The main problem with economic theory is that people aren't rational economic actors.<p>A rational billionaire would realize that he have nothing to gain from more wealth and would live the rest of his life in lavish and luxury (while donating 99.9% of it if he cares about public opinion), aiming to spend all of it before he dies. So if billionaires were rational we wouldn't have such a large inequality.<p>Similarly if poor people were rational they would organize against rich people, forcing them to share their wealth in one way or another. This could either be via violence or they could democratically elect representatives who will distribute it for them or they could even unionize to gain power.<p>The question then isn't how we stop inequality when all actors are rational, but how we stop inequality when some people have irrational tendencies to hoard wealth while others irrationally prefers to vote for those who stands for some abstract ideals rather than those who would give them the most monetary rewards.
"Two people enter into a series of transactions, and both have the same probability of winning some amount of wealth from the other, just as in a free-market transaction."<p>I don't really think this is a great description of free market transactions at all. Do you regret the decision anywhere close to 50% of the time when you buy groceries, pay rent, or buy new boots? Does the grocer, landlord or shoe store owner regret it anywhere close to 50% if the time? The answer is no in both cases.
I think that this is a pretty obvious fact, once you ignore the ideological explanations. The rich can borrow at a lower interest, the rich can have their money beget more money in riskier opportunities. Those with no money to their name can’t afford that.