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You should not be hitting the rate limit if you’re using different accounts. The messages user ‘Foo’ sends does not impact the rate limit of messages sent by user ‘Bar’. Also if one account does hit the rate limit it should not impact other accounts running on the same IP, so I would suggest checking your code, and ensuring each connection is in fact connected as a different Twitch account.
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The lowest limit applies. So You could be sending messages at a rate of 50 per 30 seconds and you’ll be fine if they’re all in a channel your bot is a moderator, but the moment you send a message in ANY channel you’re not a moderator you’ll immediately be over the limit and be banned.
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Joins and Auths have their own rate limits, which for non-verified bots would be 20 authentication attempts per 10 seconds per user, 20 join attempts per 10 seconds per user. I do not believe they count against the message limit.