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Demon Probability Tables
This is a series of tables showing the probability of various events using the system in the new World of Darkness. The system is:
Roll a pool of d10s. Any result of 8 or higher is counted as a success. Any result of 10 is kept, and the dice re-rolled (which can continue as long as 10s are rolled).There are various complications regarding how many dice you have to roll, and the special case of 'rolling 0', but we won't worry about that here.
The probabilities have been calculated with the Monte Carlo method. This involves rolling pools of 1 to 15 dice a million times each, and seeing what happens, rather than falling back on probability theory. Mathematicians would call this cheating, but I think it's good enough to let us choose dice mechanics, even if the 3rd or 4th decimal place is a bit wobbly.
For discussion of these tables and mechanics, see the Demon Conversion discussion at Shadownessence.
- Probability of getting n successes
- Probability of getting at least n successes
- Probability of getting at least n 8s
- Probability of getting at least n 6s
- Comparing success rolls
Probability of getting n successes
This table shows you how likely it is to get an exact amount of successes based on the size of your dice pool. 0 successes means a failure, of course.
| Dice Pool | Successes | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
| 1 | 70.01% | 26.99% | 2.69% | 0.27% | 0.03% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 2 | 49% | 37.81% | 11.05% | 1.84% | 0.26% | 0.04% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 3 | 34.24% | 39.71% | 19.31% | 5.43% | 1.09% | 0.18% | 0.03% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 4 | 24.09% | 37.03% | 25.08% | 10.15% | 2.86% | 0.65% | 0.12% | 0.02% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 5 | 16.79% | 32.37% | 28.28% | 15.03% | 5.51% | 1.57% | 0.37% | 0.07% | 0.01% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 6 | 11.79% | 27.22% | 28.94% | 19.05% | 8.78% | 3.08% | 0.88% | 0.22% | 0.05% | 0.01% | 0% | 0% | 0% | 0% | 0% | 0% |
| 7 | 8.24% | 22.2% | 27.94% | 21.96% | 12.17% | 5.13% | 1.69% | 0.5% | 0.12% | 0.03% | 0% | 0% | 0% | 0% | 0% | 0% |
| 8 | 5.75% | 17.8% | 25.8% | 23.43% | 15.29% | 7.53% | 3% | 1% | 0.28% | 0.07% | 0.02% | 0% | 0% | 0% | 0% | 0% |
| 9 | 4.02% | 13.97% | 23.06% | 23.9% | 17.83% | 10.1% | 4.6% | 1.73% | 0.57% | 0.17% | 0.04% | 0.01% | 0% | 0% | 0% | 0% |
| 10 | 2.85% | 10.88% | 19.99% | 23.35% | 19.54% | 12.53% | 6.55% | 2.81% | 1.04% | 0.33% | 0.1% | 0.02% | 0.01% | 0% | 0% | 0% |
| 11 | 1.98% | 8.45% | 17.02% | 22.01% | 20.48% | 14.78% | 8.58% | 4.13% | 1.7% | 0.61% | 0.2% | 0.05% | 0.01% | 0% | 0% | 0% |
| 12 | 1.39% | 6.38% | 14.24% | 20.28% | 20.78% | 16.52% | 10.62% | 5.66% | 2.57% | 1.03% | 0.36% | 0.12% | 0.03% | 0.01% | 0% | 0% |
| 13 | 0.98% | 4.86% | 11.79% | 18.16% | 20.38% | 17.79% | 12.53% | 7.34% | 3.65% | 1.6% | 0.62% | 0.21% | 0.07% | 0.02% | 0.01% | 0% |
| 14 | 0.69% | 3.68% | 9.52% | 16.07% | 19.59% | 18.5% | 14.15% | 9.01% | 4.92% | 2.37% | 0.96% | 0.37% | 0.12% | 0.04% | 0.01% | 0% |
| 15 | 0.47% | 2.76% | 7.75% | 13.88% | 18.36% | 18.64% | 15.44% | 10.71% | 6.32% | 3.25% | 1.49% | 0.61% | 0.22% | 0.08% | 0.02% | 0.01% |
Probability of getting at least n successes
This table shows you how likely it is to get at least a certain number of successes.
