The Storyteller system from White Wolf Games is a target number dice pool system. The player rolls a number of d10's equal to her attribute plus skill against a difficulty number between 2 and 10. Each die that is equal to or higher the difficulty number counts as one success. However, each die that is a "1" cancels out a success. Some tasks only require one success, while some require multiple successes. In later editions, a roll is a critical failure (or "botch") if no successes are rolled and one or more "1's" are rolled. Earlier editions had a critical failure if more "1's" were rolled than successes.
This system has the complexity that some conditions will modify the number of dice, some will modify the difficulty, and some will modify the required number of successes. For example, a longer jump requires more successes, wounds will reduce your number of dice, and poor footing will increase the difficulty. All of these have different effects on the probability. It also has the peculiarity that at high difficulties, the botch chance may increase as ability increases.
| Number of Dice | Chance of Success at Difficulty | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 1d | 90% | 80% | 70% | 60% | 50% | 40% | 30% | 20% | 10% |
| 2d | 81% | 80% | 77% | 72% | 65% | 56% | 45% | 32% | 17% |
| 3d | 97% | 92% | 87% | 81% | 74% | 65% | 54% | 40% | 22% |
| 4d | 95% | 94% | 91% | 86% | 80% | 71% | 60% | 45% | 26% |
| 5d | 99% | 97% | 94% | 90% | 84% | 76% | 65% | 49% | 28% |
| 6d | 98% | 98% | 96% | 93% | 88% | 80% | 69% | 53% | 30% |
| 7d | 100% | 99% | 97% | 95% | 90% | 83% | 72% | 55% | 32% |
| 8d | 99% | 99% | 98% | 96% | 92% | 85% | 75% | 58% | 33% |
| 9d | 100% | 99% | 99% | 97% | 94% | 87% | 77% | 60% | 35% |
The botch probabilities are below. Note that at higher difficulties the botch chance initially rises as the number of dice increase, but then eventually peaks and goes down. At difficulty 8, it peaks at 2 dice and drops from there. At difficulty 9, it peaks at 4 dice -- but you need more than 8 dice to have a lower botch chance than you had with just 1 die. At difficulty 10, the botch chance keeps rising until 7 dice.
| Number of Dice | Chance of Botch at Difficulty | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 1d | 10% | 10% | 10% | 10% | 10% | 10% | 10% | 10% | 10% |
| 2d | 1% | 3% | 5% | 7% | 9% | 11% | 13% | 15% | 17% |
| 3d | 0% | 1% | 2% | 4% | 6% | 9% | 12% | 17% | 22% |
| 4d | 0% | 0% | 1% | 2% | 4% | 7% | 11% | 17% | 25% |
| 5d | 0% | 0% | 0% | 1% | 2% | 5% | 9% | 16% | 26% |
| 6d | 0% | 0% | 0% | 0% | 1% | 3% | 7% | 14% | 27% |
| 7d | 0% | 0% | 0% | 0% | 1% | 2% | 5% | 13% | 27% |
| 8d | 0% | 0% | 0% | 0% | 0% | 1% | 4% | 11% | 26% |
| 9d | 0% | 0% | 0% | 0% | 0% | 1% | 3% | 9% | 25% |
Obviously, these results are rounded to the nearest whole percentage. For those interested, I have a text file with more detailed charts of the probabilities.