Basement Bathtub Backup
This doesn't sound like a venting problem.

If your basement bathtub is backing up, I assume it is the lowest point in your plumbing drainage piping.  This typically means that the sewer service line to the city is clogged or restricted.

What snake did you use?   How far from your property to the city sewer main?   50' doesn't sound like enough.  How old is the house / sewer line, do you trees on your property?  You might also want to rent the scope to see the problem.  

Rent the 100' sewer snake from homedepot and run that from your house out to the sewer main.