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Bitcoin Core greedily picks the ancestor sets with the highest ancestor score into its block template. When two transactions have the same ancestor score (e.g. two transactions without unconfirmed ancestors that have the same feerate) during block building, does Bitcoin Core randomly pick one, or does one get preferred per some criteria?

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As of Bitcoin Core v24.0rc1, and probably since ancestor-aware mining has been included, the txid is used as tie-breaker:

https://github.com/bitcoin/bitcoin/blob/v24.0rc1/src/txmempool.h#L293

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