$result = mysql_query(\"SELECT indvsum.sum1 + indvsum.sum2
    FROM (SELECT SUM(Cash) AS sum1,
                 SUM(Bank) AS sum2
          FROM players) indvsum         
        
This is the expected behavior.
Please check out the manual for some example about how to fetch rows:
mysql_query
This is the signature:
resource mysql_query ( string $query [, resource $link_identifier = NULL ] )
For getting the rows you should use
mysql_fetch_array
or
mysql_fetch_assoc
for example.