Write a simulation where you have n entities with an equal amount of resources. Now choose two entities at random and let them "trade", where the outcome is ran

Write a simulation where you have n entities with an equal amount of resources. Now choose two entities at random and let them "trade", where the outcome is random but fair. You will get a "wealth distribution" that is not a gaussian normal around the average but more like a poisson distribution. And this is even with no difference in competence of the market participants. You can add various corrective terms to make get "equality of outcome", but to get to a gaussian distribution around the average you need really drastic/totalitarian measures. The best system from a pure math POV would be a flat tax combined with universal basic income. But unfortunately it is naive to assume that this is politically viable. Politics largely is selling a particular group an advantage over the general population in exchange for votes. And a flat tax / basic income system is just too simple for that.