That's one of the other popular strategies, but relies on both devices have accurate clocks. With computers and servers (where the strategy is used quite a bit,

That's one of the other popular strategies, but relies on both devices have accurate clocks. With computers and servers (where the strategy is used quite a bit, sometimes in combination with challenge-response), it's quite easy. If you're working with something non-networked or battery powered like a garage door opener, clock drift becomes a serious issue.