Move your estimation point until half the big side is the same as the little side. (Although I've practiced enough to do halves, thirds, and fifths pretty well, so I might just be overgeneralizing my experience.)

Damn. I chose two random numbers and made a probability out of them. It seems I picked one of the easy ones too! :)

And yes, that algorithm does seem to work well for thirds. I lose a fair bit of accuracy but it isn't down to 'default human estimation mode' level.