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Probably it is not only me, but also other users wonder about the "Curious" badge. Is it new? I can not remember to have read of it in the "Badges" list of TeX.SX.

What about this asking a good question on 5 separate days -- what is a good question in this sense?

I am curious about this strange "Curious" badge.

Is it a feature on other SX sites too?

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According to Asking days badges, the Curious badge forms part of a hierarchy of question badges based on the principle that a user

Asked a well-received question on X separate days, and maintained a positive question record.

Here X represents

The questions left to answer are

  • What constitutes a "well-received question"?

    A well-received question is one that's open, not deleted, and has a score > 0. If you ask at least one well-received question in a UTC day and none of your questions that day are deleted, downvoted, or closed, you get one more day of credit toward the badge. Whenever the badge criteria is checked, previous asking days are re-evaluated so that there's an incentive to fix downvoted and/or closed questions. The no-deleted-questions criteria is to prevent people from asking several questions at once and deleting any that aren't upvoted or answered to ask another day. (Though this is a losing strategy in the long run.)

  • What constitutes a "positive question record"?

    (total questions - negative questions - closed - deleted) / total questions >= 0.5
    

    It triple counts a question that is downvoted, closed, and deleted. If you ask one that hits that trifecta, you'll need to ask three better questions to dig yourself out. For example, if 12 questions of a user were closed and 12 deleted out of a total of 44 questions, their score would not meet the criteria:

    (44 - 0 - 12 - 12) / 44 = 0.4545...
    

    The takeaway is that people can't sweep past indiscretions under the rug by deleting them. And they can recover from a bad start as long as they don't ask more bad questions.

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