> Just think about it. The algorithm can be changed by anybody.

It can. But the key point is if you change the algorithm by say reducing the number of hashes required (so you increase your chance of winning) it can be detected by just inspecting the block. You don't need access to the code, or be able to watch it running, or trust some hardware, or the person running it, or anything else beyond inspecting the output block and trusting calculating the hash is as hard as it appears. The easy of doing that check that is ultimately what keeps the system safe. Everybody can trivially determine you've cheated, so everybody knows you've behaved in a way that helps you and hurts them, so everybody rejects your block. I guess you could call it game theory, but it is a drop simple game that is easy to analyse and see it gets the desired end result - your bitcoins trade has been immutably recorded in the block chain.

I don't understand how PoS stake works, but the parents description ("reify the resources into in-ledger coins ... block-writers are selected randomly ... weighted by the amount of stake in escrow") makes it sound much more complex. So complex that I wonder if it can be verified by just taking a quick peek at the output block it produced. If it can't, and it's something that relies on trusting code, people or hardware, and within that complexity may well lie a hidden flaw that leads to everyone realising they lost control of their Ethereum days or weeks after it happened. The importance of days or weeks is it's already been cashed out before you realised what was happening.

But I guess that's all wild speculation, and I should look at the algorithm.

You have to differentiate between consensus rules and how the blockchain is secured.

Verifying if the consensus rules hold is equally simple in both POS and POW. But with Bitcoin's POW, the hashrate is part of the consensus rules by requiring the hash of the output block having a certain property which can only be attained in a timely manner with enough processing power and luck (in that sense, also in POW a block proposer is chosen "randomly").

With POS, you don't have the hashrate. But you have the stake which (in Ethereum's POS) is lost if you try to vote for more than one possible new block for the chain. Which is a direct economic incentive to behave correctly.

You could have 99% of the Bitcoin hashrate and start mining blocks that give you double the reward, but every other miner and node on the network would just ignore you because you aren't following the rules.