Bitcoins are mined by a uniformly random process, which means even groups with a small amount of power can mine blocks, and even can occasionally mine more than

Bitcoins are mined by a uniformly random process, which means even groups with a small amount of power can mine blocks, and even can occasionally mine more than one in a row. But instead of publishing that mined block immediately, there is a better strategy. Waiting on publishing makes a fork, and the colluders can keep mining on the fork until the strategy defines that they should publish - which is basically when the "honest" branch catches up to the colluding branch. Since the colluders don't have a majority, this will always happen, but that's ok. Due to the way that the Bitcoin protocol works, honest miners will sometimes "help out" the colluding group by mining on that published fork. This basically amplifies the power of the colluding group, which is the goal. Worse, the paper proposes that the percentage of honest miners switching to the fork can be influenced cheaply, by choosing which blocks to forward along in the p2p network.