When you are out of options. When there is nothing else you can do. When your back is against the wall, and there's no other way. Play your best card last. It is the last ditch effort to try to turn the tide in your favor.
It can also be played when it will be most effective. If you have pre-determined that when a certain opportunity has presented itself , that will be the best time to play this particular card, then you should be sure to execute it right on time. Not missing your window of opportunity.