I never thought I’d get to open a story describing a comedy sketch where a Roman polytheist, a scientist and L. Ron Hubbard get in an argument over school board budget cuts and start hurling around curses referencing Jupiter’s most virile appendage.

And that’s just one of the reasons I’m thankful for all-female sketch comedy troupe Broadminded’s fifth anniversary show, “Broadminded Turns Five,” running at the Alchemist Theatre through Feb. 26.

For those unfamiliar with the all-female group, the show offers a chance to get acquainted, offering up some of their best sketches. The four “broads” themselves — Anne Graff-LaDisa, Stacy Babl, Melissa Kingston and Megan McGee — said they made the decision to have an anniversary show while planning their upcoming comedy season.

“When we sat back and looked at it,” Babl said, “we were like, ‘You know what, it’s been around five years, and we have a bunch of sketches that we’ve never done again … so let’s do an anniversary show.’”

The show offers an opportunity to revisit the scenes that built their Milwaukee reputation over the past few years. Kingston said the Broadminded women got their start in 2006, while they were all members of ComedySportz’s semi-amateur Rec Leagues, when they got an e-mail from a fellow member suggesting they create an all-female comedy group in response to an all-male group that had just started performing in the city.

The all-male group eventually disbanded, but Broadminded held on. Originally, Graff-LaDisa said, there were seven women in the group, but three left shortly after the first show, leaving the remaining four to carry on the Broadminded name.

While Broadminded’s all-female composition may seem to imply their comedy skews toward a feminine audience, the group said this is certainly not their intent.

“We get it a lot, (people) saying, ‘Why do you gotta have an all-girl group?,’ and I don’t know that we’re ‘rah-rah effeminate,’ necessarily, but … we’re proud to be women doing funny things,” Kingston said.

“Our tagline is ‘Sketch comedy. By women. For everyone,’” Graff-LaDisa added. “The fact that we probably needed to put that out there says a lot.”

But just because their point isn’t to perform female-centric comedy doesn’t mean there’s not something unique about having a group like theirs, Babl said. She said the majority of comedians are men, and even in groups where women are included, they’re generally in the minority, so having an all-female group like Broadminded is outside the norm.

“There’s something about having four women lifting each other up and saying, ‘We’re gonna (expletive) do this,’” Babl said.

It’s a motivation that has kept the group together for five years, despite the fact that this is exclusively a side project for each member. They only meet once a week at each others’ houses to rehearse, all the way up until the week before a show.

In the early weeks of what they call a “cycle,” the focus is on writing sketches and developing ideas. This process differs for each of the four women. Graff-LaDisa, for example, said she leans toward fully scripted sketches, with slight improv, while Babl tends to go for the opposite extreme: sketches laid out with “action beats,” which outline the basic elements of the sketch and let the women ad lib in the dialogue.

“I don’t like scripting,” Babl said. “Every once in a while, I’ll throw in, like, ‘You’ve got to make sure you say this line, but I don’t care how you get to it.’”

Interestingly, it’s the unscripted sketches that the group found easier to re-memorize for the anniversary show.

“It’s not like you’re relearning them,” Babl said. “You do have to run through it again … but I don’t feel like I have to run all my lines … whereas some of the other sketches, if we haven’t done it in a long time I’m like, ‘Crap, I really need to get out that script.’”

At a certain point, however, they reach a deadline and have to separate the sketches that are ready to go from those that still need work, and start rehearsing them for the upcoming show.

Part of that preparation also involves structuring the show itself. Graff-LaDisa said most of their shows have an overarching theme, which the comedy sketches are at least loosely tied to. For example, their last show, “Lions and Tigers and Zombies?,” was a mix of “The Wizard of Oz” and zombie-themed comedy, with some musical mashups thrown in for good measure.

Being a comedic compilation, “Broadminded Turns Five” is a little different. Graff-LaDisa said most of the sketches are those considered to be the group’s favorites, all of which also had wide audience approval.

The remainder were fleshed out with “fan favorites,” all but one of which were selected via a Facebook poll. Also included was “Dentist,” which has the unexplainable distinction of earning more than 14,400 views on YouTube — about 14,000 more than the next-nearest sketch posted by Broadminded.

“We’re not really sure why,” Babl said. “I mean, it is a funny sketch, but out of all of our sketches, we’re like, ‘14,000 views, really?’”

In the show itself, “Dentist” is certainly one of the standout sketches, with a hilarious parting shot, and it’s one of many wonderful moments in the show, some of which surpass the 14,000-views-worthy scenario in quality.

The show’s best sketches are those that feature exemplary characters. Arguably, the greatest of these is super-fan Sally Ann (Graff-LaDisa), whose lispy fangirl love poem to her Jedi boyfriend Qui-Gon Jinn has only one flaw — it’s over too soon.

There’s also “Nuclear Family,” where Mother Russia and Father America struggle to teach their children, Iran and North Korea, the dangers of experimenting with nuclear technology. The closing sketch “Pluto” depicts the much-maligned dwarf planet Pluto as a teenager bullied by cool kids Jupiter and Saturn and befriended by a sensitive, caring Earth.

But there are situational sketches that shine as well. “HR Orientation” features a job applicant — from Marquette, no less — who comes in for her first day with all her important documents pinned to her shirt by her mommy. “iPod Therapy,” one of the broads’ first sketches ever, offers a new take on couples’ counseling that is hilarious, heartwarming and a pretty sweet playlist.

There are a few missteps — some of the earlier sketches are too short to have much impact, for one — but Broadminded’s successes greatly outweigh them. By the end of the show, you’ll be hoping the group makes it another five years.

And, of course, you’ll walk out of the Alchemist with a new oath that rhymes with Schmupiter’s Schmock. Who wants to miss that?

“Broadminded Turns Five” runs weekends at the Alchemist Theatre, 2569 S. Kinnickinnic Ave., through Feb. 26. Tickets are $10 and can be purchased at www.alchemisttheatre.com.