So you're saying you know that an unknown quantity is greater than another unknown quantity.

I'm saying they have massively different risk profiles.

If you want a different example that might be more obvious, "put it all on a single number on a roulette spin" and "invest in a big stock index" both have unknown rewards but they're entirely different ballparks too. (And no, those aren't supposed to map 1:1 to the coin scenario.)

I don't think I follow you. As far as I can tell, PoS is as much of a lottery as PoW. In PoW a player increases their chances of winning the lottery by spending real money on electricity. In PoS a player increases their chances of winning the lottery by spending real money on virtual tokens. The outcome should be the same, except that no electricity is wasted in the case of PoS.

At any point you can turn your tokens back into something else. And in theory the price is sufficiently stable or you wouldn't be doing anything with crypto.

Mining machines deprecate and electricity cannot be refunded. It's a production business, and that money is spent.

What is the equivalent of electricity being burnt in a PoS system? I am not seeing that cost. Not opportunity cost -- which also exists for mining Bitcoin -- but direct cost.

It depends on how it's implemented. PoS works by offering a randomly selected stakeholder the authority to update the blockchain. [1] One way this can be done is by requiring stakeholders to deposit a stake with a smart contract that charges negative interest. I don't know how current implementations of PoS work, but this doesn't look like rocket science.

[1] https://doi.org/10.1093/rfs/hhaa075