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I'm trying to determine how likely it is for multi-sigs with n > 3 are to be mined. Whether this is a sub-set of miners (say 10%) or if you need to relay them to some specific nodes.

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For plain multisigs, as far as I know only Eligius will mine transactions with n>3 as they're non-standard (so not relayed).

That being said, multisig is now usually done using pay-to-script-hash. In this case, the only limit you're facing is the maximum length of the scriptSig which is 1650 bytes. If you do the math, you can go up to n=15 safely in that space.

TL;DR Up to n=15 in a P2SH, stick to 3 otherwise.

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    All current Bitcoin Core releases will consider spends with a scriptSig above 500 bytes non-standard. It will likely be raised to 1650 bytes in the next release.
    – Pieter Wuille
    Aug 14, 2014 at 9:50

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