[ericbsmith]

Actually, it just occurred to me you can get an Electronic Yahtzee game for under $10 that will serve as a dice roller just fine and last forever on a set of batteries.

While I realise that one of the stipulations of the original post was to not have dice, the problem is that you can't generate anything approaching truly random numbers without an external tool helping you (whether it's a deck of cards, dice, or electronic app/game). Humans are particularly bad at generating random numbers, so any attempt to do so without tools is likely to be skewed (purposefully or not). Even using license plates and road signs... which license plate you choose is a conscious choice, and they are not truly randomized as you tend to travel with similar vehicles on the road or see the same road signs multiple times.