There are a variety of synonyms for the phrase "can't believe your luck." Some similar expressions include "pinch me, I must be dreaming," "unbelievable fortune," "fortunate twist of fate," "incredible stroke of luck," "amazing serendipity," and "unforeseen blessing." These phrases all express a sense of disbelief or surprise at the good luck or fortune that has come their way. They are all great ways to express gratitude and appreciation for unexpected good fortune and can be used in a variety of situations, from winning the lottery to getting a dream job or meeting the love of your life.