The first thing that comes in my mind when i experience winning is not probably to bet again because i am afraid to have regrets if i lose all of my winnings, that is why when i experience having a win streak i started to decide to stop playing gambling and play again in a another day.
I wish all the gamblers have the same mindset as you are thinking but unfortunately its the complete opposite. Gamblers tend to become more greedy when they are having a winning streak in gambling.
When I'm winning (or making my initial double), I will withdraw the profits that I got leaving my initial capital in the site since I'm gambling online. I do that so that if I lose my initial capital, it will be ok for me since I have withdraw some of the profits I got.