Oh, you can certainly use your 49% to publish a block or two, or even twelve in a row -- good for you, probability sometimes works like that -- but eventually I will have more blocks mined privately than the rest of the network does publicly, at which point I publish them (with my choice of confirmed transactions) and all your work, the transactions which you chose to confirm, and your mined coins just go down the memory hole.
The mined coins, sure, but you can include the transactions that were omitted in the revealed fork in the blocks after that. That's why the document states An attacker that controls more than 50% of the network's computing power can, _for the time that he is in control_
I'm not saying that when this would happen it would be a good day for Bitcoin by the way.
I don't understand. I think "for the time that he is in control" means "as long as he has > 50% hashing power". No need for 100%. As long as he has > 50% he can eventually overtake any fork that includes a new transaction.
In theory, given enough time (a very long time), someone able to maintain 50.0000001% of hashing power could eventually rewrite the entire blockchain after the genesis block.
If you have a 51% forever you can refuse to chain the blocks that contain the unwanted transaction. Every time it's added to a block you just fork the chain, and as you have the 51% hashing power your fork will eventually win.
The time to crush the other fork depends on how much hashing power you have. With 60% you will generate 60 more blocks in a day that the other fork, in average. With a 51% you will generate 6 more blocks per day. With a 50.1% you will generate only 1/2 extra block per day, so you need a few days to win.
