Just one of the reasons. The other mathematical reason is gambler's ruin. A person with larger pot by chance or design can gamble riskier investment much longe

Just one of the reasons. The other mathematical reason is gambler's ruin. A person with larger pot by chance or design can gamble riskier investment much longer and can diversify it more. Poorer people play a martingale, rich people play a multi-armed bandit. The less of a backstop in the society, the bigger the difference in outcomes. Rich play with armies and even if they lose they are well off. Poor play as soldiers and have nothing, not even their life, when they lose.