Because I’ve been spending a lot of time thinking about hacking the AGE system, I decided to dig into the probabilities involved in its dice mechanic. The AGE system uses a roll of 3d6 + ability versus a target number in order to determine whether actions are successful. Rolling 3d6 gives a distribution of results that is pretty close to a bell curve. Rolls can result in a value from 3 to 18 with a mean of 10.5.

The bell-shaped distribution means that a roll is more likely to be close to the mean result than near the extremes of the range of possible results. In practical terms, that means almost half of all rolls will have a result in the range from 9 to 12. The shape of the distribution also means that the effect of a single +/- 1 modifier to a roll can change the probability of success by as much as 12.5% – that’s a much bigger effect than the 5% change a +/- 1 modifier causes in a d20-based system.

The more interesting portion of the AGE system’s dice mechanic is the stunt system. Whenever at least 2 of the 3 dice show the same number on a successful roll, the roll generates stunt points that can be spent to add additional effects to the action. The number of stunt points generated is equal to the roll of the dragon die, which is one of the 3 dice rolled that is a different color from the other two. In general, you have a 44.44% chance to have doubles on a roll of 3d6, but the chance of getting doubles on a success varies based on the target number of the roll. The average number of stunt points also varies with the target number of the roll because higher target numbers means that rolls with low dragon die values are less likely to be successful.

Target Number | Success | Stunt* | Mean Stunt Points** |
---|---|---|---|

3 | 100.00% | 44.44% | 3.50 |

4 | 99.54% | 44.19% | 3.53 |

5 | 98.15% | 43.40% | 3.60 |

6 | 95.37% | 41.75% | 3.73 |

7 | 90.74% | 41.84% | 3.82 |

8 | 83.80% | 40.33% | 4.00 |

9 | 74.07% | 40.00% | 4.19 |

10 | 62.50% | 42.22% | 4.33 |

11 | 50.00% | 44.44% | 4.52 |

12 | 37.50% | 48.15% | 4.72 |

13 | 25.93% | 57.14% | 4.88 |

14 | 16.20% | 65.71% | 5.09 |

15 | 9.26% | 70.00% | 5.36 |

16 | 4.63% | 100.00% | 5.50 |

17 | 1.85% | 100.00% | 5.75 |

18 | 0.46% | 100.00% | 6.00 |

*: This is the probability of a successful roll containing doubles

**: This is the mean number of stunt points generated on a successful roll containing doubles

As you can see in the table above, the chance of a successful roll generating stunt points starts in the 40-50% range for most target numbers, but then it increases at the high-end of the target number range until every successful roll will generate stunt points. While that might not make a ton of sense, I like that it means that the rare successful roll against nearly impossible odds will be a big cinematic success.

In addition to using 3d6 to determine success and failure, the AGE system also uses 3d6 to randomly determine starting abilities. Instead of using the result of the roll directly like Dungeons & Dragons, in AGE you use a table to map the roll to an ability score that can range from -2 to +4. The table ends up resulting in a median ability of 1 with the results skewed slightly towards higher ability scores. The minimum and maximum starting abilities (-2 and +4) are both very unlikely with only a 0.46% chance of being rolled.

This

singsto the mathematician/statistician in me! 🙂 This is an excellent analysis of the AGE dice mechanic. Considering that I do this sort of thing for fun (math nerd… I know.), the next step I’d take is to see exactly how that +1 or +2 to a roll changes the chances of success when taking (TN – Skill) into account. Of course, this would require several individual graphs – a pleasing prospect to me. 😉You should be able to calculate those values pretty quickly using the success percentages in the table. For example, if you currently need a roll of 10 to succeed, an additional +1 bonus will move your chance of success from 62.50% to 74.07% (an improvement of 11.57%).

Oh, sure – looking at the table and bumping up (or down) is easy enough. But I’d like the exercise of knowing, for example, the percentage increase a +1 bump will give when the target number is 18, 17, 16…, etc.. That +1 is much more effective when the TN is higher, but how does that effectiveness change? Not that I’m asking you to do this, of course – that’s something I’d do my self. You know, for fun. 🙂

Thanks for posting these graphs – I love them!