I think maybe another way to put this is that Alice's number is in a typical set [0] of the distribution of bitstrings whereas Bob's might not be. Depending on

I think maybe another way to put this is that Alice's number is in a typical set [0] of the distribution of bitstrings whereas Bob's might not be. Depending on the tolerance, the typical set can have near-total coverage of the distribution. Another way of making this about compression is that a random code that could encode typical set strings well probably will suffer some overhead when encoding Bob's, but most strings it will encode close to optimally. [0] https://en.wikipedia.org/wiki/Typical_set https://en.wikipedia.org/wiki/Typical_set