The title of the post is a little misleading. The model presented here does not require many parts of a capitalist system. If you can own stuff and have a free market this model predicts extreme wealth inequality. This happens by pure chance.

The model is not a good argument against capitalism. It can be used as an argument for taxing rich folks and against the “trickle down” idea.

I think there is some confusion as to what this model represents. The linked article is not bad at explaining it but some things could be clearer.

First of all, the “money” in the model is not the cash you have at hand. It is the total value of all the things you own. This model does not need money and it also works if you exchange cigarettes for candy (as long as you can assign some worth to the objects).

It is also not about gambling. It assumes that every time you exchange goods with someone else, you can become richer or poorer (I like the example from the article: if you pay $200 for a watch that is worth $150, you lose $50, someone else gains $50).

It makes the extremely optimistic assumption that the chance to gain or lose money in a trade is equal. This is often obviously not the case in the real world. If you buy something from a supermarket, the owner wants to earn money, needs to pay their employees, needs to pay rent, … so you know you pay more than the value of the goods you get.

Now this simplified and very optimistic model predicts that there is an exponential distribution of wealth and it predicts that repeated exchanges between a rich and a poor person will most likely result in the rich person getting richer and the poor person getting poorer.

What can we learn from that?
1.) even under these very optimistic conditions money trickles up. The real world is stacked much more against you, making a trickle down effect unlikely (though not impossible, this model is a simplification). 2.) rich people (in the model but imo it applies to the real world as well) are not smarter or otherwise better than the average person. They were lucky.
3.) Even if we remove a lot of the advantages rich people have in the world and construct a system that is seemingly “fair” (as in every one has the same chance) you still end up with super rich people. The only way to combat this is by redistributing money - tax the rich. Note that you still get an exponential distribution in the model but it becomes flatter.

What this model says nothing about is how the real world is stacked in favor of rich people. It tries to eliminate all these factors. So using this model to argue that inequality is built into the system (as the headline suggests) is somewhat strange. The model rather suggests that the inequality always arises from simple chance - One could maybe argue from it that we need to actively combat it (depends on the personal sense of justice if earnings due to luck should be redistributed).

I agree with you on the value creation. This model treats the economy as a zero-sum game. But the real economy is typically growing and this is ignored here.

Looks like Dr who: https://youtu.be/Bb3bXgUEMk4

That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.

From https://en.wikipedia.org/wiki/Preliminary_reference_Earth_model

This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.

So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).

The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.