Well, so, 120 Tourism from your four cities and then 1600 Tourism every 10 turns is only a total of 280 Tourism per turn. That seems very low to me. What difficulty level do you play on for that to work? Of course, you could employ the same strategy with more cities. If we use the same numbers, then 10 cities would give you 700 Tourism per turn, which might be enough to win if you start early enough and if you don't have any good culture opponents. But, it's probably even better than that because 10 cities are more likely to have excess luxury copies, too!