The $5000 Compression Challenge (2001)

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.

Somewhere (discussed on HN) someone devised a "better-than-perfect" compressor. Most inputs get compressed (smaller than input), except for one input that does not. That one input is cryptographically impossible to find - or something along those lines.

Unfortunately I can't find the article I'm describing here, maybe someone else can? It was a long time ago so I might be misrepresenting it slightly.

That's how all compressors work, in that likely files (eg. ASCII, obvious patterns, etc) become smaller and unlikely files become bigger.

Right, but the point was, the case where it became bigger was ~impossible to find.