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According to blockchain.info, the largest mining pool holds less than 20% of the mining power, which is far below the dreaded 51%. But, this information is (probably) based on the pools publicly identifying themselves. Is it theoretically possible that some miners (or pools) created a secret cartel that holds together 51% of the mining power? If so, what are some signals that can help us identify such a cartel?

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An entity having over 50% of the hashing power can continue operation as it would while having less than 50% of the hashing power. It then can go undetected when carefully choosing how it distributes its newly fonud blocks.

However, given its share of the total hashing power is φ (for φ > .5, obviously), it only makes about φ of the total money made from mining. Once an entity has over half of the total hashing power, there is a very lucrative thing it can do: Make all the money made from mining. This is done by simply ignoring all blocks others mined and only mining on top of its own blocks. Because φ > .5 and the law of large numbers, every time someone else mines a block, it can be sure to at some point have the longest blockchain which then becomes the effective blockchain, redering all the money the entity made on it valid.

The blocks others mined then never are part of the longest blockchain for long, making them orphans.

For the orphan rate σ, this means that σ = 1 - φ if the entity with φ of the total hashing power operates at maximum profitability (never accepts blocks mined by others).

We don't see a high orphan rate.

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