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Comment by mkj | Hacker News Reader

If you plot it another way does it end up looking like a gaussian distribution (or something similar)?

I think it’s a power law distribution. Power laws tend to arise naturally when winning a game/interaction enables you to play more games later.

If everyone has an equal (random) chance of winning, the person who can play the most games wins in the end.

https://en.m.wikipedia.org/wiki/Power_law

You see this in sports where Steph Curry isn’t much more likely to hit any specific 3 pointer than any other NBA player. But he tries almost an order of magnitude more often. So now he’s known as one of the highest scorers in the game.

> You see this in sports where Steph Curry isn’t much more likely to hit any specific 3 pointer than any other NBA player.

Where did you get that stat from? He is almost in the top 10 of all time in terms of shooting percentage [1]. What makes that understated is how much he shoots. The people above him on the list only shot them when they were "guaranteed" whereas he shoots them all the time.

[1] - https://www.basketball-reference.com/leaders/fg3_pct_career....

Yes. See here: https://news.ycombinator.com/item?id=31861089

It should. I suspect this sim is done wrong. If each round is independent and variance is constant the CLT should dominate.

Oh, no, absolutely not. The sim is a proof that even in very primitive economic simulations, Central Limit Theorem absolutely does not apply.

'should' has nothing to do with it. It provably doesn't. Even in the absence of any complicating factors or considerations of value or merit.

Edit: my post below is not true. The overall distribution is indeed close to Gaussian; see here: https://news.ycombinator.com/item?id=31861089

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The CLT simply says that the distribution of a sum of random variables will be Gaussian (as the number of random variables being summed tends to infinity).

It is not obvious to me that the agent-level difference equations in this simulation would naturally lead to the overall distribution of wealth being a sum of random variables.

The wealth each "person" has after N rounds is equal to N trials where the expectation is zero each time, and the rounds are independent, at least according to the setup described in the title and first paragraph.

That determines the distribution for each individual, not necessarily the entire population.

However, I think you are correct and I am wrong about the population level distribution; I wrote and ran the simulation myself and got a Gaussian-looking distribution at the population level.

Not if growth is cumulative/compounding. Central Limit Theorem assumes additive growth.

Do some reading on geometric vs additive means, and on the log-normal distribution for finance.

This sim is done quite right, with the key part of the article being "This model is the same as in the basic version, but includes basic economics, like debt (whithout interest) and investments that are proportional to the respective wealths of the spending and the receiving player"

CLT dominates only if you do the sim wrong by making unrealistic simplifying assumptions (e.g. that each round is independent and variance is constant) that effectively eliminate the main parts of the simulated system and ensure that the simulation gets misleading results.

Reply on news.ycombinator.com