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Assuming I receive a bitcoin payment from someone and only accept it when it gets atleast 3 confirmations and it does, but somehow it gets double spended, what happens to my bitcoin balance?
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After 3 confirmations?
This is very unlikely. If you are worried about it, you can stop worrying.
If you just want to know to help you understand the technical details:
Before the bitcoins could be double-spent, first the confirmations would have to be eliminated. Then if someone managed to do that and accomplish a double-spend of bitcoins they had sent to you, then the bitcoins that they sent to you will vanish from existence. Your wallet will be the same as it would have been if they had never sent those bitcoins to you in the first place.