Firstly, it doesn't punch up, self deprecate or give any clever, satirical insight. The idea of 'punching up' is that you always want your joke to make fun of a more powerful target. Part of the beauty of comedy is that it lets you pull down the rich and powerful. So you make jokes about John Key; you don't make jokes about hobos.
Self-deprecation is pretty self-explanatory. It's also the key to good comedy. Everyone likes to laugh at human failure. But you don't want to laugh at the audience's failures because that makes them feel shit, and you're there to give them a good night. So self-deprecation is the solution.
Lastly, comedy can also offer incredibly intelligent, cutting insights that skewer everything you know and feel about a situation in a few words. The first problem with Cucumber Number is that it's none of these. It's not clever, it's not punching up, and it's not in the slightest self-deprecating. If anything, it's having a go at the audience (in this case the poor girls having to deep throat a vegetable.)
If this gets laughs, it gets cringe laughs. People laugh not because they're amused but because they're embarrassed and don't know what else to do.
And that's breaking another key rule of stand up. Wooing your audience. One of the most memorable things a comic ever told me was, "your audience has to like you." If your audience like you, then they find you funny and they have a good night. So you're always trying to keep them onside.
Yes, you can tease them, but you can't just make them feel like shit. They're paying to see you, remember? And Cucumber Number makes the girls feel embarrassed. Listen to the audio around it, the girls sound visibly embarrassed. They say things like, "um, no sorry, my Dad wouldn't like that." They feel awkward, and uncomfortable and often pressured into this ridiculous situation with no preamble. That is not wooing your audience. That's making them feel like squashed mice.
The whole joke of the situation hinges on it being a metaphor for blow jobs. Well, hot damn. You can talk about blow jobs. How hilarious. Oh, don't get me wrong, they can be hilarious. But they have to be included in a story about a terrible experience you had, or that takes the piss out of Bill Clinton, or something that says something ... anything ... just something that isn't the mere fact you can talk about blow jobs.
If this gets laughs, it gets cringe laughs. People laugh not because they're amused but because they're embarrassed and don't know what else to do. That was something that I was told again and again - don't go for cringe laughs. That's not comedy.
And lastly, and most importantly, why is this not funny? It is sexist.
Now, women can definitely talk or boast about their sex lives. That's cool. So if women can boast about their sex lives then surely they should be happy to demonstrate how much cucumber they could potentially suck. Well, no.
See, when talking or boasting about sex happens in the context of them telling the story on their terms to their audience it's cool. When I tell a sex story, I'm telling it because I want to make someone laugh, or because I want to make good conversation, bond with my girlfriends, or show that I can be experienced and worldly, yo. So you're telling the story to fulfill a goal that you have set and a goal that is not sexist.
What is the Cucumber Number doing? It's trying to rank girls on how much 'cucumber' that they can take. So the goal of that conversation is to see who can 'win' by taking the most. That goal is demeaning because you're talking about how far you can push a woman before she vomits.
You're also publicly ranking them on this ability. That puts them in the subordinate position to the person who ranks them. And implies that they should accept it's a good idea to put a man's pleasure over a desire to hurl.
Plus the entire conversation reduces a woman to just a sex object, whereas when a girl tells a sex story she's an entertainer, or a funny person, or bonding with you or so many things apart from someone who can take a cucumber.
So the whole 'joke' is based on this sexist assumption and exploitative power relationship. How funny.
It's not funny to make girls deep throat vegetables. It never will be. If you want to make a joke about blow jobs then go right ahead. Just don't be a dick about it.