Tried it with Tor to see if Tor provided much better privacy. Relatively it is better than another browser, but still 12.n bits of uniquely identifying informat

Tried it with Tor to see if Tor provided much better privacy. Relatively it is better than another browser, but still 12.n bits of uniquely identifying information (1:4096). From a k-anonymity perspective, I might as well transmit a full zip code to all the parties at each site the browser interacts with. I don't have the data handy, but the idea of expressing this in terms of conceptual zip codes could be useful. e.g. a 5-digit US zip code has a wide range, but handwavy, let's say the average for all 5 digits of a given zip code is a population of maybe 5k people. 4-digits could be 50k people, 3-digits 100k etc. 12-bits of information is a one in a field of 4096, which implies to me that the Tor browser finderprint yields the unique information equivalent of sending a consistent zip code, just not your physical one. It means that your net level of anonymity requires other Tor users to also be in that "zip code" of fingerprints, which seems to have a very low probability. I am surprised Tor doesn't appear to tumble these fingerprint features.