Dicing with Probability

an application of base Twelve, by Alice

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)

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:

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)

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)

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