You'd have to define what you mean by luck which would be equivalent to choosing some pattern that your compressor can recognize in a random stream of bytes and

You'd have to define what you mean by luck which would be equivalent to choosing some pattern that your compressor can recognize in a random stream of bytes and then computing the probability that pattern appeared in some random byte sequence. It's not a winnable game in any practical sense because whatever compressor you choose the probability of getting a sequence from your opponent that will conform to the patterns recognizable by your compressor is essentially 0.