Here's the math on the whole thing:
If you remember from high school math, and is multiplication, or is addition. Therefore if you have 5 caps that you want to enter, assuming that each drawing has 1500 entrants, you have a 5/1500 chance of winning. Now, if you spread that 5 caps out over 5 different drawings, your probablilty of winning is 1/500 + 1/500 + 1/500 + 1/1500 + 1/1500 = 5/1500. Using multiplication would give you the probablility of winning all of them, so we use addition to figure out the probablity of winning one. So really it is the exact same probablility of winning, assuming that all of the drawings are about the same.