Learn Polish: Przesądy są popularne, obyśmy nie mieli pecha. - Superstitions are popular, hopefully we won't have bad luck.

The particle oby expresses a strong wish (like 'hopefully' or 'if only'). To make a wish about the present or future, you combine it with the past-tense verb form (the L-participle), which is mieli here. Notice that the personal ending for 'we' (-śmy) attaches directly to oby, giving us obyśmy nie mieli instead of oby nie mieliśmy.

Why is mieli in the virile (masculine personal) form, while popularne is non-virile?

They refer to different subjects. Popularne describes the noun przesądy (superstitions), which is non-virile plural. However, mieli belongs to the hidden subject 'we'. Because this group of speakers includes at least one male, it uses the virile plural form mieli. If only women were speaking, they would say obyśmy nie miały.

Is pecha in the genitive case because of the negated verb nie mieli?

It is genitive, but this specific word is a bit of a trick! The phrase mieć pecha (to have bad luck) is a fixed idiom that treats the inanimate noun pech as if it were animate, using the -a ending even in positive sentences (like mam pecha). So, while the negation nie does require the genitive case, the word pecha does not actually change form here compared to a positive sentence.