This is called a "martingale" betting strategy. It's been extensively studied in probability theory. If you had infinite wealth and the casino would let you bet

This is called a "martingale" betting strategy. It's been extensively studied in probability theory. If you had infinite wealth and the casino would let you bet forever, it would work, but in real life neither of these conditions is true. https://en.wikipedia.org/wiki/Martingale_(betting_system) https://en.wikipedia.org/wiki/Martingale_(betting_system)