A quick look at the meaning of "ungefähr" and what estimates have to do with danger and driving.
ungefähr, die Gefahr, gefährlich, circa
The core idea of this root was:
It’s the origin of the Latin rota (wheel) and its small version rotula, which are the origin of words like rotate and (via French) the words role, to roll and roulette.
Also words like round and the German rund ultimately come from the Latin branch.
Role in the sense of character, role in a scene comes from the fact that the texts of an actor were a roll of paper back Rome and Ancient Greece.