3 ms·

I'm not forgetting that. It's just that any specific random file will have (with high probability), patterns that can be exploited. It's not guaranteed to work

I'm not forgetting that. It's just that any specific random file will have (with high probability), patterns that can be exploited. It's not guaranteed to work on all files of course. The theoretical limit (per bijection argument) is that at most half the strings of length n can be losslessly represented in strings of length n-1, because there are half as many strings of length n-1 than of length n. So if, for example, 2% of files can actually be reduced in size (I don't know what the actual number is, and if it is even computable) that's still positive EV in a $100 vs $5000 bet.

jgeralnik 14y ago
The file is not really random, though, since Mike generated it and had time to make sure it was a "good" file before sending it on. That is, if the file was truly random, it would have a chance of 1/(2^X) of being all 0, where X is the size of the file. But since Mike would reject that file, the chance is actually 0. Same for all files with easily exploitable patterns - for example, I am sure that Goldman checked that the file could not be compressed with gzip before sending it. So the EV is probably not positive, even if there is a small chance that a random file of size X can be compressed.