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That's not how the 51% attack works.

If you have >51% of the mining power, you can overpower the rest of the network. Simply pick a block in the past and start mining from there, ignoring everyone else. With >51% of the hashrate you _will_ overcome the rest of the network and enforce your new chain.

They can do it in secret. Build a secret parallel chain while they transact, then release the chain after they've got their BTC.

And 51% is not "insane". It's absolutely tiny. As I said, _any_ of the large pools could do it, right now.

OK I must be missing something here: how can any of the large pools have 51% of the mining power?

How can you have more than one pool, each with more than half the power?

EDIT: OK I see where you're coming from I think... you mean any of the pools could 51% the forked branch, right?

Yes 51% of the branch you are attacking. They have hard forked, any bitcoin mining pool could easily control 51% (like 80%) of the bitcash mining worldwide.

I assume it means any of the larger pools in Bitcoin could switch over to one of the smaller altcoins and overwhelm the much smaller pool of miners there.

I don't follow this stuff closely, so I'm clearly missing an important detail here: how can several different entities simultaneously have the ability to "easily" control 51% of the hashrate?

I kind of think it is a little bit like this.

Imagine a new sport called zoccer. It's just like regular soccer, but if a team scores 5 goals within the 90 minutes, they automatically win the match.

Right now there are only a few small teams playing. But Nike has said they are willing to sponsor a tournament, if there is enough interest.

At any point, Barcelona or Manchester United or Real Madrid or Chelsea or AC Milan or any other large soccer team team can just say "we are now a zoccer club" and swoop in take Nike's money.

They all have the power to switch and dominate the new scene.

Bitcoin (BTC) and Bitcoin-cash (BCH) share the same Proof-of-Work (PoW) algorithm. Thus, mining power is split between these two networks. Most mining power is currently on the BTC, which means that it is at least possible that multiple miners on BTC have more than 51% of the mining power currently deployed on BCH.

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