Question regarding 50 50 chance betting?

Hey guys! So I really need some help on a theoretical problem that has been on my mind for a long time :)

Ok. So you have $200 and a 50 - 50 chance of winning a game (exactly 50 50, it is not 51 49 or anything - exactly equal chances like flipping a coin).

What is the best method of betting in order to profit in the end? Is there some successful model?

For example, would it be best to bet $50, and if you win bet another $50 but if you loose bet only $25? Or bet $50, and if you win only bet $25 so that you definitely end up on top?

Theoretically this would continue indefinitely (as in you wouldn't want to "walk away" at any time, just continue making thousands or whatever).

So for those who don't like to read:

How do you turn $200 into a lot of money when there is a 50-50 chance of winning? What is the best model for doing so?