Taken from Mindhacker: 60 Tips, Tricks, and Games to Take Your Mind to the Next Level, a new book (released today), by Ron Hale-Evans and Marty Hale-Evans, discovered voa Boing Boing:

Hack 36: Role the Mental Dice
Quick! You need a way to generate random numbers using just your brain, because you’re playing in the pool, driving, falling asleep, or doing something else that makes it difficult to roll physical dice. Maybe you’re playing games (board, role-playing, or purely mental) or breaking out of a rut by making decisions randomly. Don’t panic – you can use simple math on random words from your surroundings to quickly create random numbers, just about anytime and anywhere.

For each of these procedures, you’ll need to be able to come up with a short random word, either spontaneously or from the environment. To get one, check nearby signs or reading material, ask a friend or passerby, or do anything similar that seems good to you. You’ll also need to know or work out the number value of each letter, corresponding to its place in the alphabet: A = 1, B = 2, C = 3, and so on through Z equals 26.

To emulate a 6 sided die, follow this procedure:

1. find a short word, such as “cat.”

2. Sum the numerical values of the letters in the word: C = 3, A = 1, T = 20, and then 3+1+20 = 24.

3. Calculate the number modulo 09 (see the section “How It Works” for the procedure).

If the remainder is a 0, 7, or 8, which will happen one third of the time, discard it and try a new word. Otherwise, the remainder will be a pseudo random number from 1 to 6. Congratulations! This is your 6 sided die roll. (The results for the word “cat” is 6.)