I was trying to understand why PoW makes the blockchain 51% attack resistant. From my understanding, we can think of PoW as a way to assign a leader who would decide what the next block is. I can see how this helps to achieve consensus among a set of machines, but I don't understand why this prevents bad actors or 51% attacks.

I read the bitcoin paper (https://bitcoin.org/bitcoin.pdf), and at the very end there is a discussion on how we can model the blockchain as a game of gambler's ruin, and if probability_of_honest_node_extending_chain > probability_of_bad_node_extending_chain, we can say with high confidence that after some block b cannot be altered if there are z blocks after b on the blockchain. The paper then gave a table of different confidence levels for different z.

All that makes sense to me. However, the gambler's ruin argument is generic and doesn't seem related to PoW. We can change PoW to any other consensus and the above argument still makes sense to me. For example, even if the PoW puzzles are extremely trivial, I believe the gambler's ruin argument still works.

Could someone please point out any gaps in my understanding above, and if there isn't anything wrong, what is so special about PoW?

Thank you!