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In the question Do larger blocks make it harder for smaller miners to compete? Why? there are some reasons given for why larger blocks hurt smaller pools. Is this still the case with spy mining?

Spy mining is when a mining pool connects a dummy miner to another pool to subscribe to the latest block hash, without waiting for new blocks to propagate.

Another description of spy-mining is here.

Is the only impact of larger blocks is an increased frequency of empty blocks or am I wrong?

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No, it temporarily attenuates the issue, but doesn't resolve the problem. A spy miner gains less reward for an empty block than the large miner building on its own block. Currently, transaction fees make up about 11.7% of the block rewards (average over last week). As the subsidy decreases in the longer term, the transaction fees are expected to make up an even greater relative portion. Larger blocks would exacerbate the issue as the spy miners would spend more time in the state of reduced revenue, which translates directly to reduced revenue for whomever didn't find the previous block.

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