-도록 — so that, in order to

When using this expression, the action stated in the preceding clause is the speaker's goal or reason for doing the action stated in the following clause. It is interchangeable with -게.

Details

The expression -도록 is also used to express a time limit, degree, or method related to the action stated in the following clause.

눈이 빠지도록 전회를 기다렸지만 전화가 오지 않았어요.

I waited with a craned neck for the phone call, but it never came.

동생이 밤 12시가 다 되도록 집에 들어오지 않아서 걱정했어요.

My little brother/sister didn't come home by midnight, so I became worried.

While -게 and -도록 are very similar in meaning, their precise differences are as follows.

Kimchi Reader

It expresses that the preceding clause is the goal or reason for doing the action stated in the following clause.