There is a mathematical model and theory called the yard-sale theory that proposes that any system like capitalism that gives an early-mover advantage, ends up with gross inequality eventually. Scientific American discusses it, and starts by pointing out that
as of 2010, 388 individuals possessed as much household wealth as the lower half of the world’s population combined—about 3.5 billion people
This explainer is far easier to follow, and concludes that, according to the math… if you start with 1,000 people with $1000 each and play 10,000 rounds of coin-toss bets, where your stake is 20% of net your worth… someone ends up with everything ($96,274), even though everyone wins half of the coin-toss contests.
It is a mathematical model, not accounting for how society actually works. But it proves that having a bit more money than someone else at the start leads to exaggerated outcomes over time.
Long story short, if you have more in the beginning, you can gamble more and not be wiped out by bad bets as much as someone who starts out with less.