What are the odds of scoring any value three through 20 on 2d6 if they explode on doubles? This, is of course, the same as saying “what are the odds on a T&T Saving Roll?” Because I’d like to convert the thief’s skills to T&T style talents I needed to come up with values for levels one through 20. I’d have to look up the math to do an exact probability calculation so I wrote a Perl script to do 1,000,000,000 simulations instead. The results for those who are interested:

Roll | Odds | Odds <= | Odds => |
---|---|---|---|

3 | 8.0% | 8% | 100% |

4 | 8.0% | 16% | 92% |

5 | 16% | 32% | 84% |

6 | 16% | 48% | 68% |

7 | 17% | 65% | 52% |

8 | 9.0% | 74% | 35% |

9 | 9.7% | 83.3% | 26% |

10 | 1.3% | 84.6% | 15.4% |

11 | 2.0% | 86.6% | 13.4% |

12 | 1.4% | 88% | 12% |

13 | 2.1% | 90.1% | 9.9% |

14 | 1.4% | 91.5% | 8.5% |

15 | 1.9% | 93.4% | 6.6% |

16 | 1.2% | 94.6% | 5.4% |

17 | 1.3% | 95.9% | 4.1% |

18 | 0.1% | 96.9% | 3.1% |

19 | 0.1% | 97% | 3% |

Twenty was under a tenth of a percent even rounded so I excluded it.

It is a little tricker though as you then need to add the DEX ability score which is another 3d6 normal distribution.

I'm basing it on a “minimal thief” who has a DEX of 12 or an average character with a 10.5.

Adding in that 3d6 is just too much effort for too little return.

You also need to pick a SR level. I'm basing it on a Lvl 3 (or maybe a 2 depending on how the math works).