Randomizing with a coin

[iversonian]

You are playing rock paper scissors, and you want to choose which to throw using a coin. You want a probability distribution of 1/3 for each type.

Is it possible to devise an algorithm for choosing what to throw based on a series of coin flips such that you are guaranteed to have a result in a finite number of coin flips? If not, prove. If so, what is the smallest number of coin flips in which you can guarantee a result that has a perfect 1/3 distribution for each type.

e.g. If you flip twice, where head-head = rock, head-tail = paper, tail-head = scissors, and tail-tail = redo, then it may never terminate.