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How does a miner choose which transactions go into the next block? Do all transactions go through or is there a lottery process? I understand transactions with higher fees are given priority.

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A miner can choose whichever (valid) transactions they’d like to include in a block, for any reason they’d like.

I understand transactions with higher fees are given priority.

Generally, yes, we would assume a rational miner would maximize the amount of fees they can possibly obtain. But this is not mandatory.

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