Mini Pill

I went to my post partum appointment today to get on birth control. I chose to stick with the pill. Its what I've always used aside from one time I took depo. My doctor told me she was gonna put me on the mini pill where I'm breastfeeding and wrote me a prescription for a year. She said it's less likely to mess with my supply. But she said if I quit breastfeeding to let her know so she could switch me to the regular pill because if I wasn't breastfeeding it wasn't effective. Soooooo how's that work? How does breastfeeding make it effective? What are my chances of getting pregnant on it? Is there more of a risk? Has anyone gotten pregnant on the mini pill? My husband says it sounds like an accident waiting to happen 😂😂😂😂