Its not correct to say they are no longer valid, but they are more complicated. Take the following scenario. There are 500 names in the hat, and you have 6 of them. Your chances are legitimately 1.2% when the draw starts. Assume the first name out of the hat has put in 6 tries as well. You now have 6 out of 494, or 1.21%.
It certainly was more straight forward when 1 person had only one chance, but the math doesn't change. Put in multiple chances to increase your odds, as not every person in the hat has put in multiple times.