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There is something seriously not right about this test. The first time I ran the test, this was my result:

Within our dataset of several million visitors, only one in 533,751 browsers have the same fingerprint as yours.
Currently, we estimate that your browser has a fingerprint that conveys 19.03 bits of identifying information.

After taking the test several times, my score gets lower with each test.

This is the latest result:

Within our dataset of several million visitors, only one in 43,285 browsers have the same fingerprint as yours.
Currently, we estimate that your browser has a fingerprint that conveys 15.4 bits of identifying information.

Either their test is hinky or my browser (Opera) is shutting down identifying characteristics.

They mentioned that in the .PDF paper... Here's what I believe is going on: Let's say they have 3,000,000 entries in their fingerprint database. If you are one of six people who share your fingerprint, they'll report to you that "only one in 500,000 browsers have the same fingerprint as yours."

The next time you take the test, it will think of you as the seventh person to have visited the website with that fingerprint and will report that "only one in 428,571 browsers have the same fingerprint as yours." So, you'll appear to be less unique, that is, less identifiable from a uniqueness point of view. Less unique is good.

But you do not want to repeatedly take the test over and over again because, although that number will decrease each time, it will not be giving you accurate information after your first visit.

You should only re-take the test after you've made major changes in the headers that are handed off from your browser to servers, to see whether or not the changes you've made are actually beneficial from a privacy (uniqueness) point of view.