But you don’t need to compress every possible file to make playing such a game a good idea.

Suppose if you shave 1 bit off of a sample bit stream you win and you lose if that fails. Your compressor looks at the first 2 bits and if it starts 11 it starts with 1 and otherwise it starts 0 then the bit stream. Now you have a 1 in 4 chance to compress a random string by 1 bit and. A 3 in 4 chance of making it longer by 1 bit.

It’s ultimately not about compression but what odds are worth it.