| Dice Pool | Number of Successes, or greater | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
| 1 | 29.99% | 2.99% | 0.3% | 0.03% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 2 | 51% | 13.19% | 2.14% | 0.3% | 0.04% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 3 | 65.76% | 26.05% | 6.73% | 1.3% | 0.21% | 0.03% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 4 | 75.91% | 38.88% | 13.8% | 3.65% | 0.79% | 0.14% | 0.02% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 5 | 83.21% | 50.84% | 22.56% | 7.53% | 2.02% | 0.45% | 0.09% | 0.02% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 6 | 88.21% | 60.99% | 32.05% | 13% | 4.22% | 1.15% | 0.27% | 0.05% | 0.01% | 0% | 0% | 0% | 0% | 0% | 0% |
| 7 | 91.76% | 69.56% | 41.62% | 19.66% | 7.48% | 2.35% | 0.66% | 0.16% | 0.03% | 0.01% | 0% | 0% | 0% | 0% | 0% |
| 8 | 94.25% | 76.44% | 50.64% | 27.21% | 11.92% | 4.39% | 1.38% | 0.38% | 0.1% | 0.02% | 0% | 0% | 0% | 0% | 0% |
| 9 | 95.98% | 82.02% | 58.95% | 35.06% | 17.23% | 7.13% | 2.53% | 0.8% | 0.22% | 0.06% | 0.02% | 0% | 0% | 0% | 0% |
| 10 | 97.15% | 86.27% | 66.28% | 42.93% | 23.39% | 10.86% | 4.32% | 1.51% | 0.47% | 0.13% | 0.03% | 0.01% | 0% | 0% | 0% |
| 11 | 98.02% | 89.58% | 72.56% | 50.55% | 30.07% | 15.29% | 6.71% | 2.58% | 0.88% | 0.27% | 0.07% | 0.02% | 0% | 0% | 0% |
| 12 | 98.61% | 92.23% | 77.99% | 57.7% | 36.92% | 20.4% | 9.78% | 4.12% | 1.55% | 0.52% | 0.16% | 0.04% | 0.01% | 0% | 0% |
| 13 | 99.02% | 94.16% | 82.37% | 64.21% | 43.83% | 26.04% | 13.51% | 6.17% | 2.53% | 0.93% | 0.31% | 0.1% | 0.03% | 0.01% | 0% |
| 14 | 99.31% | 95.64% | 86.12% | 70.05% | 50.46% | 31.96% | 17.81% | 8.8% | 3.88% | 1.51% | 0.55% | 0.18% | 0.06% | 0.02% | 0.01% |
| 15 | 99.53% | 96.77% | 89.03% | 75.15% | 56.78% | 38.14% | 22.7% | 11.99% | 5.67% | 2.42% | 0.94% | 0.33% | 0.11% | 0.03% | 0.01% |
Probability of getting at least n 8s
This table shows you how likely it is to get at least a certain number of 8s in the dice pool. This is based on Mala Fide's suggest for Torment on the Shadownessence forum.
| Dice Pool | Number of 8s, or greater | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1 | 11.08% | 0% | 0% | 0% | 0% |
| 2 | 20.99% | 1.24% | 0% | 0% | 0% |
| 3 | 29.79% | 3.46% | 0.14% | 0% | 0% |
| 4 | 37.5% | 6.32% | 0.49% | 0.02% | 0% |
| 5 | 44.54% | 9.85% | 1.15% | 0.07% | 0% |
| 6 | 50.64% | 13.74% | 2.12% | 0.19% | 0.01% |
| 7 | 56.2% | 17.74% | 3.4% | 0.4% | 0.03% |
| 8 | 61.04% | 22.06% | 4.99% | 0.74% | 0.07% |
| 9 | 65.35% | 26.37% | 6.85% | 1.2% | 0.14% |
| 10 | 69.24% | 30.78% | 9.08% | 1.86% | 0.26% |
| 11 | 72.61% | 34.97% | 11.46% | 2.63% | 0.43% |
| 12 | 75.71% | 39.22% | 14.07% | 3.62% | 0.67% |
| 13 | 78.39% | 43.24% | 16.87% | 4.82% | 1.02% |
| 14 | 80.74% | 47.09% | 19.73% | 6.12% | 1.44% |
| 15 | 82.91% | 50.87% | 22.86% | 7.63% | 1.93% |
Probability of getting at least n 6s
This table shows you how likely it is to get at least a certain number of 6s in the dice pool, as well as it being a successful roll. This is my rather flippant variation of the previous table.
| Dice Pool | Number of 6s, or greater (plus success) | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1 | 1.11% | 0% | 0% | 0% | 0% |
| 2 | 7.96% | 0.24% | 0% | 0% | 0% |
| 3 | 17.03% | 1.52% | 0.04% | 0% | 0% |
| 4 | 26.47% | 3.93% | 0.26% | 0.01% | 0% |
| 5 | 35.48% | 7.27% | 0.77% | 0.04% | 0% |
| 6 | 43.59% | 11.22% | 1.62% | 0.13% | 0.01% |
| 7 | 50.69% | 15.6% | 2.89% | 0.32% | 0.02% |
| 8 | 56.93% | 20.25% | 4.46% | 0.62% | 0.06% |
| 9 | 62.43% | 24.94% | 6.37% | 1.08% | 0.13% |
| 10 | 66.94% | 29.49% | 8.57% | 1.71% | 0.24% |
| 11 | 71.09% | 34.08% | 11.08% | 2.54% | 0.43% |
| 12 | 74.42% | 38.43% | 13.77% | 3.55% | 0.66% |
| 13 | 77.51% | 42.66% | 16.61% | 4.7% | 0.98% |
| 14 | 80.26% | 46.74% | 19.57% | 6.02% | 1.39% |
| 15 | 82.42% | 50.48% | 22.66% | 7.55% | 1.92% |
Comparing success rolls
This table allows shows you the chance of rolling a success and having the successful dice follow a particular pattern. The first column shows how likely it is that the number of 8s is greater than the number of 9s and 10s combined. The second column shows how likely it is that the number of 8s and 9s combined is greater than the number of 10s. This is for my sugestion of a Torment mechanic, which adds a player-chosen value to an evocation roll.
| Dice Pool | More 8s than 9s and 10s | More 8s and 9s than 10s |
|---|---|---|
| 1 | 9.97% | 19.99% |
| 2 | 15.2% | 32.84% |
| 3 | 17.94% | 41.5% |
| 4 | 19.15% | 47.42% |
| 5 | 19.74% | 52.09% |
| 6 | 19.88% | 55.64% |
| 7 | 19.7% | 58.46% |
| 8 | 19.46% | 60.98% |
| 9 | 19.09% | 62.95% |
| 10 | 18.8% | 64.94% |
| 11 | 18.28% | 66.47% |
| 12 | 17.88% | 67.98% |
| 13 | 17.46% | 69.41% |
| 14 | 17.03% | 70.68% |
| 15 | 16.68% | 71.86% |
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