Except, in your simulation you only consider accumulation of dollar amounts. Pure gambling, wealth in a vacuum. Calling these dollar amounts 'wealth' is not helpful because they need to have purchasing power, there need to be goods and services to buy, otherwise they're just meaningless entries in a ledger, bits of paper (see Zimbabwe). It's wrong to dismiss capitalism on the basis of this simulation.
In the real world there are usually side effects to these 'bets'. For example, a person, who is already rich, uses their wealth to purchase a factory and produce goods at a dollar price in the hope to earn more wealth. Those goods might be rejected by the market, but if accepted, they receive dollars and the rest of the world receives goods. The factory owner can only receive the dollars if others can afford to buy them. This means there is another road to ruin - fail to produce anything people want at a price they can afford and you'll soon go bust.
The buyers who receive goods in exchange for money, particularly durable labor saving goods like dishwashers/fridges/cars/computers, are surely more wealthy in some sense? In addition, the factory owner might make tools/machinery that enables other entrepreneurs to make stuff too.
Also consider ongoing costs, that capital has to be replaced (things break!), unexpected bumps in the road, finite lifespan, waste, and so on.
Which leads me to our current system: the rich have got richer through financialization, government lobbying, zero-interest financing et.c, that has allowed them to acquire assets that appreciate without a substantial increase in production.
The solution is to make rich people take much bigger, potentially ruinous, risks with their wealth on production instead of financial chicanery. More abundant goods and technology are the payoff while failure leads to liquidation of their assets, making assets more accessible to everyone else who might need them.
Deflation, and crashes are a feature, not a bug. Inflationism, stimulus, cheap money et.c helps protect workers in the short term during a downturn, but prolonged stimulus makes assets unaffordable. Worse it causes huge misallocations of capital into unproductive endeavors at no risk to the investor.
My belief is you don't 'prop-up' the big fish using the government/central bank. Then yes, you may still have inequality, but it won't be nearly as static, but more dynamic. i.e there may always be an extreme power law wealth distribution, but what's more important is there's regular turnover at the top and nobody spends too long in the top or the tail.