chance of winning the lottery

I was discussing the odds of winning the lottery with some people earlier. The chances of winning are roughly 14 million to 1. I said if i bought two tickets my chances would now be 7 million to 1. If i bought 4 tickets my chances would now be 3.5 million to 1 etc. Everyone seems to think this is wrong. They tried to explain to me why but it didn't make any sense. Apparently it's something to do with the numbers being so large the odds end up changing. I just can't see the logic here. If i'm wrong can someone explain why?

P.S - The tickets have different groups of numbers.