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It's especially risky to hope that a small fraction of your stack will be enough to get them to leave. If you are public that you have tons of any cryptocurrency, then they won't settle for a small amount of your stack.
As far as multi-sig, a few robbers will be willing to spend all day driving you around town to pick up enough of your priv-keys to complete a multi-sig transaction. This will be especially effective against you if you have a wife and/or children, who they can use as hostages.
That being said, multi-sig is very effective against those who would break into your house while you are away.
One of my strategies involves distributing to many people in other states who are instructed to not give me the shards outside of the next normal time I see them and only after I have given them a 2 week warning that I’d be expecting it—and anything short of that is an alarm to involve authorities with an abduction/hostage report. It’s a little more complicated than this but that’s the gist.
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"Sorry, left one of my keys in the mountains, you will need to hold them hostage until late spring in order for me to retrieve it."
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In that case, you'd be betting that the robbber's laziness is greater than his greed and malice, which is a dangerous assumption. Plus, he could return when the last privkey becomes available and start the robbery all over again. Your only option at that point would be to move somewhere that the robber can't find you.
What I'm trying to point out is that you shouldn't be trying to trick criminals. You should be shooting them when they attack you.
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