Colour-blinded

The original version of this puzzle was posted in the Discussion Forums by araya on February 11th 2000, with the title Sorting the counters.

While travelling through the uncharted highlands in the north of Puzzlania, you are waylaid and captured by a group of the nomadic barbarians that live in the area. More likely than not, they intend to sacrifice you to their dark god. Or maybe feast upon your flesh. Or perhaps just kill you for fun. Whatever the case may be, their plans for you are not something you'd enjoy. Still, this is the sort of thing one has to expect when one is an Adventuring Puzzler.

But perhaps all is not lost... As is customary in these circumstances, you are offered freedom if you can beat their challenge. Deciding that you don't have much of a choice, you agree.
You are blindfolded and led into a tent. At the beckoning of your captors, you kneel and touch the ground in front of you. On the packed earth floor of the tent are hundreds of small, smooth, circular discs. It si explained to you that each of the reindeer bone tokens in front of you has one side that is dyed red, and another that is dyed green. There are currently 129 tokens that have their red side facing up. The task you must complete is to divide the tokens into two groups, such that each group have the same amount of tokens showing red. They add that, should you decide to lift your blindfold, the man behind you will ensure that all of the tokens rather quickly turn a bright crimson.

So. Now what?