Ok if mining is free (like *actually* zero cost in the sense that energy is not longer scarce) we've circled back around to proof of stake haha

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You said 1000x cheaper, right? That's essentially free. It's not free, but it's going to cost me 0.4 cents a month instead of $400 a month to run my miners.

But then you can also expect to make 1000x times less profit, because you have 1000x times more competition

That's fine. Some BTC is better than zero BTC.

For sure! I'm just thinking through this as a thought experiment