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I'd say that, unless other nearby content points to definite sarcasm, the phrase "in my humble opinion" should generally be taken as being sincere.

The definition of humble includes an example of the phrase as being "courteously respectful". There's a latin phrase, "ut humiliter opinor", which translates as "in my humble opinion", which would indicate that the phrase is quite old and has been used for a long time (though I haven't researched this, it could well be pseudo-Latin for all I know, like "non illegitimi carborundum" ;-) ).

The phrase is used in modern writing; for instance, there's a quote by Dumbledore in the Harry Potter books that goes something like “Words are, in my humble opinion, our most inexhaustible source of magic.” (I suppose one could argue that Dumbledore has little to be humble about, but I'd certainly interpret this instance as being sincere.) It might be interesting if anyone knows of examples in "older" literature.

Having said that, in its abbreviated form, "IMHO" or "imho" as used in informal writing, emails, social media, etc., there may well be a higher percentage of sarcastic usage, but again I think this would largely depend on the context and one should assume sincerity unless there are other indicators of sarcasm.

I would suggest (though some may well disagree) that its usage in informal writing is quite similar to the phrase "my two cents", i.e. saying "here's my opinion, take it for what it's worth or feel free to ignore it". (Though this phrase always strikes me as being ironic because, in Australia, we round money to the nearest five cents, so two cents are essentially "worthless".)

"I've taken a look at the link you sent me, but there must be something about it that I missed. What was it that you were particularly wanting to draw my attention to there?"