The math behind it says that there are almost 14 million total combinations and the best probability is 3 even and 3 odd numbers with a 33% occurence every 100 draws.
But this does not mean that a set of 6 numbers which contains 3 even and 3 odd is any more likely to win.
In a 6 from 49 lottery, there are 49! / (6!(49-6)!) = 13,983,816 possible combinations.
To pick 3 even and 3 odd, then you are picking 3 from the set of 25 odd numbers, and 3 from the set of 24 even numbers.
25! / (3!(25-3)! = 2,300
24! / (3!(24-3)! = 2,024
2,300 * 2,024 = 4,665,200 possible combinations.
So the reason that 33% of all draws have 3 even and 3 odd numbers is simply because 33% of all combinations of 6 from 49 have 3 even and 3 odd numbers. However, any individual combination is just as likely to win as any other individual combination, regardless of the mix of even and odd numbers.