"the most important factor in whether you can become rich is whether you chose the right parents: Most people are going to end up with socioeconomic status close to where they started."According to a recent study of mobility (see Figure 1), the correlation between parent's income rank and children's income rank is about 0.3. That means that if you are in the 99th percentile (the much-talked-about 1 percent), your best guess is that your child will be at the 65th percentile.
To me, that seems like a lot of regression toward the mean. This is why financially successful parents often have strong bequest motives. They are smoothing consumption across generations.
Addendum: Here is the key Figure 1: