I believe the exact opposite of your thesis. Reproducing intelligently and responsibly is THE best way to win.
Smart people: have skills (and therefore usually money) and have few children. They take their money and time and invest them into one or two children, giving each child a lot of attention and grooming to give them the proper skills to succeed. Their children have enough money to go to school, start buisnesses, etc. The kids usually succeed just like thier parents did. The parent's advantageous situation is passed down to their kids.
"Dumb" people: have few skills, little money, and take that little money and spread it thin amongst many children. Few of their children have any real one-on-one time with thier parents. Even fewer have the resources for proper nutrition let alone proper schooling. The kids have to work as teens to support their massive families. That work time means less study time and fewer marketable skills. The poor kids usually are poor just as their parents were. The parent's disadvantageous situation is passed down to their kids.
Studies show the #1 determination of your success in life is the success (or lack of success) of your parents. Sheer numbers are the key that keeps the unskilled workers and their kids down. It is a vicious cycle.
Reproducing intelligently and responsibly is the ONLY way in our society for smart people to win. Imagine having a family net worth of $1 million. Imagine that family having one child per generation (or two if they marry similar families). After many generations, there is still a net family worth of $1 million. Now suppose that family has 10 children per generation. The 2nd generation has $100k each, the 3rd gets $10k each, the fourth gets $1k each, etc. The kids water the wealth down to nothing.
So by sheer numbers, your so-called "dumb" people CAN'T win.