Arguably, your best bet for this kind of test is a very blatantly fake name, like "Zxzxzx". It's entirely possible that there is someone with the last name Smith (since it's very common) who also has those six digits at the end of their SSN.

Good point.. I tried "potter" and I got Not eligible.

So either I'm a great last digit guesser (Though I'm usually not lucky in things like gambling....) I'll update my original comment.

It may not be so much a great guess as a statistical likelihood! In 2000, there were over 2.3 million Smiths in the United States: https://blogs.ancestry.com/cm/smith-a-short-history-of-ameri... (This number has likely grown roughly alongside our population, so let's use 2000 numbers for this.) In 2000, we had 281 million people in the US, which means 0.8% of Americans have the last name Smith.

If we assume every possible SSN could be handed out, a trailing six digit entry could have anywhere up to 999 possible SSNs, so you're firing out a shotgun with a pretty big number of potential targets each time you guess an SSN.