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.
Well the problem with most of the gamblers are that they become greedy on both winning and losing. Any win will not satisfy them as they keep on playing more for more profits. On the other hand, with every loss, they try to cover by playing more and losing again, making the loss even more bigger.