Bachten de Kupe
I'll usually use it first as part of a recovery from big A-N losses, and it can provide some certainty if a turn's other actions have lousy rolls. But I especially enjoy using it when a A-N -1 DRM is active (assuming China isn't also active): hah, take that!
I use it for the same (and only) purpose: to get an A/N boost when hardest needed, and when the odds are against me. Often it will be to get A/N back to 1, in order to prevent to have to give in Prestige when A/N goes down, and in order to be able to make more than one attack.
-- edit to add:
And I usually don't go further than uses of my 'right to withdraw'. I don't really know why, but it gives me a certain feeling of "freedom of choice". It only happened once that I took a fourth go with it, and I don't seem to remember that it changed anything: I don't recall wanting to higher A/N towards it's 3 position when I could not.