I know very little about this, but a little googling suggests that the measure you're looking for is entropy, which has a mathematical definition: https://en.wikipedia.org/wiki/Entropy_(information_theory)

Not sure why this got downvoted. This actually worked. Sure, I shouldn't have to negotiate with a bot, but it did get me to a human just now. (Or maybe a really convincing bot).

Sure, but it's a hassle because you've got to go to the post office and fill out a return receipt requested form, otherwise the letter could just go into a black hole. Plus, who knows how many weeks it would take to get a response?

I wonder if it would have been possible to win the challenge legitimately?

If a randomly-generated file happened to contain some redundancy through sheer chance, you could hand-craft a compressor to take advantage of it. This compressor would not work in general for random data, but it could work for this one particular case.

It's a bet worth taking, because the payoff, 50:1 ($5,000 to $100), is pretty good. Play the game 50 times and you might get a file you could compress.

The challenge, then, would be for the person offering the bet to generate a really random file that contained no such redundancy. That might not be easy.

Yup, this works. I did not think to click "Digital Services" because this has nothing to do with digital services. But it does get you to the chat.