[pa7x1]

How do the rich become gradually richer under PoS? I'm flabbergasted by the level of math education.

Assume we have 2 validators in the network; the first one owns 90% of the network, the second one owns 10%. Lets call them Whale and Shrimpy, respectively.

To make the numbers round let's assume total circulating supply of ETH is 100 initially and that the yield resulting from being a validator is 10% per year. After the first year, 10 new ETH will have been minted. Whale would have gotten 9 ETH, and Shrimpy would have gotten 1 ETH. OP is assuming that as 9 is bigger than 1, Whale is getting richer faster than Shrimpy. But, let's look at the final situation globally.

At year 0:

Total ETH circulating supply: 100 ETH

Whale has 90 ETH. Owns 90% of the network.

Shrimpy has 10 ETH. Owns 10% of the network.

At year 1:

Total ETH circulating supply: 110 ETH

Whale has 99 ETH. Owns 90% of the network.

Shrimpy has 11 ETH. Owns 10% of the network.

Whale has exactly the same network ownership after validating for 1 whole year, the network is not centralizing at all! The rich are not getting richer any faster than the poor.

TL;DR: Friends don't let friends skip elementary math classes.

[rfoo]

Sure, friends also won't let friends skip the fact that circulating supply of ETH is now decreasing instead of increasing.

Also, only ~30% tokens are staked. The 30% who chose to stake essentially tax the other 70% in use. Each of the validator do the same amount of work (ok, strictly speaking you get to do more when you have more ETH staked, but being a validator is cheap and does not cost significantly more energy even if you are being selected more frequently because running one proposal is too cheap, that's the whole environmental point, right?) except what they receive is proportioned to how much they stake.

I hate being mean, but sorry, remembering to check one's assumption is a habit I gained after elementary school, so maybe that's too hard for you.

[pa7x1]

> Sure, friends also won't let friends skip the fact that circulating supply of ETH is now decreasing instead of increasing.

This changes absolutely nothing of the calculation. Furthermore, the change in circulating supply last year was of 0.07%.

> Also, only ~30% tokens are staked.

Correct.

> The 30% who chose to stake essentially tax the other 70% in use.

There is something called opportunity cost. With the existence of liquid staking derivatives the choice to stake or not is one of opportunity cost. Plenty of people may consider the return observed by staking insufficient given the opportunity cost and additional risks. Participating in staking is fully permissionless, stakers are not taxing non-stakers. They are being remunerated for their work.

> Each of the validator do exactly same amount of work (that's the point, right) except what they receive is proportioned to how much they stake.

Incorrect. A staker does proportionate amount of work to its stake. That's why it gets paid more. A staker gets paid for fulfilling its duties as defined in the protocol (attesting, proposing blocks, participating in sync committees). For each of those things there are some rewards and some punishments in case you fail to fulfill them. If a staker has more validators running you simply fulfill more of those duties more often, hence your reward scales linearly with number of validators.

[hanniabu]

> Also, only ~30% tokens are staked. The 30% who chose to stake essentially tax the other 70% in use.

And in PoW miners tax 100% of holders.

> what they receive is proportioned to how much they stake

Wealthy miners with state of the art ASICS benefit more than some kid mining at home with an old GPU. Maintenance/cost of mining equipment benefits from economies of scale too.

I hate being mean, but sorry, remembering to check one's assumption is a habit I gained after elementary school, so maybe that's too hard for you.