[Siegmund]

Don't want to worry about a source of randomness?

This is a real handy reason to memorize the first 10 or 20 digits of pi or e. You will of course not ALWAYS start with the first digit mod 3, the second digit mod 3, etc... but unless you are going to play dozens of games against the same person, just picking "start from the fourth digit" or "work backwards from the tenth digit" or whatever is real handy to save you from thinking about each new play as it comes up.