So the whole of Bismarck's career absolutely rested on the longevity of the old man

Bismarck was able to achieve all this not just because he was a shrewd politician, but because Kaiser Wilhelm lived for ninety-one years, as Jonathan Steinberg explains:

'Wilhelm I was born in 1797. Had he lived his biblical three score and ten, he would have died in 1867, before the unification of Germany. Friedrich III would have come to the throne as a youngish man and he would have fired Bismarck. He in fact did not come to the throne in 1867, nor in 1877, nor in 1887, because the old man would not die, and as long as Wilhelm I was there - he died in March 1888 at the age of ninety-one - Bismarck had a job. So the whole of Bismarck's career absolutely rested on the longevity of the old man.' 

N. MacGregor, Germany: memories of a nation (2014), 394