This is where your mistake is: they can't be using the other blocks as well, because they are erasing their own (uncensored) transactions by doing so. Let's sa

This is where your mistake is: they can't be using the other blocks as well, because they are erasing their own (uncensored) transactions by doing so. Let's say that MiningPoolA controls 51% of hashpower, and MiningPoolB controls 49%. MiningPoolA is refusing to mine transactions from/to some wallet W. Time T1: MiningPoolA: OldChain -- Block1(no W) MiningPoolB: OldChain -- Block1'(W receives 1BTC) still in progress Any client will accept the chain with Block1 (no transactions from/to W) Time T2 - if MiningPoolB tries to compete MiningPoolA: OldChain -- Block1(no W) -- Block2 (no W) MiningPoolB: OldChain -- Block1'(W receives 1BTC) -- Block2' (parent=Block1') still in progress Any client will accept the chain with Block1 (no transactions from/to W), and MiningPoolB will never be able to catch up Time T2 - if MiningPoolB decides to accept MiningPoolA's chain, but add the transaction in the second block: MiningPoolA: OldChain -- Block1(no W) -- Block2 (no W) MiningPoolB: OldChain -- Block1(no W) -- Block2' (parent=Block1, adds transaction W receives 1BTC) still in progress Any client will accept the chain with Block1 (no transactions from/to W), and MiningPoolB will never be able to catch up If a mining pool had 51+% of hashpower, they would always be mining the longest chain, no one would be able to compete with them and publish another block (in principle, at least; in practice, since mining is not entirely deterministic, someone else will occasionally win the lottery and propose a new block faster).