Quote from: R2D221 on February 10, 2015, 03:06:05 PM

You know what happens when you do work for half the time? You do half the work. So, having 51% of the hashpower half the time means you effectively have only 25.5% of the hashpower.

Also, about letting others mine... Well, you can't just stop them from working (unless you seize their equipment). This has nothing to do with it.

With this, though, you have 51% of the hash power all of the time, it's just that you use that power (all of it) on different chains at different times.

It's just like a miner with 51% making a longer chain that retakes the whole chain by starting one block back to enable a double spend. They can just use this ability to make another chain that stays the same length as the chain the network is working on.

-------------------------------------------

Suppose the chain is at this state (each * is a block)

-- * -- * -- * -- *

Now the miner with 51% decides he is going to launch this attack. The network solves a block:

-- * -- * -- * -- *
   \ -- *

Now the miner solves blocks on the chains opposite to it until the chain takes over. This might take a few blocks while the network is still working on the main chain.

   / -- * -- * -- * -- *
-- * -- * -- * -- *
   \ -- * -- * -- *

At which point the network switches to the top chain and the miner switches to mining on the bottom chain. The same thing happens, the miners chain will eventually overtake the network chain (which is now the top chain), but it might take a few blocks.

   / -- * -- * -- * -- * -- * -- *
-- * -- * -- * -- *
   \ -- * -- * -- * -- * -- * -- * -- *

Now everyone in the network switches back to the bottom chain, and the miner switches to mining the top chain. The miner can keep doing this until the fork becomes ridiculously long and the data between the two chains is completely incompatible.