In trying to tweak my ODBC connection use, I was trying to limit the number of max_links.  I could change the number in php.ini, but didn't see the change in phpinfo() output.  I changed

uodbc.max_links = -1
            to
uodbc.max_links = 10

Then, looking at the phpinfo() output, I saw the variable was actually called odbc.max_links, so changing the line to:

odbc.max_links = 10

did the trick.   Your documentation also specifies the parameter as "uodbc".  This could be an artifact of me using libiodbc, instead of unixODBC, not sure. 

The uodbc -> odbc name change effects all the odbc variables (allow_persistent, check_persistent, etc)