All numbers in this article are in base twelve; T stands for T and E for eleven; the "dozenal point" is represented by an apostrophe.

If we throw a six-sided die the chance of throwing the number six is simply one in six (assuming, of course, that the die is fair).

One Die (6 outcomes)

Score | ways | chance |
---|---|---|

1 | 1 | 0'2 |

2 | 1 | 0'2 |

3 | 1 | 0'2 |

4 | 1 | 0'2 |

5 | 1 | 0'2 |

6 | 1 | 0'2 |

totals | 6 | 1'0 |

The game of Craps uses two dice; the player rolls the two dice and adds the numbers shown on the dice to make his score. The least he can score is 2 (with both dice showing "1") and the most 10 (both showing "6").

The scores gained by throwing two dice are shown in the table:

Die 2 | ||||||

Die 1 | 1 | 2 | 3 | 4 | 5 | 6 |

1 | 2 | 3 | 4 | 5 | 6 | 7 |

2 | 3 | 4 | 5 | 6 | 7 | 8 |

3 | 4 | 5 | 6 | 7 | 8 | 9 |

4 | 5 | 6 | 7 | 8 | 9 | T |

5 | 6 | 7 | 8 | 9 | T | E |

6 | 7 | 8 | 9 | T | E | 10 |

There are more ways of throwing a "7" than any other number; of the 30 possible results 6 of them are a "7"; 6 out of 30 is one-sixth, or 0'2, or 20 per gross. (Note how base twelve makes the numbers simple; because of the factor 6.)

Two dice (6^2 = *30 outcomes)

score | ways | chance | per gross |
---|---|---|---|

2 | 1 | 0'04 | 4 |

3 | 2 | 0'08 | 8 |

4 | 3 | 0'10 | 10 |

5 | 4 | 0'14 | 14 |

6 | 5 | 0'18 | 18 |

7 | 6 | 0'20 | 20 |

8 | 5 | 0'18 | 18 |

9 | 4 | 0'14 | 14 |

T | 3 | 0'10 | 10 |

E | 2 | 0'08 | 8 |

10 | 1 | 0'04 | 4 |

totals | 30 | 1'00 | 100 |

With three dice the scores go from 3 to 16 (3 ones, 3 sixes); note that the number of outcomes for T and E are the most frequent with 23 each; the pobability of scoring T or E is 23/160 or 1 in 8 (0'16 or 16 per gross).

Three dice (6^3=160 outcomes)

score | ways | chance | per 1000 |
---|---|---|---|

3 | 1 | 0'008 | 8 |

4 | 3 | 0'020 | 20 |

5 | 6 | 0'040 | 40 |

6 | T | 0'068 | 68 |

7 | 13 | 0'0T0 | T0 |

8 | 19 | 0'120 | 120 |

9 | 21 | 0'148 | 148 |

T | 23 | 0'160 | 160 |

E | 23 | 0'160 | 160 |

10 | 21 | 0'148 | 148 |

11 | 19 | 0'120 | 120 |

12 | 13 | 0'0T0 | T0 |

13 | T | 0'068 | 68 |

14 | 6 | 0'040 | 40 |

15 | 3 | 0'020 | 20 |

16 | 1 | 0'008 | 8 |

totals | 160 | 1'000 | 1000 |

Footnote by Alice: I prefer an upturned "V" (like an "A" without the bar) for ten.