
| 9 | 45% | 1.2 : 1 | 37.5% | 1.7 : 1 |
| 10 | 50% | 1 : 1 | 50.0% | 1 : 1 |
| 11 | 55% | 1 : 1.2 | 62.5% | 1 : 1.7 |
| 12 | 60% | 1 : 1.5 | 74.1% | 1 : 2.9 |
| 13 | 65% | 1 : 1.8 | 83.8% | 1 : 5.2 |
| 14 | 70% | 1 : 2.3 | 90.7% | 1 : 9.8 |
| 15 | 75% | 1 : 3 | 95.4% | 1 : 20.6 |
| 16 | 80% | 1 : 4 | 98.1% | 1 : 53 |
| 17 | 85% | 1 : 5.7 | 99.5% | 1 : 215 |
| 18 | 90% | 1 : 9 | 100% | 1 : inf |
| 19 | 95% | 1 : 19 | - | - |
| 20 | 100% | 1 : inf | - | - |
One big difference between d20 and 3d6 is the likelihood of getting a particular number. For d20 it’s exactly the same for each number. For 3d6 you are much more likely to get a number toward the center of the range (around 10) than at the extremes (3 or 18). The table below gives the percent likelihood of rolling each number.
Note that about half of the rolls are in the 9-12 range. 25% are 8 or below and 25% are 13 and above.
| STATISTIC | Probability % | The % <= N | STATISTIC | Probability % |
The % <= N |
| 18 | 0.4630% | 100.00% | 10 | 12.500% | 50.00% |
| 17 | 1.3889% | 99.54% | 9 | 11.5741% | 37.5% |
| 16 | 2.7778% | 98.15% | 8 | 9.7222% | 25.93% |
| 15 | 4.6296% | 95.37% | 7 | 6.9444% | 16.2% |
| 14 | 6.9444% | 90.74% | 6 | 4.6296% | 9.26% |
| 13 | 9.7222% | 83.80% | 5 | 2.7778% | 4.63% |
| 12 | 11.5741% | 74.07% | 4 | 1.3889% | 1.85% |
| 11 | 12.500% | 62.50% | 3 | 0.4630% | 0.46% |
Here is a graph showing the distribution.
