多亏 / 幸亏 / 亏得【duōkuī / xìngkuī / kuīde】

多亏 gives credit: the good result happened because of this person or thing. It takes a noun or a clause, often with 了, and 才 frequently marks the result.

It can also come second, after the result.

幸亏

幸亏 is about luck. It takes a clause, and the bad outcome that was avoided often follows with 不然 or 要不然.

Because it needs a clause, 幸亏 can't take a bare person the way 多亏 can.

• × 幸亏你，我们没迟到 → 多亏你，我们没迟到 / 幸亏你来了，我们没迟到

亏得 means the same and is more colloquial.

Good outcomes only

None of the three can blame. For a bad result caused by someone, use 都怪 or 因为.

• × 多亏他，我们迟到了 → 都怪他，我们迟到了