This seems like a fundamental misunderstanding of how this sort of watermarking works. (Either that, or I have a fundamental misunderstanding of how it works lol.) It doesn't change the probability distribution of the next token at all. If you were getting XYZ 48% of the time before, you're still getting XYZ 48% of the time. What's changed is where the random numbers come from. But as far as you're concerned, there's just as random as they were before, just like an encrypted message is indistinguishable from random bytes if you don't know the key.
This seems like a fundamental misunderstanding of how this sort of watermarking works. (Either that, or I have a fundamental misunderstanding of how it works lol.) It doesn't change the probability distribution of the next token at all. If you were getting XYZ 48% of the time before, you're still getting XYZ 48% of the time. What's changed is where the random numbers come from. But as far as you're concerned, there's just as random as they were before, just like an encrypted message is indistinguishable from random bytes if you don't know the key.